Showing papers on "Velocity gradient published in 1992"
TL;DR: In this article, an analytical solution to the equations of magnetohydrodynamics that can be used to model the effect of a transverse magnetic field on buoyancy driven convection in a two-dimensional cavity was proposed.
353 citations
TL;DR: In this paper, the velocity gradient tensor has been shown to satisfy a nonlinear evolution equation of the form (dAij/dt)+AikAkj− (1/3)(AmnAnm)δij=Hij, where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of velocity gradient.
Abstract: The velocity gradient tensor satisfies a nonlinear evolution equation of the form (dAij/dt)+AikAkj− (1/3)(AmnAnm)δij=Hij, where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of the velocity gradient. The homogeneous case (Hij=0) considered previously by Vielliefosse [J. Phys. (Paris) 43, 837 (1982); Physica A 125, 150 (1984)] is revisited here and examined in the context of an exact solution. First the equations are simplified to a linear, second‐order system (d2Aij/dt2)+(2/3)Q(t)Aij=0, where Q(t) is expressed in terms of Jacobian elliptic functions. The exact solution in analytical form is then presented providing a detailed description of the relationship between initial conditions and the evolution of the velocity gradient tensor and associated strain and rotation tensors. The fact that the solution satisfies both a linear second‐order system and a nonlinear first‐order system places certain restrictions on the solution path and leads to an asymptotic velocity gradient field with a geometry that is largely but not wholly independent of initial conditions and an asymptotic vorticity which is proportional to the asymptotic rate of strain. A number of the geometrical features of fine‐scale motions observed in direct numerical simulations of homogeneous and inhomogeneous turbulence are reproduced by the solution of the Hij=0 case.
293 citations
TL;DR: In this paper, the mean velocity distributions and all six components of Reynolds stress are made for the two boundary layers developed on the rotating disk (rotor) and the stationary end wall (stator) for the turbulent flow due to an enclosed rotating disk and it is revealed that the velocity distributions in the respective boundary layers show a similarity at constant local Reynolds number.
134 citations
TL;DR: In this paper, the shear flow behavior of a unidomain nematic solution of poly(n−hexyl isocyanate) (PHIC) subjected to an electric field was studied experimentally in a parallel plate rotational rheometer.
Abstract: The shear flow behavior of a unidomain nematic solution of poly(n‐hexyl isocyanate) (PHIC) subjected to an electric field was studied experimentally in a parallel plate rotational rheometer. At a shear rate of 0.4 s‐1, the Miesowicz viscosity ηc (with the director oriented along the velocity gradient) was found to be 35 times greater than the steady shear viscosity in the absence of an electric field. The mechanism for this electrorheological (ER) effect is the orientation of the permanent dipole moment of the PHIC molecules; the ER effect is an order of magnitude larger than that for low molecular weight liquid crystals. Director tumbling is postulated to occur at a shear rate of 0.4 s−1 for the PHIC solution if the applied dc electric field is lower than approximately 0.4 MV/m. At higher electric fields, flow alignment is regained. In this case, the transient stress undershoot is suppressed. Steady state viscosity vs electric field data were fit to Carlsson and Skarp’s two‐dimensional approximation of t...
106 citations
TL;DR: In this paper, the authors examined the combined effects of a sudden change in surface roughness and of superimposed scales of resistance on the structure of the turbulent boundary layer in coarse grained channels.
Abstract: Heterogeneous coarse grained channels are often characterized by local transitions in bed surface roughness. Distinct spatial zones in terms of grain size have been reported, for example sand ribbons and bedload sheets. The transition from areas of finer to coarser grained surface sediment is often abrupt. However, the effects of these transitions on the shape of the velocity profile and associated shear velocity and roughness length estimates have not been investigated in detail in coarse grained channels. This paper therefore examines the combined effects of a sudden change in surface roughness and of superimposed scales of resistance on the structure of the turbulent boundary layer. Measurements along roughness transitions from smooth to rough beds were conducted in a flume using artificial roughness features and in a natural gravel bed river. Immediately at the transition from a zone of close packed roughness to a rougher section dominated by obstacles superimposed on the more or less uniform roughness surface, boundary shear stress and roughness length increase considerably. Downstream from this transition, velocity profiles become concave upwards. Downstream and upstream sections show significant differences in terms of near bed velocities (deceleration downstream of the transition), velocity gradient and turbulence intensity of the streamwise velocity component. Comparing the mean velocity profiles corresponding to these two different roughness surfaces gives some indication of the proportion of total shear velocity (or shear stress) associated with the pressure drag produced by large and isolated obstacles.
