Critical Flux Values Research Articles

The Direct Contact Condensation of Steam in a Pool at Low Mass Flux

The direct contact condensation of steam at low mass flux (in the chugging region) and the pressure oscillation induced by steam condensation were investigated and analyzed. During the experiment, the steam was discharged into a square subcooled water pool in the horizontal direction. The main experimental parameters were the steam mass flux in the range of 10–80 kg/m2·s and the subcooled water temperature in the range of 30–80°C. Also, two different nozzles (5/8, 6/8 inch) were used. In the chugging region, the high pressure pulses were generated with relatively low frequency. The frequency was little affected by the subcooled water temperature, but increased with increasing steam mass flux. A critical value of steam mass flux was found where the pressure pulse generation rate increased suddenly. This critical value for the 5/8 inch nozzle was found to be lower than that for the 6/8 inch nozzle. The pressure pulse was observed to be generated on the occurrence of sudden condensation of the steam bubble which was detached from the nozzle exit by the necking phenomenon.

Ice formation process by cooling water–oil emulsion with stirring in a vessel

An emulsion, which was a mixture of silanol-aqueous solution and silicone oil, was investigated as a heat storage material for a dynamic type ice storage system. The emulsion was poured into a vessel, which was immersed into a constant temperature bath at a low temperature, and frozen with stirring. Using stainless steel vessels coated with PFA resin and PTFE vessels with different thickness, the experiments were carried out under various conditions of temperature. Measuring the temperature history in the vessel, overall heat transfer coefficients before the start of freezing and during the ice formation were obtained. The effects of the material of the cooling surface and the thermal resistance of the wall on the ice formation process were clarified. If the heat flux of the wall was less than a critical value, slurry ice was formed without adhesion to the cooling surface. The results obtained under the same condition of the thermal resistance proved that it was effective against ice adhesion to coat PFA resin inside the vessel. It was found by the experiments in which the PTFE vessels were used that the critical value of the heat flux was nearly constant regardless of the thermal resistance.

Experimental study on the enhancement of yeast microfiltration with gas sparging

AbstractGas‐sparged microfiltration experiments with baker's yeast suspensions were performed using a 0.15 µm PCI multi‐tubular membrane module. The permeate flux and the enhancement from gas sparging were measured over the following operational parameter ranges: yeast suspension concentration 0.01–10% (wt), transmembrane pressure 0.5–4.0 bar, liquid crossflow velocity 0.36–1.8 ms−1, gas superficial velocity 0.18–1.02 ms−1. It was demonstrated that injecting air to create a gas–liquid two‐phase crossflow operation can significantly increase the permeate flux. The observed enhancement, resulting from injecting a relatively small amount of gas with a superficial velocity of 0.18 ms−1, ranges from 10% when fouling is insignificant to 135% when fouling tendency is severe. Controlled pulse injection leads to further increase in permeate flux. Examining the dependence of permeate flux on transmembrane pressure, it is clearly demonstrated that the injection of gas will elevate the value of the limiting flux. There is also evidence to show that the value of critical flux is increased when gas injection is applied. Further quantitative analysis will be performed in our future work.© 2001 Society of Chemical Industry

Ignition of char-forming polymers at a critical mass flux

A simple model of ignition is discussed in the context of char-forming polymers. The model in question assumes that ignition occurs at a critical value of volatile mass flux from the degrading material. The char-forming mechanism chosen for the study is the simplest possible formulation preserving finite-rate kinetics—char and volatile products are formed together in a single step. This simple pyrolysis model has the advantage that the ultimate char yield is known a priori, and is in fact a parameter of the model. Results are presented and discussed for a number of cases, depending on char yield and char thermal properties. Complex ignition behaviour is exhibited by the model and practical consequences of the model predictions are discussed.

Microfiltration of activated sludge using submerged membrane with air bubbling (application to wastewater treatment)

