Steady Upward Flow Research Articles

Lattice Boltzmann Method Simulation of Natural Convection Heat Transfer in Horizontal Annulus

The lattice Boltzmann method is employed to simulate the stability and transitions of natural convection in a horizontal annulus with the Prandtl number varying from 0.1 to 0.7 and the Rayleigh number ranging from to . Different flow patterns including steady upward flow, oscillatory upward flow, steady downward flow, and oscillatory downward flow are found for different values of the parameters. The flow pattern is very complex when the Rayleigh number is large. The critical Rayleigh number increases with the increase of the Prandtl number and with the decrease of the aspect ratio.

Advection and buoyancy-induced turbulent mixing in a narrow vertical tank

AbstractWe describe new experiments to examine the buoyancy-induced turbulent mixing which results from the injection of a small constant volume flux of dense fluid at the top of a long narrow vertical tank with square cross-section, in which a steady laminar upward flow of less dense fluid is present. To conserve volume of fluid in the tank, fluid leaves the tank through two small openings near the top of the tank. Dense source fluid vigorously mixes with the less dense fluid of the upward flow, such that a dense mixing region of turbulent fluid propagates downwards during the transient mixing phase of the experiment. Eventually, the transport of dense fluid associated with the buoyancy-induced turbulent flow is balanced by the transport of less-dense fluid associated with the steady upward flow, such that the mixing region evolves into a layer of finite extent which stays approximately constant in height during a statistically steady mixing phase of the experiment. With an ideal source of downward constant buoyancy flux ${B}_{s} $ at the top of the tank, tank width $d$, and speed of the upward flow ${u}_{u} $, we perform experiments with Froude numbers $\mathit{Fr}= {u}_{u} {d}^{1/ 3} / { B}_{s}^{1/ 3} $ ranging between $O(0. 01)$ and $O(1)$. The steady-state height of the mixing region and the maximum reduced gravity as found near the source of buoyancy flux at the top of the tank increase with decreasing Froude number. For the experiments with intermediate values of the Froude number, we find that the steady-state mixing region is small enough to be contained in the experimental tank, but large enough not to be dominated by developing turbulence near the source of buoyancy flux. For these experiments, we show that the key buoyancy-induced turbulent mixing properties are not significantly affected by the upward flow. We use a dye-attenuation technique to obtain vertical profiles of the time- and horizontally averaged reduced gravity to show a good agreement between the experimental profiles and the solution of a nonlinear turbulent advection–diffusion equation during the steady mixing phase. Furthermore, we discuss the characteristic time scale of the transient mixing phase. We compare our experimental results with the numerical solution of a time-dependent nonlinear turbulent advection–diffusion equation during the transient mixing phase. We also describe three reduced models for the evolution of the reduced gravity distribution in the mixing region, and we demonstrate these models’ usefulness by comparison with our experimental results and the numerical solution of the time-dependent nonlinear turbulent advection–diffusion equation.

On steady linear diffusion-driven flow

Wunsch (1970) and Phillips (1970) (Deep-Sea Res. vol. 17, pp. 293, 435) showed that a temperature flux condition on a sloping non-slip surface in a stratified fluid can generate a slow steady upward flow along a thin ‘buoyancy layer’. Their analysis is extended here to the more-general case of steady flow in a contained fluid where buoyancy layers may expel or entrain fluid from their outer edge. A compatibility condition that relates the mass flux and temperature gradient along that edge is derived, and this allows the fluid recirculation and temperature perturbation to be determined in the broader-scale ‘outer flow’ region. The analysis applies when the Wunsch–Phillips parameterRis small, in the linear case for which the density variations are dominated by a constant vertical gradient.

Entropy generation minimization in turbulent mixed convection flows

This paper reports the results of a numerical investigation of turbulent mixed convection from a symmetrically heated vertical channel, bathed by a steady upward flow of cold air. The computations have been performed using FLUENT 6.2 by employing the k– ε model for turbulence with enhanced wall treatment. The entropy generation rates due to (i) heat transfer across a finite temperature difference and (ii) irreversibility due to fluid friction have been calculated as post-processed quantities with the computed velocity and temperature profiles. Optimal inlet velocities at which the total entropy generation rate reaches a minimum value are found to exist, for every set of heat flux and aspect ratio. Further, this optimum velocity turns out to be independent of the aspect ratio and increases linearly with the heat flux. Simple and easy to use correlations for the optimum Reynolds number and the dimensionless average wall temperatures corresponding to the optima are developed. Plots of total entropy generation rate against the velocity clearly demonstrate that near the optimum conditions, buoyancy does not have a significant role to play in deciding the optimum. For the range of parameters considered in this study, it is seen that for optimum conditions, the ratio of the entropy generation due to fluid friction to total entropy generation rate, known in literature as the Bejan number, varies within a narrow band (0.14–0.22).

