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Showing papers on "Fluid dynamics published in 1997"


Journal ArticleDOI
TL;DR: In this article, a numerical method for solving incompressible viscous flow problems is introduced, which uses the velocities and the pressure as variables and is equally applicable to problems in two and three space dimensions.

2,797 citations



Journal ArticleDOI
TL;DR: In this paper, the authors introduced the idea of time-varying coefficients which fits more naturally with a particle formulation, which is a Lagrangian particle method for fluid dynamics which simulates shocks by using an artificial viscosity.

419 citations


Journal ArticleDOI
TL;DR: In this paper, a specific energy equation instead of the thermal energy equation is used to handle shocks in smooth particle hydrodynamics (SPH) and the resulting equations are very similar to the equations constructed for Riemann solutions of compressible gas dynamics.

397 citations


Journal ArticleDOI
TL;DR: In this article, the effects of the EDL at the solid-liquid interface on liquid flow and heat transfer through a microchannel between two parallel plates at constant and equal temperatures were investigated.

353 citations


Journal ArticleDOI
TL;DR: In this article, a contour dynamics algorithm for the Euler equations of fluid dynamics in two dimensions is presented, which is applied to regions of piecewise-constant vorticity within finite-area-vortex regions (FAVRs).

348 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders are investigated using a lattice Boltzmann formulation.
Abstract: The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

275 citations


Journal ArticleDOI
TL;DR: In this article, a lattice Boltzmann description of fluid flow in heterogeneous porous media is presented which is intended for modeling flow processes which occur in liquid composite molding applications.
Abstract: A lattice Boltzmann description of fluid flow in heterogeneous porous media is presented which is intended for modeling flow processes which occur in liquid composite molding applications. The lattice Boltzmann method is equivalent to solving a hybrid method of the Stokes and Brinkman equations, with the Brinkman equation being implemented to model flow through porous structures, while the Stokes equation is applied to the open regions outside the porous structures. The Brinkman equation is recovered through a modification of the particle equilibrium distribution function, which reduces the magnitude of momentum at specified lattice sites, while leaving the direction of momentum unchanged. As a test of the new lattice Boltzmann model, steady transverse flow (saturated) through a square array of porous cylinders of elliptical cross section is investigated. Cell permeabilities obtained from the lattice Boltzmann simulations are in excellent agreement with a lubrication model, validating the lattice Boltzman...

259 citations


Journal ArticleDOI
TL;DR: In this paper, Vortmeyer et al. measured radial velocity profiles below the bed at empty tube velocities of air of 05 m/s

233 citations


Journal ArticleDOI
TL;DR: A generalized approach to the use of pulsed-gradient spin echo (PGSE) NMR methods for the measurement of flow and diffusion in porous media is presented, in which the fluid dynamics is probed over well-defined temporal and spatial domains.
Abstract: A generalized approach to the use of pulsed-gradient spin echo (PGSE) NMR methods for the measurement of flow and diffusion in porous media is presented, in which the fluid dynamics is probed over well-defined temporal and spatial domains. Various NMR techniques based on PGSE encoding are described in the context of standard theories of dispersion, with reference to Eulerian and Lagrangian coordinate frames. This array of methods provides access not only to the dispersion coefficient and the mean local velocity but also to propagators relevant to spatial and temporal correlations. Methods investigated include flow imaging average propagator analysis, dispersion measurement, velocity exchange spectroscopy, and flow diffraction based on scattering analysis. We apply these to a study of flow and dispersion of water in a packed bed of 90.7-μm-dia. polystyrene latex spheres. Our measurements of the dependence on Peclet number of dispersion (parallel and perpendicular to the mean flow direction) are in excellent agreement with results reported in the literature. The scattering approach used here has potential for studying complex flow properties involving the interplay between hydrodynamic and structural characteristics of porous media.

226 citations


Journal ArticleDOI
TL;DR: In this article, the decay of pneumatic foam is studied in detail and the fundamental equations, the assumptions involved and the results obtained are discussed in detail, and presented within a unified framework.

Journal ArticleDOI
TL;DR: In this article, the Navier-Stokes equations are used to model the dynamics of coherent structures in turbulent flows and the statistical technique of Karhunen-Loeve or proper orthogonal decomposition is used in the case of turbulence.