65 citations
TL;DR: In this article, the authors present a mathematical model for field dependent materials which is consistent with the phenomena which have been observed, such as the flow between parallel plates, Couette flow, and flow in an eccentric rotating disc device.
Abstract: Summary. An electro-rheological fluid is a material in which a particulate solid is suspended in an electrically non-conducting fluid such as oil. On the application of an electric field, the viscosity and other material properties undergo dramatic and significant changes. In this paper, the particulate imbedded fluid is considered as a homogeneous continuum. It is assumed that the Cauchy stress depends on the velocity gradient and the electric field vector. A representation for the constitutive equation is developed using standard methods of continuum mechanics. The stress components are calculated for a shear flow in which the electric field vector is normal to the velocity vector. The model predicts (i) a viscosity which depends on the shear rate and electric field and (ii) normal stresses due to the interaction between the shear flow and the electric field. These expressions are used to study several fundamental shear flows: the flow between parallel plates, Couette flow, and flow in an eccentric rotating disc device. Detailed solutions are presented when the shear response is that of a Bingham fluid whose yield stress and viscosity depends on the electric field. During the past few years, there has been a great deal of interest in the manufacture and use of a class of materials which can be classified as field dependent theological materials. These materials are essentially fluids which are imbedded with particulate solids which react to an electrical field in that on the application of a field the viscosity and other material properties undergo dramatic and significant changes. Such materials are being touted as agents for enhancing the performance and efficiency of a variety of engineering devices in very diverse fields. Much of the activity in this area is devoted to producing this material and performing experiments in order to understand the scientific basis for their behavior. Little, if any effort has been devoted to mathematically modeling these materials. The need for understanding the mechanics of such materials and mathematically modeling their behavior is made all the more important as these materials are already finding day-to-day applications in the design of ubiquitous devices like clutches and brakes in cars, vibration dampers and absorbers, lubricating fluids in bearings to name some. In this paper we shall present a mathematical model for field dependent materials which is consistent with the phenomena which have been observed. We shall solve a series of boundary value problems the results of which can be compared with future experiments, as these boundary value problems are in domains which are amenable to experimentation. Unlike the field of magnetohydrodynamies, we do not have an equation like Maxwell's equation which governs the applied field, as the fluid which forms the base for the particulate media is non-conducting. The presence of the field alters the basic material properties of the particulate imbedded fluid, which is considered as a homogeneous continuum. Thus, for instance, the Cauchy stress is dependent on the gradient of the
59 citations
TL;DR: In this paper, a profile-unbiased thermostat is proposed for nonequilibrium-molecular-dynamics simulations of dense liquids undergoing a stationary planar shear flow, where the local temperature is related to the width of a local Maxwellian velocity distribution function.
Abstract: Methodological problems of the temperature control (thermostat) in nonequilibrium-molecular-dynamics simulations of dense liquids undergoing a stationary planar shear flow are addressed. They arise in connection with a transition into a shear-induced ordered state at high shear rates which goes along with inhomogeneities of the fields of density, temperature, and velocity gradient (shear rate) on the length scale of a particle diameter. We demonstrate that a meaningful local description of the thermodynamic fields can be achieved by a smoothing procedure. In particular, the local temperature is related to the width of a local Maxwellian velocity-distribution function. These results are employed for a formulation of a so-called profile-unbiased thermostat which fulfills the criterion of the local-equilibrium hypothesis.
