The droplet evaporation and heating rates are very sensitive to the physical property values used in the rate equations, so it is important to use appropriate temperature and composition assumptions for property evaluation. The most common method for evaluating properties is to compute averaged properties based on reference values for the temperature and vapor mass fraction as follows ([442], [7], and [553]):

(12–185)

(12–186)

This averaging method is known as the 1/3 rule because of the most commonly used value for the parameters = 1/3.

Assuming that the species mass fractions in the reference mixture are proportional to the mass fractions in the far field gas mixture, except for the evaporating species, the mass averaged property can be obtained from:

(12–187)

where and are the vapor and far field gas mixture properties at the reference temperature , that is:

(12–188)

(12–189)

If the evaporating species mass fraction in the bulk is 0, Equation 12–187 reduces to the simple mass averaging formula:

(12–190)

The averaging coefficients are assigned values between 0 and 1. As follows from equations Equation 12–185 and Equation 12–186, = 1 corresponds to free stream conditions, while for = 0, the temperature and composition are those of the particle surface.

For multicomponent evaporation, the averaging formula takes the form:

(12–191)

where the subscript refers to the vapor of the ^th evaporating species, and the subscript refers to the ^th species in the far field gas mixture.

The property averaging equations Equation 12–187 and Equation 12–191 are applied for all physical properties in the droplet and multicomponent rate equations, respectively, except averaged density , which is computed for temperature and mass fractions directly from the density property model equation defined for the gas phase mixture material:

(12–192)