I checked the paper you are referring to but it did not have the same equations numbering. Step back to the TKE Equation before going to the Dissipation .Just look to this term from the paper of Enwald:
it is just added to the TKE equation of gas phase without getting multiplied with volume fraction. This is not the case in Fluent where the term get multiplied with alpha_g*rho_g and it has that already in the formulation.
Please explain which equations are you referring to and how you did the derivation.
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New Post - Reply To: possibly a mistake in the source term of the turbulent dissipation rate