The combustion efficiency and other spray properties

Equations for the representative spray properties n- and r may be derived for systems in which Gj o is given by equation (22). If equation (15) is substituted into equation (20), use is made of equations (12) and (22), and the variable of Integration is changed from r to 

Carrying out a similar operation with equation (21) yields 

FIGURE 11.2. The ratio of the number flux of droplets of kind/ to its value at x = 0 as a function of the dimensionless distance Zj for various values of (tj 1)/ . 

The property of the spray that is of greatest practical importance is the combustion efficiency, which is given by equation (18). When Gj q is of the generalized Rosin-Rammler form [equation (22)], by using equations (12) and (23) in equation (18), we find that 

It is of interest to consider a bipropellant rocket motor (M = 2) in which liquid fuel FJ = 1) and liquid oxidizer (OJ = 2) undergo the overall reaction v F + v O products. Since the present model prevents us from considering gaseous reactions, the fuel and oxidizer must evaporate in stoichiometric proportions—that is, by the same kind of reasoning that was used in Section 11.2.3. 

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For initial droplet-size distributions given by equation (22), the combustion efficiency and other spray properties may be expressed in terms of the function... 

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