Journal ArticleDOI
TL;DR: In this article, it is shown that once the vertical extent of reacted rocks is comparable to the compaction length, compaction processes caused by the difference between confining and fluid pressure gradients generate a positive fluid pressure anomaly (effective pressure < 0) above the reaction front, irrespective of the reaction volume change.
Abstract: The obstruction to fluid flow formed by the rocks overlying a metamorphic devolatilization front causes the fluid pressure gradient in the reacting rocks to diverge from lithostatic. This drives deformation in tandem with the fluid pressure anomaly generated by the volume change of the reaction. Numerical simulations show that once the vertical extent of the reacted rocks is comparable to the compaction length, compaction processes caused by the difference between confining and fluid pressure gradients generate a positive fluid pressure anomaly (effective pressure < 0) above the reaction front, irrespective of the reaction volume change. Consequent dilational deformation propagates the anomaly upward, leading to underpressuring and densification at the reaction front and detachment of a wave of anomalous fluid pressure and porosity. Creep is a viable mechanism for such wave propagation for crustal viscosities < 10 15 MPa s. Continuous upward strengthening of the crust increases the wavelength and amplitude of the fluid pressure waves and thereby the likelihood of hydrofracture. Order of magnitude strength contrasts are adequate to arrest wave propagation, forming water sills that become increasingly stable in the absence of deviatoric stress. Although the fluid pressure gradient within a wave may be near hydrostatic, Rayleigh convection is unlikely. Thus, in the absence of lateral perturbations, fluid flow is upward and episodic, despite continuity of devolatilization. Porosity waves provide a mechanism for temporal focusing of metamorphic fluid fluxes with the potential to increase the efficacy of heat and mass transport.

Journal ArticleDOI
TL;DR: In this article, a governing equation stemming from the principle of mass conservation and the assumption that the cubic law holds locally is derived for incompressible laminar fluid flow in irregular fractures under steady state conditions.
Abstract: Fluid flow in a rock fracture bounded by two irregular surfaces is complex even under a laminar flow regime. The major factor causing deviation of predicted fracture flow behavior from the ideal parallel plate theory is the nature of nonparallel and nonsmooth geometry of fracture surfaces. Important questions on the validity of the cubic law and the Reynolds equation for complicated fracture geometries have been studied by many researchers. The general conclusion from these efforts is that the cubic law is valid provided that an appropriate average aperture can be defined. Many average apertures have been proposed, and for some cases, some work better than others. Nonetheless, to date, these efforts have not converged to form a unified definition on the fracture aperture needed in the cubic law, which stimulates the current effort to develop a general governing equation for fracture flow from a fundamental consideration. In this study, a governing equation stemming from the principle of mass conservation and the assumption that the cubic law holds locally is derived for incompressible laminar fluid flow in irregular fractures under steady state conditions. The equation is formulated in both local and global coordinates and explicitly incorporates two vectorial variables of fracture geometry: true aperture and tortuosity. Under the assumption of small variations in both tortuosity and aperture, the governing equation can be reduced to the Reynolds equation. Two examples are provided to show the importance and generality of the new governing equation in both local and global coordinate systems. In a simple fracture with two nonsmooth and nonparallel surfaces, the error in permeability estimation can be induced using the Reynolds equation with the apparent aperture and can reach 10% for a 25° inclination between the fracture surfaces. In a fracture with sinusoidal surfaces, the traditional method can cause significant errors in both permeability and pressure calculation.

Journal Article
TL;DR: In this paper, the basic equations of fluid mechanics are stated, with enough derivation to make them plausible but with-out rigour, and the physical meanings of the terms in the equations are explained.
Abstract: SUMMARY: The basic equations of fluid mechanics are stated, with enough derivation to make them plausible but with- out rigour. The physical meanings of the terms in the equations are explained. Again, the behaviour of fluids in real situa- tions is made plausible, in the light of the fundamental equations, and explained in physical terms. Some applications rele- vant to life in the ocean are given.