Multi-day radon signals with a radioactive decay limb—Occurrence and geophysical significance

Multi-day signals, generally with duration of 2–10 days, are a prominent temporal variation type of radon (Rn) in geogas in the unsaturated zone. Rare multi-day Rn signals have been found which are characterized by: (a) a declining limb lasting up to 10 days which conforms to the radioactive decay of Rn, (b) recurs at the same location and (c) is recorded in diverse situations—volcanic and seismogenic. It suggested that a Rn blob is injected at a lower level on a steady upward flow of geogas whereby the rise and final fall of the signal are attributed to the edges of the blob while the central Rn-decay segment records the passing of the decaying blob itself. Rn-decay signals are a small subset of multi-day Rn signals which are considered as highly irregular and unusable for the understanding of geophysical processes. In difference, it is concluded that multi-day Rn signals are probably proxies of subtle geodynamic processes at upper crustal levels and are therefore significant for studying such processes.

Effect of Freeze–thaw Cycle on the Parameters of the Green and Ampt Infiltration Equation

In humid and temperate regions, application of hydrologic models based on the Green and Ampt infiltration equation, during the spring season, often creates problem due to freezing and thawing of soils. These climatic conditions result in significant changes in hydrological and hydraulic properties of the soil. Three soil properties which are used to estimate parameters of the Green and Ampt infiltration equation were measured on repacked soil cores after subjecting them to a number of freeze–thaw cycles. The saturated hydraulic conductivity, air entry potential and total porosity tests were conducted to determine the influence of repeated freeze–thaw cycles on these properties and to incorporate the interactive effect of soil type, bulk density and saturation on these variables. The three soil types chosen for the experiment were silt loam, clay loam and loamy sand. Saturated hydraulic conductivity was measured using a steady upward flow constant head permeameter. The air-entry potential was estimated from the relationship between soil matric head and volumetric water content. Volumetric water content at saturation was used to approximate total porosity. Results from factorial analysis of variance indicate that the means of saturated hydraulic conductivity, total porosity and air-entry potential proved to be significantly different among soil types and bulk density. Changes in saturated hydraulic conductivity values for the three different soil types by the impact of continuous freeze–thaw cycles is most severe at lower degree of saturation and reduces in severity as the degree of saturation increases.

Tortuosity, Mean Residence Time, and Deformation of Tritium Breakthroughs from Soil Columns

AbstractTritium breakthrough curves (BTCs) are widely used to estimate the hydrodynamic dispersion coefficient (D) of the convection‐dispersion equation (CDE). However, D alone often provides inadequate fit. Therefore, a second parameter is commonly added to describe tritium BTCs. We tested the validity of describing tritium transport using an effective path length (Le) or a tortuosity factor (τ) in the CDE. We obtained the dimensionless parameter τ from fitted Le and column length L such that τ = L/Le. Miscible displacement experiments were used to obtain tritium BTCs for several soils and materials in uniformly packed columns under water‐saturated and steady upward flow. Two types of tritium pulses were applied: the first was a small pulse (≈ 0.03 pore volume) and used to determine mean residence time (tm) in soil columns. The tm values were obtained from the first time moment of BTCs and were subsequently used to estimate Le and τ. The second type of input pulse was about one pore volume and used to obtain the parameters D and Le using the CDE. Tritium results exhibited double peaks and extensive deformations of BTCs for several soils; these were more distinct with increasing pore water velocity. Using the principle of superposition, bimodal peaks from large pulse inputs were successfully described based on small‐pulse BTCs. In addition, agreements between estimated τ using small pulses and fitted τ from large pulses support the use of the fitting parameters D and Le in the CDE as an alternative method for describing tracer BTCs in soils.

