Draft theoretical

Xu, M., A Theoretical and Experimental Investigation of Spouted Beds with Draft Tubes, Ph.D. Dissertation, West Virginia University, Morgantown, WV (1993)... 

This work was supported by NSF Grants DMR-9973976 and PHY99-07949, the latter of which supports the Kavli Institute for Theoretical Physics, where much of this work was completed. 1 would also like to acknowledge Marshall Fixman and Hans-Christian Ottinger for helpful correspondence, and Shriram Ramanathan for reading and commenting on an earlier draft of the manuscript. 

We wish to acknowledge generous assistance from many friends and colleagues, especially Dr. John W. Cahn, Dr. Rowland M. Cannon, Prof. Adrian P. Sutton, Prof. Kenneth C. Russell, Prof. Donald R. Sadoway, Dr. Dominique Chatain, Prof. David N. Seidman, and Prof. Krystyn J. Van Vliet. Prof. David T. Wu graciously provided an unpublished draft of his theoretical developments in three-dimensional grain growth which we have incorporated into Chapter 15. We frequently consulted Prof. Paul Shewmon s valuable textbooks on diffusion, and he kindly gave us permission to adapt and reprint Exercise 3.4. 

The design of large natural draft cooling towers and analysis of their performance are complicated by the effects of variations in ambient air humidity. Often the effluent air from the tower is assumed to be at 100% relative humidity, to simplify calculations for design parameters. This study avoids the simplification, and proposes a procedure for determining the major design parameters for a natural draft tower. The theoretical and empirical relationships applicable to heat balance, heat transfer and transport, and tower draft and air resistance are given. 13 refs, cited. 

Use of LCAO and plane wave bases does not necessarily make the parts of the text where they arc used independent, since wc continually draw on insight from both outlooks. The most striking case of this is an analysis in Chapter 2 in which the requirement that energy bands be consistent for both bases provides formulae for the interatomic matrix elements used in the LCAO studies of. sp-bonded solids. This remarkable result was obtained only in late 1978 by Sverre Froyen and me, and it provided a theoretical basis for what had been empirical formulae when the text was first drafted. The development came in time to be included as a fundamental part of the exposition it followed on the heels of the much more intricate formulation of the corresponding LCAO matrix elements in transition metals and transition metal compounds, which is described in Chapter 20. 

As everyone who has used a fireplace knows, when a fire bums in a furnace, a draft, or slight vacuum, is induced that causes the hot combustion gases and entrained particulate matter to flow up and out of the stack. The reason is that the hot gas in the stack is less dense than air at ambient temperature, leading to a lower hydrostatic head inside the stack than at the furnace inlet. The theoretical draft D(N/m ) is the difference in these hydrostatic heads the actual draft takes into account pressure losses undergone by the gases flowing in the stack. 

This gives the maximum theoretical draft with no flow taking place. The actual draft obtained is about 20 per cent less, due to chimney friction, and head required to create velocity of gases. 

Figure 7.27 shows theoretical results for how the O2 concentration decreases with an increase in air temperature and relative humidity. These calculations are based on a constant furnace draft level with 3% excess O2 corresponding to air at 60°F (16°C) and 0% relative humidity (baseline point). The results show that the excess O2 drops off as the air temperature increases. Also notice that the variation of O2 is more dramatic with changes in air temperature as the relative humidity increases. Next, a couple of scenarios are given to demonstrate how these variations can result in dramatic changes in NOx and CO emissions. 

Since aerosolized reaction products surround the flame as dense white smoke, a complex relation exists between smoke formation and light. At our present state of the ait, a superior white-light source cannot do without the presence of whitesmoke from magnesium oxide and sodium oxide (formed from nitrate). By reflection of the light, such smoke can have some beneficial effect, but of course it will be detrimental for illumination. This is a physicochemical as well as a topical problem. The position of the flame, the ambient air currents, and the convective draft from the heat of the reaction combine to keep the flame visible or to obscure it. However, it has been indicated from theoretical consideration that the magnesium oxide within the flame... 

The theoretical draft (lift, suction) of a tall column of hot gas, as in a furnace, vertical duct, or stack is ... 

Several days later he and Conant received a copy of a draft report forwarded from the National Defense Research Committee liaison office in London. The report, prepared by a group codenamed the UD Committee and set up by the British in spring 1940 to study the possibility of developing a nuclear weapon, maintained ftat a sufficiently purified critical mass of uranium-23S could fission even with fast neutrons. Building upon theoretical work on atomic bombs performed by refugee physidsts Rudolf Peierls and Otto Frisch in 1940 and 1941, the MAUD report estimated that a critical mass of... 

A forced-draft unit has a fan below the tube bundle which pushes air across the finned tubes. An induced-draft unit has a fan above the tube bundle which pulls air across the finned tubes. Theoretically, a forced-draft unit requires less horsepower because air is pumped at the highest available density (lowest available temperature). However, in practice induced-draft units require no more power than forced-draft units and in many cases actually require less power. 

Except for the conical distributor plate, no simple gas bypassing relationship exists. No rigorous theoretical model has thus far been proposed. The quantitative gas bypassing information is usually determined experimentally. Qualitatively, the gas bypasses from the draft tube side into the downcomer side for small draft-tube-to-downcomer area ratios and vice versa. Gas bypasses exclusively from the downcomer side to the draft tube side when the distance between... 

Experience indicates that a simple theoretical model to predict gas bypassing that takes into account all the design and operating variables cannot be developed. Empirical correlation, however, can be obtained by conducting experiments with tracer gas injection for a given distributor plate design at different operating conditions and at different distances from the draft tube inlet. 

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