Journal ArticleDOI
TL;DR: In this article, a numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows is described, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence.
Abstract: This paper describes a novel numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows, the most important examples of which are the earth's atmosphere and oceans. the algorithm combines two radically different algorithms, one Lagrangian and the other Eulerian, to achieve an unexpected gain in computational efficiency. The algorithm is demonstrated for multi-layer quasi-geostrophic flow, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence. the turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-dimensional, vertically-coherent character of the flow. Ongoing extensions of the algorithm to the generally ageostrophic flows characteristic of planetary fluid dynamics are outlined.

Book ChapterDOI
TL;DR: In this article, the most general possible relations between the stress and strain-velocity components, which can be obeyed by an incompressible, visco-inelastic fluid, are derived.
Abstract: The classical theory of the hydrodynamics of viscous fluids depends on the assumption of a particular law governing the relations between the components of stress in a fluid and those of the strain-velocity. This assumption limits its applicability to Newtonian fluids. Here, the most general possible relations between the stress and strain-velocity components, which can be obeyed by an incompressible, visco-inelastic fluid, are derived. These relations also apply to an incompressible, visco-elastic fluid in a steady state of laminar flow. It is shown how equations of motion and boundary conditions can be obtained if these relations are known. Two problems involving laminar flow are then discussed in some detail. These are: (i) the torsional motion of a cylindrical mass of fluid, produced by means of forces applied to its plane ends, and (ii) the laminar flow of a mass of fluid contained between two coaxial cylinders rotating with different angular velocities.

Journal ArticleDOI
01 Dec 1997-Fractals
TL;DR: In this paper, the shape of each volume element can be optimized such that the elemental volume-to-point flow resistance is minimal (constructal theory) and a strategy for constructing the architecture of the volume-topoint path such as a tree network is presented.
Abstract: The function of many natural flow systems is to connect by a fluid flow a nite-size volume and one point. This paper outlines a strategy for constructing the architecture of the volume-topoint path such that the flow resistance is minimal (constructal theory 1 ). The given volume is viewed as an assembly of volume elements of various sizes. The main discovery is that the shape of each element can be optimized such that the elemental volume-to-point flow resistance is minimal. This optimization principle applies at every volume scale. The smallest volume element contains a fluid saturated porous medium with Darcy flow, which is collected by and channeled through a high permeability path (e.g., ssure) to one point on the element boundary. The geometric optimization is repeated for larger volume elements, which are constructs (assemblies) of optimized smaller volumes. The flow integrated over each new assembly is channeled through a high-permeability path to a point on the side of the assembly. One remarkable feature of the emerging minimal-resistance flow path is that the highpermeability channels of the various volume elements form a tree network which is completely deterministic. The interstices of the network are lled with low permeability porous medium. The method is extended to applications where the high-permeability paths are empty spaces (e.g., parallel-plate channels). It is shown that when the total void volume is constrained it can be distributed optimally among the volume elements to further decrease the overall flow resistance.

Journal ArticleDOI
TL;DR: In this paper, phase Doppler anemometry is used to discriminate the turbulence characteristics of the carrier fluid from the sediment grains (0.22 mm diameter) and shows that the presence of mobile sediment increases the near-wall velocity gradient and shear velocity when compared with the clearwater values.
Abstract: The presence of sand moving at low transport rates over a flat bed modulates the production of turbulence when compared to clearwater flow at similar mean flow conditions. Phase Doppler anemometry is used to discriminate the turbulence characteristics of the carrier fluid from the sediment grains (0.22 mm diameter) and shows that the presence of mobile sediment increases the near-wall velocity gradient and shear velocity when compared with the clearwater values. This increased shear velocity is associated with a greater bed roughness height and near-bed turbulence intensities and smaller mixing lengths. Quantification of slip velocities between the fluid and sediment phases reveals particle Reynolds numbers that range from 1 to 30. Turbulence enhancement is shown to occur at lower values of both the Stokes number and ratio of the particle size-to-turbulent length scale than in past work. Several mechanisms of turbulence modulation may be invoked to explain these changes, including increased bed roughness, eddy shedding from large grains, grain inertial effects, and particle-coherent structure interactions. These mechanisms may be significantly influenced by both particle-particle and particle-wall interactions. Since mobile sediment modulates the carrier fluid turbulence, there is a need for modification of existing theories of sediment suspension and for caution when interpreting velocity profiles that are obtained without discriminating the fluid and sediment phases.