51 citations
TL;DR: In this paper, the authors derived a set of non-linear mode coupling equations for weakly interacting low-frequency electrostatic fluctuations that are driven by a sheared ion velocity flow in a non-uniform dusty plasma embedded in an external magnetic field.
34 citations
TL;DR: In this paper, it was shown that for the thin cylinder limiting case, the transverse force on a circular cylinder is incorrectly given by the conventional approach, in that the product of transverse fluid velocity (in the direction of the required force) with the longitudinal velocity gradient should be added to the water particle acceleration, when computing the added mass component of the force.
Abstract: Wave loads on the cylindrical members of fixed offshore structures are generally calculated by using Morison’s Equation. The inertia force component of this equation is conventionally quoted in a form derived from theoretical calculations for a uniformly accelerating fluid. In this paper the correct form for the inertia force in a general fluid flow is derived from first principles by pressure integration and, independently, from earlier work, by energy arguments. It is shown that, for the thin cylinder limiting case, the transverse force on a circular cylinder is incorrectly given by the conventional approach, in that the product of transverse fluid velocity (in the direction of the required force) with the longitudinal velocity gradient should be added to the water particle acceleration, when computing the added-mass component of the force. Axial divergence, in other words, appears to play the role of a rate-of-change of added mass. It is shown that the mathematical origin of this extra term is the classical three-dimensional flow feature of a ‘zonal harmonic’, which produces a convective fluid acceleration but zero loading. A more elaborate formula is derived for non-circular cylinders, and the nature of point loads occurring at cylinder ends is also discussed.
32 citations
TL;DR: It is shown that a dilute, sterically stabilized lyotropic smectic liquid crystal, subjected to a sufficiently large velocity gradient in the plane of the layers, will undergo a phase separation, with regions of reduced layer spacing coexisting with regions devoid of any layer material.
Abstract: I show that a dilute, sterically stabilized lyotropic smectic liquid crystal, subjected to a sufficiently large velocity gradient in the plane of the layers, will undergo a phase separation, with regions of reduced layer spacing coexisting with regions devoid of any layer material. The critical shear rate for this transition should go as $(layer spacing)^{-3}$.
28 citations
TL;DR: In this paper, the rate of fluctuation of the liquid mass transfer coefficient (velocity gradient) variations as a function of liquid and gas flow rates was analyzed in a trickle-bed reactor by using microelectrodes in a nonconducting wall.
TL;DR: The data demonstrate that when quantitating inplane phase-flow images, significant velocity underestimations may occur when the net flow-induced phase shifts are small and the MR slice thickness is an appreciable fraction of the vessel diameter.
Abstract: Quantitative MR phase imaging is frequently used to measure spin velocities. A potential difficulty may arise, however, when in-plane phase images are acquired of a vessel carrying laminar flow, for which the fluid velocity profile is parabolic. In that case, depending on the flow velocity (v), the vessel diameter (D), and the chosen MR slice thickness (ST), a spin velocity gradient will be present to some extent within each intraluminal voxel. The resulting intravoxel phase dispersion may be expected to affect the net pixel phase value, and hence compromise the assumed linear correlation between phase shift and velocity. In this study, the effects of alterations of v, D, and ST on the apparent image phase are investigated for the case of laminar flow directed parallel to the sequence read gradient. A theoretical model is developed and the conclusions experimentally tested using a flow phantom. The data demonstrate that when quantitating inplane phase-flow images, significant velocity underestimations may occur when the net flow-induced phase shifts are small and the MR slice thickness is an appreciable fraction of the vessel diameter.
TL;DR: In this paper, two 3D sequential imaging studies were carried out at Strathcona Mine in Sudbury, Ontario, Canada, where the average static images indicated an association between the location of induced microseismicity and a zone of both high velocity and high gradient.