The feasibility of in situ treatment of soil to promote desorption of hazardous wastes, thus permitting capture and treatment

In humid and temperate regions, application of hydrologic models based on the Green and Ampt infiltration equation, during the spring season, often creates problem due to freezing and thawing of soils. These climatic conditions result in significant changes in hydrological and hydraulic properties of the soil. Three soil properties which are used to estimate parameters of the Green and Ampt infiltration equation were measured on repacked soil cores after subjecting them to a number of freeze–thaw cycles. The saturated hydraulic conductivity, air entry potential and total porosity tests were conducted to determine the influence of repeated freeze–thaw cycles on these properties and to incorporate the interactive effect of soil type, bulk density and saturation on these variables. The three soil types chosen for the experiment were silt loam, clay loam and loamy sand. Saturated hydraulic conductivity was measured using a steady upward flow constant head permeameter. The air-entry potential was estimated from the relationship between soil matric head and volumetric water content. Volumetric water content at saturation was used to approximate total porosity. Results from factorial analysis of variance indicate that the means of saturated hydraulic conductivity, total porosity and air-entry potential proved to be significantly different among soil types and bulk density. Changes in saturated hydraulic conductivity values for the three different soil types by the impact of continuous freeze–thaw cycles is most severe at lower degree of saturation and reduces in severity as the degree of saturation increases.

Effect of soil loosening on the hydraulic properties of a duplex soil

In a duplex, transitional red-brown earth, the relationships between hydraulic conductivity K, diffusivity D, soil water potential (�) and volumetric water content (�) in different soil layers were evaluated. Changes in these relationships and in the derived parameters; macroscopic capillary length and characteristic microscopic pore radius due to soil loosening were examined. Replicated large undisturbed and repacked cores of 0.75 m diameter and 1.35 m deep, located in a lysimeter, were used in this study. The K- � relationships were measured during steady upward flow from a watertable at different depths. The � � relationships were measured during a soil drying cycle. The undisturbed soil showed similar soil water characteristics (�-� curves) in all soil layers, at depths greater than 0.25 m. In contrast, K at high � was significantly lower in the upper subsoil, 'throttle' layer with high clay content, compared with the deeper soil layers. However, previous studies on a similar soil have also shown that factors other than pore size distribution, such as tortuosity and pore connectivity, markedly influence the hydraulic conductivity properties of clay soils. Coefficients in the log � on log� and in the log K(�) on log � relationships for all soil layers combined differed markedly from the coefficients for individual layers, indicating the need to measure these properties separately for different subsoil clay layers of this duplex soil. The repacking of the soil to a lower bulk density caused an increase in K at high � values. This was accompanied by a significant decrease in slope of the log � -log � relationship, from 17-21 to around 7, in the subsoil layers. The slope of the regression of log � - K(�) on log� changed from 24 in undisturbed soil to 9 in the repacked soil. This was mainly due to large changes in the � -�relationship, in combination with smaller changes in the K- � relationship. The decrease in diffusivity D with reduction in 0 was less marked in the repacked soil compared with the undisturbed soil. Thus, soil repacking shifted D(�) towards a constant value, for the range of � measured. This was mainly due to a slower rate of change in K with decrease in � on the repacked soil, combined with a compensating increase in d � /d� values. The calculated values of macroscopic capillary length decreased and characteristic pore radius increased, reflecting the changes in pore sizes and hydraulic conductivities due to soil loosening. However, at any given supply and antecedent �, the sorptivity was greater in the loosened soil due to larger changes in water content and hydraulic conductivities. The potential application of these soil properties in evaluating water flow in undisturbed or loosened soils is briefly discussed.

Melting of a Vertical Ice Wall by Free Convection into Fresh Water

A steady-state two-dimensional finite difference analysis is presented for the heat and momentum transfer resulting when the leading portion of a semi-infinite vertical ice sheet at 0°C melts into fresh water by natural convection. Fluid properties are assumed to be constant and are evaluated beyond the edges of the boundary layers with the exception of fluid density which varies with the local temperature. Results of the analysis are presented for free stream temperatures from 0 to 24.0°C. They include streamlines, velocity profiles, melt velocities, and average Nusselt numbers for the leading 0.7632 m portion of a semi-infinite ice sheet. Overall, the results show three distinct flow regimes: steady upward flow for T∞ ≤ 4.50°C, steady downward flow for T∞ ≥ 6.0°C and steady dual or bi-directional flow for 5.70 ≤ T∞ ≤ 6.0°C. In the range 4.50°C < T∞ < 5.70°C the solution failed to converge and since the method is capable of accounting for local recirculations, it is suggested that this flow regime may be transitory in nature.

Moisture profiles in swelling soils

In situ moisture profiles are examined, in two soils of clay texture and in a loam, for the condition of equilibrium about a water table. In addition, moisture profiles during periods of approximately steady upward flow are examined in one of the soils of clay texture. Equilibrium moisture profiles in the clay soils are typical of the 'hydric' profiles which have been predicted for swelling materials. Upward water movement occurs against the moisture gradient. The equilibrium profile in the loam is typical of those observed for non-swelling materials.