Journal ArticleDOI
TL;DR: In this article, a numerical model is developed to predict transient behaviors of electric vehicle lead-acid batteries during discharge and charge processes, which not only accounts for coupled processes of electrochemical kinetics and mass transport occurring in a battery cell, but also considers free convection resulting from density variations due to acid stratification.
Abstract: A numerical model is developed to predict transient behaviors of electric vehicle lead-acid batteries during discharge and charge processes. The model not only accounts for coupled processes of electrochemical kinetics and mass transport occurring in a battery cell, but also considers free convection resulting from density variations due to acid stratification. A single set of conservation equations valid for both porous electrodes and the free electrolyte region is derived and numerically solved using a computational fluid dynamics technique. This numerical methodology is capable of simulating a two-dimensional cell with the fluid flow taken into consideration and requires only tens of minutes of central processing unit time on engineering workstations. Four sample calculations are presented in this work to provide rigorous validation of the developed simulator. The simulator is capable of predicting the transient behavior of the acid concentration, the porosity of the electrodes, and the state of charge of the battery during discharge, rest, and charge cycles. The model can also be used to investigate the effects of various system parameters, such as electrode dimensions, separator design, temperature, and electrolyte composition on the battery performance (voltage, power, cold cranking amperage, etc.).

Patent
28 Jul 1997
TL;DR: In this article, the pseudorandom coding and decoding can be used to filter out pressure-response crosstalk caused by multiple fluid infusion segments feeding into a common line.
Abstract: Flow parameters in a fluid delivery assembly are determined by monitoring pressure responses and processing those responses along with information regarding the fluid flow. In one aspect, a processor controls the pump to pump flow quantities in accordance with a pseudorandom code. Portions of the resulting pressure signal sensed are then decoded in accordance with the pseudorandom code. An estimate of the equilibrium pressure is generated from the decoded pressure values, while a summation of the pressure samples is generated from the undecoded pressure signals. The resistance to fluid flow of the system is determined from the estimated equilibrium pressure and pressure summation. For low flow rates, a processor controls the pump to pump fluid in a series of fluid boluses, with each fluid bolus delivered in the beginning of a separate timeslot. The equilibrium pressure is measured at the end of each timeslot, and a summation of the pressure samples is generated from the pressure signals. For high flow rates, the pump is controlled to vary the flow rate and the change in pressure is divided by the change in flow to directly determine the resistance. A resistance display continuously displays the resistance of the system. The pseudorandom coding and decoding can be used to filter out pressure-response crosstalk caused by multiple fluid infusion segments feeding into a common line.

Journal ArticleDOI
TL;DR: In this article, it is shown that in the absence of time-dependent boundary conditions (e.g., shearing boundary conditions via explicit cell dynamics or Lees-Edwards boundary conditions), a conserved energy exists for the equations of motion.
Abstract: The nonequilibrium molecular dynamics generated by the SLLOD algorithm [so called due to its association with the DOLLS tensor algorithm (D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic, New York, 1990)] for fluid flow is considered. It is shown that, in the absence of time-dependent boundary conditions (e.g., shearing boundary conditions via explicit cell dynamics or Lees–Edwards boundary conditions), a conserved energy, H exists for the equations of motion. The phase space distribution generated by SLLOD dynamics can be explicitly derived from H. In the case of a fluid confined between two immobile boundaries undergoing planar Couette flow, the phase space distribution predicts a linear velocity profile, a fact which suggests the flow is field driven rather than boundary driven. For a general flow in the absence of time-dependent boundaries, it is shown that the SLLOD equations are no longer canonical in the laboratory momenta, and a modified form of the SLLOD dynamics is presented which is valid arbitrarily far from equilibrium for boundary conditions appropriate to the flow. From an analysis of the conserved energy for the new SLLOD equations in the absence of time-dependent boundary conditions, it is shown that the correct local thermodynamics is obtained. In addition, the idea of coupling each degree of freedom in the system to a Nose–Hoover chain thermostat is presented as a means of efficiently generating the phase space distribution.