Abstract: Sequential imaging of the temporal changes inP-wave velocity offers a practical tool to monitor a rock mass. Using established correlations between the location of seismic events and velocity structure, the temporal seismic potential characteristics of the rock may be monitored. Furthermore, the temporal velocity differences isolate the time dependent factors effecting velocity such as stress, while cancelling static factors such as lithology. Various sequential imaging techniques were compared with respect to accuracy. Differences between successive velocity images were found to have relatively high associated error estimates. However, images of velocity differences calculated from measured travel time delays between successive velocity surveys were found to have lower error estimates. In particular, travel time delays measured using cross-correlation techniques resulted in the most accurate sequential image. Two 3D sequential imaging studies were carried out at Strathcona Mine in Sudbury, Ontario, Canada. Results of the average static images indicated an association between the location of induced microseismicity and a zone of both high velocity and high gradient. Additional examples are described from the global seismology literature which also show a similar correlation between seismicity and velocity structure. We attribute this association to an interrelated stress and strength effect. The Strathcona Mine sequential images show zones of significantly decreased velocity in regions of concentrated microseismic activity, which are postulated to be indications of localized destressing and relaxation of the clamping forces resulting in the microseismicity. The zones of decreased velocity corresponded to an increase in the velocity gradient. One of the case studies also shows an increase in velocity in a zone of high static velocity, which is later the site of amN 2.5 mining-induced seismic tremor. The increase in velocity is believed to correspond to a region of stress concentration, resulting in the subsequent seismic tremor.
Patent•
16 Jan 1992
TL;DR: In this paper, a method for forming a flow of fluid into a spray of fine particle size, notably one with a mass median particle size less than 12 micrometres, is described.
Abstract: The present invention provides a method for forming a flow of fluid into a spray of fine particle size, notably one with a mass median particle size less than 12 micrometres, which method is characterised in that the flow is caused to adopt an annular flow through a duct and in that the velocity gradient within that flow is sufficient to cause shear between components of the flow to break the flow up into a spray, preferably without the need to use a fine nozzle aperture to atomise the flow.
TL;DR: In this article, the authors derived the viscosity tensor of a ferrofluid under external flow by modeling the system as a suspension of rigid dumbbells with a dipole moment in the direction of their bond vector.
Abstract: We obtain the expression for the viscosity tensor of a ferrofluid under external flow. The system is modeled as a suspension of rigid dumbbells with a dipole moment in the direction of their bond vector. Our starting point is the Kramers–Kirkwood expression for the stationary viscous pressure tensor whose average is computed with the stationary solution of the corresponding diffusion equation. We obtain the pressure tensor up to second order in the velocity gradient and for any value of the magnetic field. From the pressure tensor, we derive the viscosity tensor including non‐Newtonian effects. The components of the pressure tensor are related to different viscosity coefficients which are analyzed for flow through a pore and for planar elongational flow.
TL;DR: In this article, the effect of gas velocity on mass transfer is essentially due to a change in the velocity gradient close to the particle surface, thus increasing the particle terminal velocity, which in turn affects positively the mass transfer coefficients.
TL;DR: It is concluded that low velocity flow cytometry makes possible the quantification of weak intercellular adhesion phenomena, and is potentially useful for the future development of new biomechanical techniques and other applications.
Abstract: When analyzed in a flow cytometer, particles are suddenly accelerated to high velocities (1–10 m.s−1) over very short distances. This feature is essential to obtain high analysis rates and low coincidence levels, but translates into very strong velocity gradients (> 105 s−1): particles experience strong hydrodynamic stresses that elongate them acid tend to dissociate weakly associated complexes.
In order to analyze fragile conjugates formed by heterotypic adhesion between two cell types, a flow cytometer was modified to make hydrodynamic stress not only much weaker but also adjustable. A new and easily adaptable flow cell was designed for the instruments of the FACS™ series; it provided satisfactory hydrodynamic conditions on a wide continous range of flow rates. Accompanying electronic adaptations permitted standard analysis between 0.01 and 10 m.s−1.
At 0.01 m.s−1, the velocity gradient roughly amounts to 50 s−1. Conjugates formed by the adhesion between human B and resting T lymphocytes, disrupted in conventional flow cytometers, could be detected and precisely quantified provided analysis velocity was kept below 0.1 m.s−1. We conclude that low velocity flow cytometry makes possible the quantification of weak intercellular adhesion phenomena, and is potentially useful for the future development of new biomechamical techniques and other applications.
