Extended model of combustion in a liquid-propellant rocket motor

EXTENDED MODEL OF COMBUSTION IN A LIQUID-PROPELLANT ROCKET MOTOR 

In the model of rocket combustion given in Section 11.2, expressions for the parameters Xj and Vj remained undeveloped. An analysis given by Spalding [51], [52] determines these parameters by addressing gas flow. When the interaction of the particles with the gas is considered, the equations become so complicated that exact analytical results are obtainable only in very simple cases. Consequently, in addition to the approximations 

Although analyses in which some of these assumptions are removed, for example, by accounting for finite gas-phase reaction rates [53], for non-uniform particle-size distributions [54], [55], [56] and for droplet breakup [57], [58], are more realistic in that correlations with observed rocket-motor performance sometimes can be obtained, they involve numerical integrations which may tend to obscure the essential ideas. Simple analytical results have, however, been 3eveloped for a model that accounts in an approximate way for nonuniform size distributions [59]. Comprehensive reviews of related studies may be found in [58] and [60], The major drawback to all of these analyses is the one-dimensional flow approximation, which excludes from consideration the three-dimensional flows generally observed in real engines. 

Since the droplets are all of the same size in our present model, they will all disappear simultaneously at a finite distance from the injector, contrary to the results of Section 11.2. Therefore, instead of focusing attention on the combustion efficiency, we shall attempt to determine the minimum chamber length required for complete combustion rj = 100%), which will be denoted by x.  

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Extended Model of Combustion in a Liquid-Propellant Rocket Motor... 

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