Journal ArticleDOI
TL;DR: In this article, several forms proposed for these models are summarized and different descriptions of granular temperature are investigated, as well as an alternative approach derived from soil mechanics is tested, and measurements of a two-dimensional bubbling bed are finally used to verify the results.

Journal ArticleDOI
TL;DR: In this article, the growth of the gradient of a scalar temperature in a quasigeostrophic flow is studied numerically in detail, and the critical time at which the temperature gradient attains the first local maximum is found to depend double logarithmically on the Reynolds number, suggesting the global regularity of the inviscid flow.
Abstract: The growth of the gradient of a scalar temperature in a quasigeostrophic flow is studied numerically in detail. We use a flow evolving from a simple initial condition which was regarded by Constantin et al. as a candidate for a singularity formation in a finite time. For the inviscid problem, we propose a completely different interpretation of the growth, that is, the temperature gradient can be fitted equally well by a double-exponential function of time rather than an algebraic blowup. It seems impossible to distinguish whether the flow blows up or not on the basis of the inviscid computations at hand. In the viscous case, a comparison is made between a series of computations with different Reynolds numbers. The critical time at which the temperature gradient attains the first local maximum is found to depend double logarithmically on the Reynolds number, which suggests the global regularity of the inviscid flow.

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations are combined with a set of differential equations which take the place of these equations; however, only very few solutions of this set of equations exist.

Journal ArticleDOI
TL;DR: In this article, a new analytical approach which takes into consideration a three-dimensional irradiance distribution and its influence on fluid flow and radial heat transfer is presented, and it is shown that a volumetric receiver consisting of sufficiently small absorber modules which are equipped with an additional orifice plate at the rear side will always run under stable flow conditions.

Journal ArticleDOI
TL;DR: In this paper, an incompressible fluid flow across a bank of circular cylinders is studied and modeled as a non-Darcy flow through a porous medium, where the continuity equation and the momentum equation in pore scale are solved on a Cartesian grid system.

Journal ArticleDOI
TL;DR: In this paper, a universal solution for the relative velocity of two particles due to turbulent accelerations in a gaseous or liquid system is presented, taking into account the effects of the inertia of the particles and the difference in densities of the fluid and the particles.
Abstract: A review of previous derivations of particle collision rates in turbulent fluid flow shows that these are applicable only to limited cases. A more general derivation is given, taking into account the effects of the inertia of the particles and the difference in densities of the fluid and the particles. A universal solution for the relative velocity of two particles due to turbulent accelerations in a gaseous or liquid system is presented. In gaseous systems the acceleration mechanism becomes predominant at particle sizes far below the Kolmogorov microscale of turbulence. In liquid systems, the particle inertial and added mass effects become important above the Kolmogorov microscale. Here the particle collision rate cannot be estimated from the fluid turbulent velocity fluctuations only.

Journal ArticleDOI
TL;DR: In this paper, the authors present a theoretical and numerical study of the reorganization of a porous matrix due to fluid flow coupled with dissolution or precipitation processes, and find that under certain conditions, flow of corrosive fluids results in unstable growth of the permeability and increasing disequilibrium in fluid chemistry with time.
Abstract: We present a theoretical and numerical study of the reorganization of a porous matrix due to fluid flow coupled with dissolution or precipitation processes. We find that under certain conditions, flow of corrosive fluids results in unstable growth of the permeability and increasing disequilibrium in fluid chemistry with time. High-permeability channels may form parallel to the direction of flow. In time, these channels cause the distribution of porosity to become increasingly correlated and anisotropic and cause flow rates to be increasingly variable. Flow coupled with crystallization has the opposite effect: With time, permeability reduction occurs at a decreasing rate. Mineral composition in the fluid approaches chemical equilibrium. Precipitation destroys existing preferred paths for flow and acts to homogenize and disperse the flow. Connectivity of the porous media is reduced. Implications of these results for two geological systems are discussed: (1) Modes of melt extraction from the Earth's mantle, where the expected different modes of flow and reaction may help explain different geochemical and geological observations at hot spots and mid-ocean ridges, and (2) Precipitation and formation of abnormal pressure zones in sedimentary basins.

Journal ArticleDOI
TL;DR: In this paper, the applicability of the capillary model for high voidage beds composed of spheres and fibers is investigated in both linear and non-linear laminar flow regimes.