Early Stages Of Flow Research Articles

Experiment, Model, and Mechanism of Multiscale Dynamic Diffusion-Permeability in Coal under Different Fluids.

The permeability of coal exhibits multiscale characteristics in space and time, which is caused by the presence of micro and nanopores in coal. Water, free gas, and adsorbed gas are common engineering fluids in coal seams during gas extraction. Thus, it is of significance to study the multiscale characteristics and mechanisms of seepage-diffusion of different fluids in coal for gas extraction engineering. Experiments of seepage-diffusion for He, CH4, and water are carried out using ϕ50 × 100 mm cylindrical coal. It is found that the apparent diffusion coefficient for He, CH4, and water are not a constant but a variable that decays dynamically with time. The phenomenon is independent of fluid properties and determined only by the multiscale characteristics of pores in coal, and then a novel model of multiscale dynamic apparent diffusion that can accurately describe the full-time process of flow in various fluids is proposed. The mechanism of dynamic seepage-diffusion for different fluids in coal is elucidated based on a new proposed geometrical model of multiscale pores. At the early stage of flow, fluids first flow in or out of the largest pores outside coal, and at the later stage of flow, fluids flow in the micro and nanopores inside the coal matrix. The pore sizes through which the fluid flows decrease with time, which leads to a dynamic attenuation of the apparent diffusion-permeability with time. The initial apparent permeability K 0 for He/CH4 shows a "U"-shaped pattern of decreasing and then increasing with the decrease of gas pressure. When the gas pressure is lower than the turning point, the slip effect dominates, making the initial apparent permeability K 0 decrease with the increase of gas pressure. When the gas pressure is higher than the turning point, the effect of the pressure difference of the gas dominates, and K 0 increases with the increase of gas pressure. When water flows in multiscale pores, it occupies the space of large pores, making the homogeneity of pores increase, and the decay coefficient of apparent permeability becomes smaller. The multiscale permeability can explain the reason for the rapid attenuation of coalbed methane production in the late stage. It is of great significance for coalbed methane productivity prediction.

Heat transfer between two parallel porous plates for Couette flow under pressure gradient and Hall current

The aim of the present paper is to study the unsteady magneto-hydrodynamic viscous Couette flow with heat transfer in a Darcy porous medium between two infinite parallel porous plates considering Hall effect, and temperature dependent physical properties under constant pressure gradient. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is flowing through a porous medium that is assumed to obey Darcy’s law. A numerical solution for the governing nonlinear partial differential equations coupled with set of momentum equations and the energy equation including the viscous and Joule dissipations is adopted. The effect of the porosity of the medium, the Hall current and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions are investigated. It is found that the porosity number M has a marked effect on decreasing the velocity distribution (owing to a simultaneous increase in Darcy porous drag). Also the temperature T is decreased considerably with increasing porosity number. With increasing Hall current parameter m, the velocity component u (x-direction) is considerably increased, whereas velocity component w (z-direction) is reduced. Temperatures are decreased in the early stages of flow but effectively increased in the steady state with increasing m.

Finger tip behavior in small gap gradient Hele-Shaw flows

Finger tip splitting and finger tip narrowing phenomena are not commonly observed during early flow stages in parallel-plate rectangular Hele-Shaw cells. However, an interesting experimental study performed by Zhao [Phys. Rev. A 45, 2455 (1992)] showed that finger tip behavior can be significantly affected by the addition of a small gradient to the gap of the cell, so that the plates are no longer exactly parallel. It was found that pattern forming events at the finger tip are dictated by the sign of the gap gradient, where positive (negative) sign produces wider (narrower) fingers. We approach the nonparallel-plate situation analytically through a perturbative mode coupling theory and show that these important finger tip features can be predicted at early nonlinear stages of the dynamics.

Rheooptical study of the early stages of flow enhanced crystallization in isotactic polypropylene

The effect of a shear flow on the early stages and the kinetics of isothermal crystallization of an isotactic polypropylene has been studied experimentally. In the shear rate region where crystallization proceeds through point-like precursors, the magnitude of the shear rate, the shearing time as well as the instant in time at which the deformation starts have all been varied, in combination with rheooptical measurements. These include depolarized light intensity and birefringence. In agreement with previous work, above a critical shear rate and a critical shearing time, the crystallization kinetics are enhanced. Somewhat surprisingly, below a characteristic time, t0,max, the kinetics are not affected by the instant in time at which flow is applied or stops. As long as flow takes place before this critical dwell time, only the shearing time and primarily the magnitude of the shear rate seem to matter. When flow is started only after t0,max, its effect to accelerate crystallization kinetics becomes less efficient. The range over which the different parameters have an effect have been compared to the rheological relaxation times and to the measurements of global chain extension. To investigate the effects of flow on the early stages in more detail, time resolved Small-Angle Light Scattering experiments were used to detect changes in the density and orientation fluctuations. Measurements explicitly compare the effect of temperature and shear flow on the kinetics and the intensity of the density fluctuations.

