Heat dispersion in stationary mixed convection flow about horizontal surfaces in porous media

An analysis has been performed to study the influence of velocity dependent dispersion on transverse heat transfer in mixed convection flow above a horizontal wall of prescribed temperature in a saturated porous medium. The Boussinesq approximation and boundary layer analysis were used to numerically obtain gravity affected temperature and velocity distributions within the frames of Darcy's law and a total thermal diffusivity tensor comprising both of constant coefficient heat conduction and velocity proportional mechanical heat dispersion. Dependending on Pe_∞, the molecular Peclét number basing on the effective thermal diffusivity and the velocity of the oncoming flow, density coupling has distinct influences on heat transfer rates between the wall surface and the porous medium flow region. For small Peclét numbers, when heat conduction is the prevailing mechanism, wall heat fluxes are the higher the larger the density difference between the oncoming and the near wall fluid is. The opposite is true for larger Peclét numbers, when mechanical heat dispersion is the main cause of heat spreading. For Pe_∞ tending to infinity these wall heat fluxes approach finite maximum values in the total heat diffusivity model, they grow beyond any limit if only constant coefficient heat conduction is considered. Thus, the inclusion of mechanical heat dispersion effects yields physically more realistic predictions. Received on 18 September 1996     

Gas absorption in a thin liquid film flow on a horizontal rotating disk

An analytical model for the rate of gas absorption into laminar non-wavy film flow on a horizontal rotating disk is obtained assuming short contact times. Literature data for the oxygen mass transfer coefficient in a wavy film is correlated by means of the dimensionless numbers deriving from the model. The rate enhancement due to waves is found to vary from 6 to 13 times. It is established that the absorption process in the film on the disk as compared to that in a gravitational wavy film flow can be intensified up to 14 times by means of a moderate rotation speed.     

The presence of slug flow in horizontal two-phase flow

One of the flow regimes occurring in horizontal two-phase flows is characterized by periodic large waves “surging” along the tube. This flow, called “slug” flow, has been frequently observed in low and high pressure gas liquid systems, but it has been noticed that slugging is absent in certain liquid-liquid two-phase systems. A method is developed giving the necessary conditions for the presence of slug flow. This method quantitatively explains the observed absence of slugging in certain liquid-liquid flows.     

Velocity distribution in horizontal slug flow

An experimental device for measurement of the velocity distribution in a two-phase slug is developed. Velocity profiles both in the film and the liquid slug besides velocity variation along the pipe bottom (at a distance of 1 mm) through the slug front are presented.     

Solute dispersion in a pulsating flow

The one-dimensional model proposed by Taylor [1] of the dispersion of soluble matter describes approximately the distribution of the solute concentration averaged over the tube section in Poiseuille flow. Aris [2] obtained more accurately the effective diffusion coefficient in Taylor's model and solved the problem for the general case of steady flow in a channel of arbitrary section. Many papers have been published in the meanwhile devoted to particular applications of this theory (for example, [3–5]). Various dispersion models have been constructed [6–8] that make the Taylor—Aris model more accurate at small times and agree with it at large times. The acceleration of the mixing of the solute considered in these models in the presence of the simultaneous influence of molecular diffusion and convective transport also operates in unsteady flows. In particular, the presence of velocity pulsations influences the growth of the dispersion even if the mean flow velocity is equal to zero at every point of the flow. In the present paper, the Taylor—Aris theory is extended to the case of laminar flows with periodically varying flow velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 24–30, September–October, 1982.     

Variable porosity and thermal dispersion effects on vortex instability of a horizontal natural convection flow in a saturated porous medium

A numerical analysis is made to analyze the variable porosity and thermal dispersion effects on the vortex mode of instability of a horizontal natural convection boundary layer flow in a saturated porous medium. The porosity of the medium is assumed to vary exponentially with distance from the wall. In the base flow, the governing equations are solved by using a suitable variable transformation and employing an implicit finite difference Keller Box method. The stability analysis is based on the linear stability theory and the resulting eigenvalue problem is solved by the local similarity approximations. The results indicate that both effects increase the heat transfer rate. In addition, the thermal dispersion effect stabilizes the flow to the vortex mode of disturbance, while the variable porosity effect destabilizes it.

     

Dividing annular flow in a horizontal tee

The prediction of mixture composition in a branch from a manifold in which two-phase mixtures flow has been examined. A linear relationship is found to exist between the branch mass flowrates of the individual phases over a range of flow conditions. This observation is used as the basis of a correlation which contains coefficients that are functions of the manifold flow condition. 90 per cent of the data are correlated to within ±20 per cent.     

