Group combustion number

An interesting approach to the spray problem has been suggested by Chiu and Liu [29], who consider a quasi-steady vaporization and diffusion process with infinite reaction kinetics. They show the importance of a group combustion number (G), which is derived from extensive mathematical analyses and takes the form... 

Keywords Diffusion flame Droplet evaporation Droplet interaction Flame propagation Group combustion number Penetration distance... 

The ratio of penetration length Ls to spray radius R expresses how deep the influence of the outer diffusion flame can penetrate into the spray region by diffusion. It is equal to the inverse of the square root of the group combustion number G = 4nanR introduced by Chiu, i.e.. 

When the group combustion number exceeds unity due to a reduction of the spray radius, the influence of the outer diffusion flame on the opposite side overlaps near the center line of the spray stream. Thus, the diffusion flame front rapidly approaches the center line and burning of clustered droplets occurs near the center line as well (internal group combustion). 

The value of G was shown to have a profound effect upon the flame location and distribution of temperature, fuel vapor, and oxygen. Four types of behaviors were found for large G numbers. External sheath combustion occurs for the largest value and as G is decreased, there is external group combustion, internal group combustion, and isolated droplet combustion. 

Isolated droplet combustion obviously is the condition for a separate flame envelope for each droplet. Typically, a group number less that 10 2 is required. Internal group combustion involves a core with a cloud where vaporization exists such that the core is totally surrounded by flame. This condition occurs... 

Approach. The use of continuum models is defensible only when the particles are suflBciently far apart that suitable averaged oxidizer and fuel mass fraction can be defined. This implies not only the Rp/L < < 1 but also the Rf/L < < 1, where Rf is the individual envelope flame radius, and L is the interparticle distance. Indeed, the use of a continuum approach to establish the incipient group combustion criterion may be suspect since this last inequality is not met. Further, continuum models cannot be defended when the number of particles in the cloud is small... 

Table 2 3 lists the heats of combustion of several alkanes Unbranched alkanes have slightly higher heats of combustion than their 2 methyl branched isomers but the most important factor is the number of carbons The unbranched alkanes and the 2 methyl branched alkanes constitute two separate homologous senes (see Section 2 9) m which there is a regular increase of about 653 kJ/mol (156 kcal/mol) m the heat of combustion for each additional CH2 group... 

Cycloalkane Number of CH2 groups Heat of combustion per CH2 group... 

All phosphoms oxides are obtained by direct oxidation of phosphoms, but only phosphoms(V) oxide is produced commercially. This is in part because of the stabiUty of phosphoms pentoxide and the tendency for the intermediate oxidation states to undergo disproportionation to mixtures. Besides the oxides mentioned above, other lower oxides of phosphoms can be formed but which are poorly understood. These are commonly termed lower oxides of phosphoms (LOOPs) and are mixtures of usually water-insoluble, yeUow-to-orange, and poorly characteri2ed polymers (58). LOOPs are often formed as a disproportionation by-product in a number of reactions, eg, in combustion of phosphoms with an inadequate air supply, in hydrolysis of a phosphoms trihahde with less than a stoichiometric amount of water, and in various reactions of phosphoms haUdes or phosphonic acid. LOOPs appear to have a backbone of phosphoms atoms having —OH, =0, and —H pendent groups and is often represented by an approximate formula, (P OH). LOOPs may either hydroly2e slowly, be pyrophoric, or pyroly2e rapidly and yield diphosphine-contaminated phosphine. LOOP can also decompose explosively in the presence of moisture and air near 150° C. 

We next consider a number of plants in which the combustion process is modified by changing the oxidation of the fuel. Table 8. ID and Figs. 8.18-8.20. The first group (Dl, D2 and D3) are plants with PO—insufficient air is supplied to the PO reactor, less than that required to produee stoichiometric combustion. The second group (D4, D5 and D6) are plants where air is replaced as the oxidant by pure oxygen whieh is assumed to be available from an air separation plant. 

As experiments at Sun Oil Co. in the early 1930s indicated, there were serious disadvantages associated with alcohol. Wliile alcohol did in fact appear to increase the octane number, it left large amounts of deposits in the engine. Alcohol also vaporized out of the gas tank and engine at rapid rates. And the combustion temperature of the alcohol group is lower than for hydrocarbons because it is already partially oxidized. 

With the discussion of oxygenafe, pofentially bioderived, fuels and fuel additives such as alcohols, ethers, or esters, the need for defailed information on their combustion chemistries is becoming acute. Additional functional groups in the fuel molecule lead to a larger number of possible structural isomers. The influence of the chemical structure of the fuel molecule... 

The assumption is made at present that elemental combustion analysis for carbon, hydrogen, and fluorine provides a good approximation to the extent of incorporation of fluoroalkyl residues, i.e. alcohols and ethers. We have ruled out trifluoromethylcarbonyl groups since no evidence is seen for their presence in either the infrared spectra or the 19F-NMR spectra. Thus, our values for percent modification reflect the best fit of the combustion data to an idealized stoichiometry for the product in Equation 1, where (m+n+o) = 100, and the percent modification (% mod.) is given by the expression [100 x (m+o)/(m+n+o)], equivalent to the number of fluoroalkyl residues per one hundred methylenes. An appropriately normalized formula was used to fit the data for polypropylene (sample 10). 

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