TL;DR: In this article, a mathematical model for velocity gradient in two-dimensional turbulent flow that can also be applied to flow in fluidized beds in the transitional state was developed The theory of fluidization in a circular cross-section column was presented The existence of a viscous sublayer around each fluidized solid particle and the laminar sublayer thickness at the wall were neglected to evaluate the theoretical expressions, numerical applications are carried out for filter-bed materials of two different types of sands and anthracite coal.
Abstract: Backwashing of deep bed filters is achieved by fluidizing the filter media A mathematical model for velocity gradient in two-dimensional turbulent flow that can also be applied to flow in fluidized beds in the transitional state was developed The theory of fluidization in a circular cross-section column was presented The existence of a viscous sublayer around each fluidized solid particle and the laminar sublayer thickness at the wall were neglected To evaluate the theoretical expressions, numerical applications are carried out for filter-bed materials of two different types of sands and anthracite coal An indirect verification of the existence of an optimum porosity around 070–075 during filter backwashing was observed in the laboratory experiments The velocity gradient in backwashing of granular filters was found to be a function of power dissipation in a unit volume and coefficient \IC\N that indicates the effect of turbulence in total power dissipation It was also found that turbulence intensity decreases with an increase of porosity, and the arithmetic mean shear stress has a maximum value between porosity values of 070 and 075
TL;DR: In this article, the authors describe an investigation of structure in moderately dilute three-dimensional shear flows, defined as a dynamic inhomogeneity or fluctuation in the spatial concentration field.
Abstract: This paper describes an investigation of structure in moderately dilute three-dimensional shear flows. Structure is defined as a dynamic inhomogeneity or fluctuation in the spatial concentration field. Numerical experiments are performed with large numbers of identical frictionless, inelastic spheres. The spheres are contained in a fully periodic cubic control volume. A state of shear is maintained in the control volume by moving the upper periodic image in one direction and the lower image in the opposite direction. As the coefficient of restitution of the spheres is lowered, conditions in the control volume deviate from a state of simple shear, exhibiting strong wavelike fluctuations in the concentration, stress, and velocity fields. Visual inspection of the spatial concentration field reveals a strong tendency for spheres with a low coefficient of restitution to form dense clouds. The clouds are, in general, oriented such that they are aligned with the mean velocity and normal to the direction of the mean velocity gradient created by the moving periodic images of the control volume.
TL;DR: In this article, the boundary layer motion of a weak suspension is investigated with allowance for the effect on the particles not only of the Stokes force but also of the additional transverse force resulting from the transverse nonuniformity of the flow over the individual particle.
Abstract: The boundary layer motion of a weak suspension is investigated with allowance for the effect on the particles not only of the Stokes force but also of the additional transverse force resulting from the transverse nonuniformity of the flow over the individual particle. As distinct from studies [1–3], in which the limiting values of the transverse force (Saffman force) were used [4], the velocity and density of the dispersed phase have been determined with allowance for the dependence of the Saffman force on the ratio of the Reynolds numbers calculated from the velocity of the flow over the individual particle and the transverse velocity gradient of the undisturbed flow, respectively [5, 6].
TL;DR: In this article, the rotational diffusion equation for rotational ellipsoidal particles in solution has been approximately solved when the solute particles oriented by a shear flow are acted on by a rectangular and reversing electric pulse along the direction of the velocity gradient of flow.
Abstract: The rotational diffusion equation for rotational ellipsoidal particles in solution has been approximately solved when the solute particles oriented by a shear flow are acted on by a rectangular and reversing electric pulse along the direction of the velocity gradient of flow. The angular distribution function is obtained up to the fourth order for an electric field and/or a hydrodynamic field, and it is used in order to calculate the birefringence and the extinction angle. A similar calculation is performed for the process in which the solute is returning to a steady state influenced by a shear flow after an electric field is suddenly removed. Furthermore, the equations for the intensities of light transmitted through the analyzer are shown in two cases. One is when the polarizer is oriented at 0°, and the other is when the polarizer is oriented at 45° with the direction of the electric field. The intensity at low fields in the latter case (45°) is expressed by the sum of a term of the square of the hydrodynamic field and a term of the square of the electric field. The intensity in the former case (0°), to the first order, is proportional to a hydrodynamic field; to the second order, it is proportional to the product of the hydrodynamic field and the square of the electric field. The initial slope of the intensity change for the buildup, reverse, or decay process in the former case (0°) is a function of the axial ratio and the electric property of the solute, even at low fields.