Contribution of a short separating plate on the control of the swirling process downstream a half-cylinder

Within the framework of a “passive” control, for various gaps, the action of a “short separating element” placed on the median axis of a uniform flow downstream a half-cylinder is studied. In a range of moderate Reynolds numbers (200–5000) it is shown that, for flow rates lower than 300 the separating element set close to the model led to a minimum of the swirling frequency process and that beyond this critical flow Reynolds value, only a broader plate-gap led to a comparable result. The transition between these two “scenarii” is singular. Beyond Re=300 and up to Re=900 the greatest plate-gap tested leads to a minimum of the shedding process with, according to lowest flow rates, no intermediate transition plate-sets. Beyond Re=900 an intermediate position of the separating element between both previous ones ensures a minimum for the shedding process that in flow rate variation phases can facilitate the leading up of an adaptive control. In the range of studied plate-gaps (−2 D to 2 D, with D the cylinder diameter) a formulation is proposed to determine the frequency of the swirling process according to the half-cylinder separating element geometrical configuration reserved. Finally solid links between the topological phenomena noted in transient state during the early flow stages [Exp. Thermal Fluid Sci. 16 (1998) 100] and those raised in this study are displayed.

A low‐dimensional spectral approach for transient axisymmetric free‐surface flow inside thin cavities of arbitrary shape

AbstractA low‐dimensional spectral method is used to solve the transient axisymmetric free surface flow inside thin cavities of arbitrary shape. The flow field is obtained on the basis of the lubrication equations, which are expanded in terms of orthonormal functions over the cavity gap. The formulation accounts for nonlinearities stemming from inertia and front location. The work is of close relevance to the filling stage during die casting, and injection molding, or the flow inside annular (extrusion) dies. Both flows under an imposed flow rate, and an imposed pressure at the cavity entrance are examined. The influence of inertia, aspect ratio, gravity, and wall geometry on the evolution of the front, flow rate, and pressure is assessed particularly in the early stage of flow, when a temporal behavior of the ‘boundary‐layer’ type develops. The multiple‐scale method is applied to obtain an approximate solution at small Reynolds number, Re. Comparison with the exact (numerical) solution indicates a wide range of validity for the multiple‐scale approach, including the moderately small Re range. Copyright © 2002 John Wiley & Sons, Ltd.

Influence of inertia on the transient axisymmetric free-surface flow inside thin cavities of arbitrary shape

The influence of inertia is examined for transient axisymmetric free surface flow inside a thin cavity of arbitrary shape. The flow field is obtained by solving the lubrication equations, which are averaged over the cavity gap by expanding the velocity in terms of Chandrasekhar functions and using the Galerkin projection method. The formulation accounts for the transverse flow, as well as nonlinearities stemming from inertia and front location. Both flows under an imposed flow rate, and an imposed pressure at the cavity entrance are examined. The influence of inertia, aspect ratio, gravity, and cavity geometry on the evolution of the front, flow rate, and pressure is assessed particularly in the early stage of flow. Comparison with existing results shows full qualitative agreement for cavities of various geometries and flow conditions. Inertia is found to have a significant influence on early transient behavior, leading to the development of a flow of the “boundary-layer” type upon inception. The effect of inertia is further explored by developing a multiple-scale analysis to obtain an approximate solution at small Reynolds number, Re. Comparison with the exact (numerical) solution indicates a wide range of validity for the multiple-scale approach, even in the moderately small Re range.