A membrane bioreactor is one of the applications of membrane technology to wastewater treatment. In this study we present the results obtained using hollow fiber microfiltration membranes directly immersed in the bioreactor. Two sizes of equipment were used: laboratory scale with a specially designed set of microfiltration hollow fibers (filtration area 0.016 m 2) and pilot scale with a bundle of hollow fibers (filtration area 0.5 m 2). Filtered liquid was pumped at a constant flow rate by suction through the membranes at a fairly low transmembrane pressure (less than 300 kPa). The bubbles produced by aeration of the biomass were essential for cake removal. The study was performed with short-term and long-erm experiments successively. In the short-term experiments, the critical conditions, which were the limit of steady operation, were identified. In our conditions of operation the value of critical flux was about 30 l/h.m. 2. The influence of air flow rate on critical flux was investigated. It was demonstrated that aeration was a significant factor governing the filtration conditions and decreasing fouling resistance. With application of optimal air flow rate, it was possible to perform in quasi-steady conditions with a permeate flow rate which was about 30% of the initial pure water flux. During long-term trials, the influence of the impact of sludge residence time (10, 20 and 30 days) was compared in three bioreactors operated in parallel, considering sludge production, sludge concentration and the fouling potential of the different fractions of activated sludge (solid fraction and liquid fraction). Neglecting the negative effect of the anti-foaming agent, very high efficiency of COD removal could be obtained (up to 90%) at a volumetric load of 3.2kg COD/m 3/d and a sludge residence time of 20 days.

Analytical model of propagating sand ripples

We formulate a simple phenomenological model of aeolian sand ripple migration based upon a balance between grain hopping driven by saltation and grain rolling or avalanching under gravity. We develop a set of model equations governing the evolution of the ripple slope. The model has solutions describing steadily propagating isolated ripples, produced by a horizontal saltation flux, and periodic trains of ripples, which develop when the saltation flux is inclined to the horizontal. In the case of an inclined saltation flux, the ripple wavelength is controlled by the length of the shadow zone, as suggested by R. P. Sharp [J. Geol. 71, 617 (1963)]. Although very simple, our model predicts some of the qualitative features shown by sand ripples in experimental or field studies [R. A. Bagnold, The Physics of Blown Sand and Desert Dunes (Methuen and Co., London, 1941); R. P. Sharp, J. Geol. 71, 617 (1963)]. We find that ripples only develop above a certain threshold value of the saltation flux intensity. Furthermore, at relatively low saltation fluxes, the lee slope of the ripple is a smooth curve, whereas above a critical value of the saltation flux, a slip face develops near the crest. The model predicts a decrease in the speed of propagation as the ripple becomes larger, consistent with observations that smaller ripples are eliminated by ripple merger [R. P. Sharp, J. Geol. 71, 617 (1963)], and also with numerical simulations [R. S. Anderson, Earth-Sci. Rev. 29, 77 (1990); S. B. Forrest and P. K. Haff, Science 255, 1240 (1992); W. Landry and B. T. Werner, Physica D 77, 238 (1994)].

Effect of root temperature on plant response functions for tomato: comparison of static and dynamic salinity stress indices

The agronomic study of plant response to salinity uses root zone salinity as a primary treatment variable. Root zone salinity is a static index in that its value does not depend on any variable factors in the soil-plant-air continuum (SPAC) that simultaneously affect growth. In order to take into account the effect of variable parameters in the SPAC, the concept of a dynamic index was introduced and defined as the salt flux to the shoot relative to growth rate. The objective of this study was to compare the variability of these two indices as measures of salt tolerance in different environments and to ascertain which correlative variable is more directly linked to yield reduction; root zone salinity, a static index, or ion flux to the shoot, a dynamic index. This was accomplished by comparing the root temperature dependence of threshold values for each index respectively. Yield response to salinity was obtained for tomato (Lycopersicon esculentum Mill., cv. Heinz 1350-vf) at two root temperatures, 18 °C and 25 °C, using 14 levels of salinity, 0 to 140 mM Cl, with a 2:1 Na-Ca ratio. Based on parametric analysis, the root zone chloride concentration threshold was increased 92% over the root temperature studied. In contrast, the threshold values of the dynamic indices were not statistically different at the two root temperatures. Plant shoot chloride concentration factor, expressed as the ratio of salt concentration in the shoot to salt concentration in the nutrient solution, decreased exponentially from 8 to 2 with increasing root zone salinity and was independent of temperature. Water use exhibited a strong temperature dependence and showed a sharp decline at root zone salinities corresponding to root zone salinity threshold values. Root/shoot ratio was independent of root zone salinity at least up to 80 mM Cl, and was significantly higher at the lower root temperature. It was concluded that root zone osmotic potential is not the fundamental causative factor determining the onset of yield reduction for the two temperatures studied, and that other elements related to growth and ion transport combine to determine a threshold value. These results indicate that it is a critical value of the salt flux to the shoot in relation to shoot growth rate that determines the onset of yield reduction and therefore is related more to the average salinity in the shoot than the average root zone salinity. This is evidence that specific biochemical mechanisms responsible for yield reduction reside in the shoot.