TL;DR: In this paper, it was shown that the energetic particle driven Alfven wave instability saturates when the wave fluctuations are still quasi-coherent, and the saturation is due to particle velocity space diffusion which steepens the velocity gradient of the resonant particles, thereby enhancing wave damping.
TL;DR: The generalized eddy-viscosity hypothesis presented in this article relaxes this limitation by recognizing the influence of gradients in the turbulent length scale and the shear on boundary layer flows.
Abstract: The standard eddy-viscosity concept postulates that zero velocity gradient is accompanied by zero shear stress. This is not true for many boundary layer flows: wall jets, asymmetric channel flows, countercurrent flows, for example. The generalized eddy-viscosity hypothesis presented here, relaxes this limitation by recognizing the influence of gradients in the turbulent length scale and the shear. With this new eddy-viscosity concept, implemented into the standard k-e model, predictions of some boundary layer flows are made
TL;DR: In this article, the profiles of liquid velocity and gas hold-up in convection cells of bubble columns were calculated numerically and a limit of stability for the development of circulation cells has been obtained.
Abstract: The profiles of liquid velocity and gas hold-up in convection cells of bubble columns were calculated numerically. Development of a circulation cell was calculated from momentum and mass balances. Breakdown of the circulation cell was calculated taking into account the drift motion of bubbles ascending in accordance with the velocity gradient of the liquid. A limit of stability for the development of circulation cells has been obtained.
Journal Article•
TL;DR: In this paper, velocity and velocity gradient fields arising at the entrance of a small capillary during free-converging flow of aqueous solution of poly(ethylene oxide), as well as the degree of the coil-stretch transition of the macromolecule were experimentally studied.
Abstract: Velocity and velocity gradient fields arising at the entrance of a small capillary during the free-converging flow of aqueous solution of poly(ethylene oxide), as well as the degree of the coil-stretch transition of the macromolecule were experimentally studied. The hydrodynamic field arising under the converging flow conditions resulted in a considerable (∼60%) degree of polymer stretching which, in turn, led to a readjustment of the hydrodynamic field itself
TL;DR: In this article, a throughflow with swirling inflow in an annular diffuser is calculated under the assumption of small cross-flow, the flow near inner and outer wall surfaces is calculated based on the three-dimensional momentum integral equation of the boundary layer.
Abstract: In this paper, a throughflow with swirling inflow in an annular diffuser is calculated. Under the assumption of small cross-flow, the flow near inner and outer wall surfaces is calculated based on the three-dimensional momentum integral equation of the boundary layer. The potential flow outside the boundary layer is computed by means of the iteration method based on the velocity gradient equation along the quasi-orthogonal direction of the meridional projection of the stream-line on the meridional surface and the constancy of flux equation[1]. The numerical results agree with the experiments quite well. This method is useful for analyzing the throughflow with pre-swirl in the annular diffuser.
TL;DR: In this article, a two-dimensional, semigeostrophic and uniform potential vorticity Eady model is considered, where momentum diffusion and wave dispersion are incorporated into the model to prevent the ultimate development of a discontinuity in the alongfront geostrophic velocity υ(υx = ∞).