A mechanical model for Merapi-type pyroclastic flow

A numerical simulation model of Merapi-type pyroclastic flow for predicting a potential hazardous area is given, and its applicability is examined by numerically reproducing actual phenomena that occurred in 1991 at Unzen Volcano, Kyushu Japan. Merapi-type pyroclastic flow arises from collapse of the lava dome whereby large lava blocks are crushed into smaller particles during movement down the steep slope. The early stage of flow (it may be called the debris avalanche stage), in which the dominant particles are coarser than about 1mm in diameter, is considered as a grain (granular) flow. In an inertial grain flow particle collision stress plays an important role in the mechanism of flow, and the effect of gas emitted from the lava blocks is minimal. Most of the particles composing the inertial grain flow deposit over a comparatively short range on steep slope due to marked resistance within the flow. The remainder which is composed of mainly fine particles smaller than 1mm continues to run down by a support of the upward flow of gas ejected from the material itself, thereby the resistance to flow becomes small. Thus, the pyroclastic flow stage in a narrow sense appears. The main body of the pyroclastic flow is composed of lower insufficiently fluidized layer (bottom layer) and upper fluidized layer in which the entire weight of the particles is supported by the upward gas flow. Sometimes, the fluidized layer cannot exist if gas emission is insufficient. As the slope down which the pyroclastic flow moves becomes milder downstream, the bottom layer deposits some solids because the driving force due to gravity within this layer becomes smaller than the resistance due to inter-particle contact. Then, a part of the fluidized layer, if exists, changes to a part of the bottom layer because of the shortage of the upward gas flow that is caused by deposition of the gas-emitting particles upstream. Thus, the entire main body stops when it arrives at a gently sloping area. Smaller particles and gas escape from the main body, generating a hot ash cloud layer above the main body. The hot ash cloud layer can travel independent of the main body, but its development or attenuation depend on the conditions of the supply of particles and gas from the main body. When the hot ash cloud lacks the supply of particles and gas due to the stopping of the main body upstream, or by its swerving from the course of the main body, it becomes soon weakened and stops. The entrainment of ambient air, the escape of air and ash from the upper boundary as a buoyant plume, and the particle settling also affect the behaviors of the hot ash cloud. Fundamental mechanics of the grain (granular) flow stage, the pyroclastic flow stage and the transition from the former to the latter stages are discussed theoretically and experimentally, and mathematical formulae describing the phenomena are obtained. These one-dimensional equations are extended to fit the planar two-dimensional system. Behaviors of the main body as well as the hot ash cloud are simulated using the obtained system of equations. The results of simulation are very satisfactory in comparison to the actual phenomena.

Cooling and crystallization of lava in open channels, and the transition of Pāhoehoe Lava to 'A'ā

Samples collected from a lava channel active at Kilauea Volcano during May 1997 are used to con- strain rates of lava cooling and crystallization during early stages of flow. Lava erupted at near-liquidus tem- peratures (F1150 7C) cooled and crystallized rapidly in upper parts of the channel. Glass geothermometry indi- cates cooling by 12-14 7C over the first 2 km of trans- port. At flow velocities of 1-2 m/s, this translates to cooling rates of 22-50 7C/h. Cooling rates this high can be explained by radiative cooling of a well-stirred flow, consistent with observations of non-steady flow in proximal regions of the channel. Crystallization of plag- ioclase and pyroxene microlites occurred in response to cooling, with crystallization rates of 20-50% per hour. Crystallization proceeded primarily by nucleation of new crystals, and nucleation rates of F10 4 /cm 3 s are similar to those measured in the 1984 open channel flow from Mauna Loa Volcano. There is no evidence for the large nucleation delays commonly assumed for plagioclase crystallization in basaltic melts, possibly a reflection of enhanced nucleation due to stirring of the flow. The transition of the flow surface morphology from pahoehoe to 'a'aoccurred at a distance of 1.9 km from the vent. At this point, the flow was thermally stratified, with an interior temperature of F1137 7C and crystallinity of F15%, and a flow surface tempera- ture of F1100 7C and crystallinity of F45%. 'A'afor- mation initiated along channel margins, where crust was continuously disrupted, and involved tearing and clotting of the flow surface. Both observations suggest that the transition involved crossing of a rheological threshold. We suggest this threshold to be the develop- ment of a lava yield strength sufficient to prevent vis- cous flow of lava at the channel margin. We use this concept to propose that 'a'aformation in open chan- nels requires both sufficiently high strain rates for con- tinued disruption of surface crusts and sufficient groundmass crystallinity to generate a yield strength equivalent to the imposed stress. In Hawai'i, where lava is typically microlite poor on eruption, these combined requirements help to explain two common observations on 'a'aformation: (a) 'a'aflow fields are generated when effusion rates are high (thus promoting crustal disruption); and (b) under most eruption conditions, lava issues from the vent as pahoehoe and changes to 'a'aonly after flowing some distance, thus permitting sufficient crystallization.

Thermal and thermomechanical effects on defect evolution in an Al–Li superplastic alloy

A commercial Al–Li alloy, in which the superplastic microstructure is developed by “strain-assisted continuous recrystallization” in early stages of flow, was studied using positron annihilation lifetime spectroscopy. Results revealed that exposing the material to a temperature of 525 °C (optimal temperature of superplastic deformation for this alloy) led to agglomeration of single vacancies into vacancy clusters of size of approximately four vacancies. Evidence for superplastic strain-induced cavitation was not found at 450 °C up to an elongation of 432% and at 525 °C up to 341%, the initial strain rate of deformation in both cases being 1.0 ×10−3 s−1. These results have practical significance.