Persistent current of a Hubbard ring threaded with a magnetic flux.

The persistent current in microscopic and mesoscopic Hubbard rings threaded with magnetic flux is studied as a function of the flux and the Coulomb repulsion parameter U. For microscopic rings having very large U, we find that as the flux is increased by one quantum, a magnon hole traverses the magnon sea, generating a periodicity of 1/${\mathit{N}}_{\mathit{c}}$ in the persistent current, but with no changes in the overall spin magnetization, in contrast to the earlier suggestion of Kusmartsev. For non-half-filled mesoscopic rings, we use methods developed by Woynarovich for the zero-flux case to build a rather complete picture of the variation of persistent current with magnetic flux. We find the periodicity to be a half flux quantum or a whole one, and show how the critical flux values at which the current reverses vary with system parameters. We show how the behavior characteristic of microscopic rings goes over to that of mesoscopic rings as ${\mathit{N}}_{\mathit{c}}$/U increases.

A stomatal resistance model illustrating plant vs. external control of transpiration

A stomatal resistance model is proposed that is specifically designed for use within atmospheric boundary layer models. Stomatal resistance is expressed as a product of linear discontinuous functions of leaf water potential and solar flux; vapor pressure deficit is included indirectly by allowing for a gradient of leaf water potential between the surface and the interior of the leaf. An important assumption is that stomatal resistance increases sharply beyond a critical value of leaf water potential and/or critical solar flux. The model is able to simulate a transpiration plateau; this plateau may occur because of high atmospheric demand and/or a limitation in soil water.

Evaluation of Carpets in the National Bureau of Standards Flooring Radiant Panel

The burning behavior of carpets of very similar construction and contract com mercial carpets made from different fibers and blends in the National Bureau of Standard Flooring Radiant Panel were significantly affected by the pile fiber com position. Carpets of 100% wool and 80/20 wool/nylon produced critical radient flux (CRF) values > 0.5 W/cm2 and these values were not affected by underlays. The CRF values of nylon carpets depended significantly on carpet construction, with low weights producing low CRF values, and decreased significantly with underlays. An increase in the imposed heat flux decreased the CRF values for nylon, but in the case of wool, CRF values significantly increased. This is probably associated with the different heat outputs and melting or charring behavior of the two fibers. Other carpet parameters that can affect CRF values are Zirpro flame-retardent treat ment of wool, shorn pile density, backing fiber composition (jute or polypropylene), and flame retardant latex.

A note on the maximum ground level concentration for inversion-limited chimney plumes

A model is proposed for the determination of the maximum ground level concentration for buoyant chimney plumes whose rise is limited by the inversion overlying a convective atmospheric boundary layer. Manins' critical parameter for inversion penetration is shown to be equivalent to a geometric constraint on the solution for maximum plume rise in the author's model for unrestricted plume rise. A proposed solution for maximum surface concentration based on an effective source rate at the inversion modified for inversion entrainment has the same functional form as a previous solution for the unrestricted case. Experimental analysis suggests the existence of the critical value of source buoyancy flux in terms of ambient parameters, and supports the validity of the form and order of magnitude of the maximum surface concentration.

Moment transport equations for wave-particle interactions in the magnetosphere

The particle transport equation which describes radial diffusion combined with quasi-linear diffusion by waves is analytically intractable and is usually dealt with by fixing a priori either the radial transport term or the wave diffusion term. For the case of electromagnetic cyclotron waves simplification results by taking moments of this equation, thereby generating three equations for the total number density of the energetic particles, their total energy , and their total perpendicular energy . The quasi-linear conservation equations for and allow one to estimate the total wave intensity in terms of the particle moments and their radial derivatives and thus to express wave diffusion entirely in terms of these moments. The resulting moment transport equations for the particles describe relaxation of toward a critical value /subc/ (or equivalently a critical value $beta$/subc/ of the plasma $beta$); when is less than /subc/, there can be no finite amplitude waves. From /sub c/ a critical flux value can be estimated which is never greater than the stably trapped flux limit (STFL) of Kennel and Petschek. It is shown that the STFL controls the anisotropy of the energetic plasma, while /sub c/ controls the loss rate. As one expects, the effective loss ratemore » is greater for than for , since particles may lose energy before they are precipitated. (AIP)« less