Abstract: The two-dimensional, semigeostrophic and uniform potential vorticity Eady model is considered. An unstable baroclinic wave develops large velocity and temperature gradients in a narrow zone. Momentum diffusion and wave dispersion are incorporated into the model to prevent the ultimate development of a discontinuity in the alongfront geostrophic velocity υ(υx = ∞). Diffusion and dispersion act to reduce the amplitude of the growing baroclinic wave, and these processes also act to expand the width of the frontal zone, where the maximum velocity gradient is located. Explicit relationships are derived that reveal how these processes are dependent on two parameters: ϵ, the nondimensional eddy diffusion coefficient, and λ the ratio of a dispersion coefficient μ to ϵ2. The total dissipation of kinetic energy D is separated into two parts,D1andD2:D1 provides the dissipation that is largely confined to the relatively narrow frontal zone, and D2 = D − D1 provides the dissipation that is associated with the...
01 Jan 1992
TL;DR: In this paper, the authors provide an overview of hydrodynamics and dispersion near bounding surfaces of a porous media, and discuss a semi-empirical treatment based on the velocity slip, a theoretical treatment for interfacial hyddynamics, and a general, 2D direct simulation of the flow for a two-dimensional porous medium.
Abstract: This chapter provides an overview of hydrodynamics and dispersion near bounding surfaces of a porous media. There are many problems in which fluid flow and heat transfer occur through the bounding surfaces of the porous media. These velocity and heat flux vectors may be parallel or perpendicular to the bounding surfaces or may be at an arbitrary angle. The chapter reviews the recent treatments of fluid and heat flow near the interface of a porous and a plain medium. The plain medium is occupied by a solid or a fluid. The chapter also discusses the Brinkman continuum treatment of the interface, the Beavers-Joseph slip treatment, and a direct simulation of the flow for a two-dimensional porous medium. The chapter also discusses the recent results for dispersion in the porous media, and reviews the anisotropy in the dispersion tensor and its nonuniformity near the solid-bounding surfaces. A general energy equation for porous media that includes the dispersion effects can be obtained by averaging the local energy equation over a representative elementary volume.. The chapter discusses a semi-empirical treatment based on the velocity slip, a theoretical treatment for interfacial hydrodynamics, another semi-empirical treatment based on an effective viscosity, and a general, two-dimensional direct simulation. Their experimental results showed that the slip velocity could be correlated with the square root of the permeability and with the velocity gradient in the fluid layer evaluated at the interface. The idea behind the construction of such a correlation was the notion of continuity in the shear stress across the interface. The nonuniformities in the phase distribution at and near the bounding surface, and its effects on the fluid flow and heat transfer were most significant if the primary heat transfer was through these surfaces.
Patent•
22 Jun 1992
TL;DR: In this paper, the authors proposed a method to make it possible to calculate a stream function of a flow field in a short time by a method wherein the velocities of all combinations obtained by taking three flow velocity data out of three or more of them at measuring points in the vicinity of a grid point for which interpolation is to be made, are calculated by a specific formula, a statistical processing is executed and thereby an approximate flow velocity is obtained.
Abstract: PURPOSE:To make it possible to calculate a stream function of a flow field in a short time by a method wherein the velocities of all combinations obtained by taking three flow velocity data out of three or more of them at measuring points in the vicinity of a grid point for which interpolation is to be made, are calculated by a specific formula, a statistical processing is executed and thereby an approximate flow velocity is obtained. CONSTITUTION:An array of grid points is prepared in an area to be analyzed and flow velocity data in the number of (n) at flow velocity measuring points K, L, M, N... within a prescribed range from a grid point G for which interpolation is to be made are extracted. Then, interpolating computation of the data at the grid point is executed by using one set of combinations of nC3 sorts in all obtained by taking three out of the data in the number of (n). Herein interpolation data (u) are obtained by a formula wherein a flow velocity (vector) at the grid point G is denoted by (u). In the formula, (dx)K, (dy)K, (dx)L, (dy)L, (dx)M and (dy)M denote distances between the measuring points and the grid point G, du/dx and du/dy denote a velocity gradient at the grid point G and uK, uL and uM denote the flow velocity data. In the same way, interpolation data in the number of nC3 are determined, a statistical processing is executed and thereby a median is calculated. By executing such a processing as the above for all the grid points in the interpolation area, a stream function of a flow field can be calculated in a short time.