Gas hemisphere

Fig. 5.73 Radiation of a gas hemisphere with the radius R on a surface element d.4 at the centre of the sphere...

As we will show in section 5.6.4, the complicated determination of the emis-sivities g and q °f any shape of gas space can be traced back to the standard case of the gas hemisphere we have just dealt with. A mean beam length sm is determined for the gas space under consideration from the following condition a gas hemisphere with the radius R = sm should give rise to the same spectral irradiance on a surface element at its centre as that for the radiation from any shaped gas volume on a certain element of its surface. As follows from (5.188) and (5.191)... 

The emission of gas radiation depends on the size and shape of the gas space it is described quantitatively by the irradiance, which the gas radiation generates at the surface of the gas space. The decisive equations (5.188) and (5.189) include the spectral emissivity e))(. and the emissivity integrated over all wavelengths q, which, according to (5.193) and (5.194), can be replaced by the emissivity of a gas hemisphere with a radius the same as the mean beam length. sni of any shaped gas space. 

The mean beam length sm of a gas space of any shape that radiates on an element dA = dA2 of its surface, is defined by the fact that the spectral irradiance I a,g of dA 2 has exactly the same magnitude as the spectral irradiance of a surface element in the centre of a gas hemisphere of radius R = sm. According to section 5.6.2, the spectral irradiance of this surface element is... 

An optically thin gas hemisphere of radius R = sm causes, according to (5.200), the spectral... 

For the radiation of the gas hemisphere on a surface element at its centre, we have exactly... 

T. E. Taubert and R. P. Daimer, Thjsical and Thermocfynamic Properties of Pure Chemicals, Suppl /, CIO2 Gas Property Section, Hemisphere Publishing Corp., Bristol, Pa., 1991. 

A. H. Lefebvre, Gas Turbine Combustion, Hemisphere Publishing Corp., Washiagton, D.C., 1983. 

A number of successful devices have been in use for finding mass-transfer coefficients, some of which are sketched in Fig. 23-29, and all of which have known or adjustable interfacial areas. Such laboratoiy testing is reviewed, for example, by Danckwerts (Ga.s-Liquid Reac-tion.s, McGraw-Hih, 1970) and Charpentier (in Ginetto and Silveston, eds., Multiphase Chemical Reactor Theory, De.sign, Scaleup, Hemisphere, 1986). 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

Single gas bubbles in an inviscid liquid have hemispherical leading surfaces and somewhat flattened wakes. Their rise velocity is governed by Bernoulli s theory for potential flow of fluid around the nose of the bubble. This was first solved by G. I. Taylor to give a rise velocity Ug of ... 

Lihou and Maund (1982) used soap bubbles filled with flammable gas which were blown on the bottom of a fireball chamber to form fireballs. A hemispherical bubble was formed on a wire mesh 200 mm above the base of the measuring chamber in order to permit study of elevated sources. The gas bubble was ignited by direct contact with a candle flame, and the combustion process was filmed at a speed of 64 frames per second. The fireball s color temperature was measured. 

The vessel under gas pressure bursts into equal fragments. If there are only two fragments and the vessel is cylindrical with hemispherical end-caps, the vessel bursts perpendicular to the axis of symmetry. If there are more than two fragments and the vessel is cylindrical, strip fragments are formed and expand radially about the axis of symmetry. (The end caps are ignored in this case.)... 

The blast originating from a hemispherical fuel-air charge is more like a gas explosion blast in wave amplitude, shape, and duration. Unlike TNT blast, blast effects from gas explosions are not determined by a charge weight or size only. In addition, an initial blast strength of the blast must be specified. The initial strength of a gas-explosion blast is variable and depends on intensity of the combustion process in the gas explosion in question. 

Whilst the calculation of the radiant heat flux from a gas to an adjoining surface embraces inherent spectral and directional effects, a simplified approach has been developed by Hottel and Manglesdorf 54, which involves the determination of radiation emission from a hemispherical mass of gas of radius L, at temperature 7, ... 

L Separation of surfaces, length of a side or radius of hemispherical mass of gas m L... 

Hemispherical, temperature-regulated, heating mantle, 500-W, Horst or equivalent Gas washing tubes, in glass, 250-mL (Pyrex), equipped with spherical socket joints Trapping (absorption) tube, in glass, 250-mL (Pyrex), equipped with spherical socket joints... 

Gas cylinder. A welded or forged vessel usually with a ratio of length to diameter from 5 1 to 50 1, usually with hemispherical or other specially designed heads. 

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