Weakly Nonlinear Investigation of the Saffman–Taylor Problem in a Rectangular Hele–Shaw Cell

We analyze the Saffman–Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and viscosity contrast. Symmetry breaking occurs through enhanced growth of sub-harmonic perturbations. Our results explain the absence of finger tip-splitting in the early flow stages, and saturation of growth rates compared with the predictions of linear stability.

A laboratory study of stratified accelerating shear flow over a rough boundary

Experiments are made in which a stratified shear flow, accelerating from rest and containing a level where the direction of flow reverses, is generated over a rough floor. The roughness elements consist of parallel square bars set at regular intervals normal to the direction of flow. Radiating internal gravity waves are generated in the early stages of flow, whilst flow separation behind the bars produces turbulent mixing regions which eventually amalgamate and entirely cover the floor. This turbulent layer spreads vertically less rapidly than the internal waves. Observed features of the waves are compared with those predicted by a model in which the floor is assumed to be sinusoidal, and fair agreement is found for the amplitude, phase and vertical wavenumber of the waves, even when the latter becomes large.The rate of spread of the turbulent layer depends on the separation of the bars. Some interaction between the turbulence and the internal waves occurs near the edge of the turbulent layer. Wave-breaking is prevalent and the vertical scale of the waves is affected by turbulent eddies. The radiating internal waves are suppressed by replacing the bars by an array of square cubes, but there is continued evidence of features resembling internal waves near the boundary of the turbulent region. Structures are observed which bear some similarities to those found at the foot of the near-surface mixing layer in a lake.

The early stages of flow in molybdenum single crystals

The early stages of flow of high purity molybdenum single crystals with central axial orientations have been studied by thermal activation strain rate analysis over the temperature range 80 K to 398 K. The results clearly demonstrate that it is necessary to independently measure the true plastic strain rate when analyzing deformation behavior in the early stages of flow. This is because a significant amount of plastic strain is required before the plastic and total strain rates approach the value dictated by the cross-head speed. Thermal activation analysis indicates that more than one dislocation mechanism operates at strains less than about 3 pct.

The Chaoborus (Diptera: Chaoboridae) component of the invertebrate drift of the Mwenda river, Lake Kariba, Central Africa

Chaoborus larvae were collected from the riverine drift of the Mwenda River during the 1972/3 rainy season. Large numbers of larvae were found in the early stages of flow following the 1972 dry season, fewer were found ten days later.

Stress-Strain Characteristics and Slip-Band Formation In Metal Crystals: Effect of Crystal Orientation

The plastic properties of extended silver and copper crystals of varying purity were studied as a function of crystal orientation in the early stages of flow. Variations in the gross shape of the shear stress-shear diagram and in the properties of critical shear stress and shear-hardening coefficient were correlated with changes in slip-band developments. The phenomenon of work hardening is discussed in terms of the existing dislocation theory.

Studies of Plastic Flow of Steel, Especially in Two-Dimensional Compression

The experimental methods are described by which rectangular blocks are subjected to two-dimensional compressional stresses and at the same time flow is maintained two-dimensional with deviations of less than one percent. Within this range of flow a rather wide range of stress conditions is possible, so that the equations of plastic flow can be examined over a correspondingly wide range of conditions. It is found that two-dimensional flow is much more sensitive than three-dimensional flow to shearing instabilities initiated at the edges where there are singularities in the mathematical solution. By proper lubrication it is, however, possible to produce approximately homogeneous deformations in two-dimensional compression at least up to shortenings to two-thirds the initial length. It is found that the transverse stress Xx required to maintain two-dimensional flow is consistently higher than the theoretical value ½Zz; for some materials the excess above the theoretical value may rise to as much as 20 percent. This excess tends to be less in the early stages of flow, and does not tend to increase beyond strains of 10 percent. The failure of Xx to be equal to ½Zz indicates a failure of the fundamental condition of isotropy of flow; this failure may be demonstrated in other ways. The time rate of primary flow is studied at various points on the strain-hardening curve. The rate of flow rises rapidly as the stress increases above the limiting strain-hardening curve. The rate of increase of the rate of flow for a given displacement from the limiting curve is much greater in the early stages of flow. It is this which makes possible the calculation of the rate of propagation of a plastic disturbance from the parameters of the static strain-hardening curve. Beyond the early stages of flow new time effects begin to appear. The flow loses its smoothness and becomes more and more inclined to be jerky. At high strains, flow may not start at once when the load is increased, but there may be an initiation period during which flow is built up. The application of the results to the generalized strain-hardening curve is discussed. In view of the failure of isotropy, strictly speaking, a generalized strain-hardening curve does not exist. Within the strain limits of this paper it is found that both the maximum shearing stress criterion and the ``significant'' stress-strain criterion apply with errors of the order of 10 percent, the maximum shearing stress criterion being on the whole perhaps somewhat better.