Entrainment for horizontal annular gas-liquid flow

Measurements of entrainment are presented for air and water flowing in horizontal 2.54 and 5.08 cm pipelines. After the initiation of atomization, entrainment increases with the third power of the gas velocity. At very high gas velocities a fully entrained oendition in reached for which further increases in the gas velocity do not cause a decrease in the flow rate of the wall film. Gas density bas a small effect provided comparisons are made at the same gas velocity rather than at the same mass flowrate. The results are interpreted by asauming that the rate of deposition of droplets on the wall film varies linearly with the concentration of droplets and that the rate of atomization of the wall film varies linearly with its flow rate.     

Unsteady saturated-unsaturated flow to horizontal drains

On irrigated ground with poor natural drainage, artificial drainage is used to prevent secondary salinization and swamping. The calculation of the drainage parameters requires the solution of problems of saturated-unsatated flow in the region between the drains [1–6]. The influence of the motion in the unsaturated region on the total flow of ground water is most important when the water-saturated region is thin and especially in the case of finely grained soil. If the capillary border intersects the surface of the ground and there is an alternation of the processes of infiltration, redistribution, and evaporation of moisture, rapid oscillations in the ground water level are possible. Under these conditions, calculation of the drainage parameters using hydraulic models [7], which do not take into account motion in the region of incomplete saturation, is made difficult by the need to specify the coefficient which measures the incompleteness of saturation, and also the rates of flow between the aeration region and the ground water. The present paper gives the mathematical formulation, an algorithm for numerical solution, and examples of calculations for a two-dimensional problem of unsteady joint flow of ground water and soil moisture.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–87, September–October, 1981.     

Slug initiation and evolution in two-phase horizontal flow

A series of two-phase air–water experiments was carried out in order to study the initiation and the subsequent evolution of hydrodynamic slugs in a horizontal pipeline. Experiments were carried out at atmospheric pressure, 4.0 bar(a) and 9.0 bar(a), and the effects of superficial liquid and gas velocities were investigated. The test section used for these experiments is 37 m in length, with an internal diameter of 0.078 m. To study the interfacial development, measurements of interfacial structures were made at 14 axial locations along the test section, with data acquired at a sampling frequency of 500 Hz. A large number of slugs were initiated within the first 3 m of the test section, with the frequency subsequently reducing towards the fully developed value before the end of the pipe. This reduction in frequency was strongly influenced by the magnitude of the gas and liquid velocities. The frequency of slugging was not strongly affected when the system pressure was changed from 1 atmosphere, to 4.0 and 9.0 bar(a), closely similar values being obtained at the 10 downstream locations. However, higher pressure delayed the onset of slug initiation, with “slug precursors” being formed further downstream as the pressure was increased. The statistical distributions of slug lengths and of the time intervals between slug arrivals were examined in detail and compared to several standard distributions. This showed that slug initiation may be reasonably approximated as an uncorrelated Poisson process with an exponential distribution of arrival times. However, once slugs have developed, there is strong correlation and the arrival time intervals, as well as the lengths, are best represented by the log-normal distribution.     

Secondary flow in horizontal channels heated from below

Experiments have been performed to investigate onset and development of the buoyancy driven secondary flow in a horizontal parallel plate channel with uniform bottom heating. Flow visualization in water (Pr ≈ 7) was performed by injecting a continuous sheet of dye into the bottom boundary layer just up-stream of the heated surface, and operating conditions in the ranges 125 < Re < 1,000 and4.7 x 10⁴ < Gr ^* < 8.0 x 10⁶ were considered. Top, side, and end views revealed onset of the secondary flow as thermal plumes, which rise from the heated surface and form pairs of counter-rotating vortices. Subsequent development of the flow is characterized by a breakdown in the regular plume structure and transition to buoyancy driven turbulence. Onset of the secondary flow is advanced by increasing the heat flux and/or decreasing the flow rate, and results may be correlated in terms of a critical Grashof number and a dimensionless longitudinal distance. Liquid crystal sheets applied to the heated surface reveal significant spanwise temperature variations due to the secondary flow. The unsteadiness of the flow is discussed and comparisons are made to previous experimental and numerical work.     

Liquid-phase axial mixing in two-phase horizontal pipe flow

The liquid-phase axial dispersion coefficient and volume-averaged fractional phase hold-ups have been measured in two-phase horizontal pipe flow. Radioactive ^99mTc—technetium-99 metastable—(as an aqueous solution of sodium pertechnate) was used as a tracer. The pulse technique with two-point measurement was employed. Superficial gas (air) and liquid (water) velocities were varied in the range 20–2300 and 30–800mm/s, respectively. The flow regimes covered were bubbly, elongated bubbly, stratified, wavy and slug. Experiments were also performed using single-phase pipe flow. The liquid-phase dispersion coefficient has been shown to depend upon the flow regime and the superficial gas and liquid velocities.     

Two-phase flow patterns in short horizontal rectangular microchannels

The two-phase flow in a short horizontal channel of a rectangular cross-section with the height of 100–500 µm and width of 9–40 mm was studied experimentally. The use of the Schliren and fluorescent methods made it possible to reveal the flow of liquid in the channel and to determine its characteristics quantitatively. The features of the churn, jet and drop flow patterns were studied in details. Two particular regimes that can be distinguished represent formation of immobile drops on the channel walls because of the liquid film or liquid bridges breakage and appearance of mobile drops due to the two-phase flow instabilities. It is found out that formation of various two-phase flow patterns and transitions between them are determined by instabilities of the liquid–gas flow in the side parts of a channel. Frontal instability has been observed during the liquid–gas interaction in the region of liquid output from the nozzle. It is shown that a change in the height and width of the horizontal channels has a substantial effect on the boundaries between the flow regimes. One of the results is that the region of the churn regime increases significantly with decreasing thickness of the channel.     

Exact analysis of laminar dispersion in non-Newtonian flow

An exact analysis is presented for dispersion of a solute in an Eyring model fluid flowing between two parallel plates under uniform pressure gradient. Using a generalised dispersion model, which is valid for all time after injection of the solute, expressions have been developed for the time-dependent longitudinal dispersion coefficient as well as of the area-mean concentration. It is observed that the dispersion coefficient markedly decreases as the fluid parameterG increases, which is attributable to the gradual flattening of the velocity profile. Consequently the concentration distribution becomes steeper at largerG. It is also established that forG<1, the extent of dispersion is practically same as in the case of Newtonian flow.

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Exakte Analyse einer laminaren Dispersion in einer Nicht-Newtonschen Strömung

Zusammenfassung Es wird eine exakte Analyse für eine Dispersion in einer Eyring-Modellflüssigkeit vorgestellt, die zwischen zwei parallelen Platten unter gleichmäßigem Druckgefälle fließt. Es wurden sowohl Formeln für den zeitabhängigen Longitudinaldispersionskoeffizienten, als auch für die mittlere Umgebungskonzentration entwickelt, wobei ein allgemeines Dispersionsmodell benutzt wurde, welches für den ganzen Zeitraum nach dem Einleiten der Lösung gültig ist. Es wird beobachtet, daß der Dispersionskoeffizient deutlich abnimmt, wenn der FlüssigkeitsparameterG sich erhöht, was bezeichnend für die allmähliche Abflachung des Geschwindigkeitsprofils ist. Folglich wird die Konzentrationsverteilung mit steigendemG steiler. Es wurde bewiesen, daß für G 1 die Ausdehnung der Dispersion praktisch mit der Newtonschen Strömung identisch ist.

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Nomenclature a half of channel width - A, B Eyring model parameters - C local concentration of the solute - C ₀ concentration of uniform slug - ¯ C dimensionless local concentration - ¯ C _m area-average concentration defined by (8) - D molecular diffusivity - G dimensionless Eyring model parameter - K ₁() time-dependent dispersion coefficient - Pe Peclet number - t time - u axial velocity - U average axial velocity - x axial coordinate - x _s length of uniform slug - X dimensionless axial coordinate - X _s dimensionless slug length - y transverse coordinate - Y dimensionless transverse coordinate Greek symbols dimensionless Eyring model parameter - coefficient of viscosity - dimensionless time     

Particle dispersion in a single-sided backward-facing step flow

The paper describes the particle dispersion in a single-sided backward-facing step flow. Particles of well-known sizes in the diameter range from 1 to 70 μm were suspended in an air flow and the particle motion over a step was measured by mean of a laser-Doppler anemometer. Thus, the local and integral flow quantities, i.e. the mean and turbulent velocity data could be measured precisely. In the experiments, monodispersed particle size distributions were used to exclude particle size related information ambiguity, known as triggering effects or size bias. The results of this study show qualitatively and quantitatively the difference in time-averaged particle dynamics for selected particle sizes in a backward-facing step flow. The experiments show, for different sizes, the changes in the particle velocity field in comparison with the velocity field of the continuous phase deduced from the 1 μm particles, and also imply the strong influences which different particle sizes have on flow data evaluation when size effects are not taken into account with particle-related optical measuring techniques.     

A flow pattern map for gas—liquid flow in horizontal pipes

Various flow pattern maps for two-phase gas—liquid flow in horizontal pipes are tested against the 5935 flow pattern observations presently contained in the UC Multiphase Pipe Flow Data Bank.A new flow regime correlation representing an extension of the work done by Govier and Aziz [3] is presented and is shown to be in better agreement with the data than the other correlations tested. A computer program for this correlation is included.It is also shown that there is no significant improvement obtained by including the effects of the physical properties of the fluids using any of the physical property parameters which have been proposed so far.