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The multi-scale turbulence approach is useful in predicting mean flows in problems containing complex turbulent structures that are otherwise unattainable using standard Reynolds-averaged Navier-Stokes models. In crossflow simulations using the multi-scale turbulence approach, turbulent mass diffusion in the resolved field showed variations not correlated with the eddy viscosity. This work is aimed at modifying the multi-scale turbulence approach to allow the resolved field to adaptively influence the value of turbulent Schmidt number in the Reynoldsaveraged Navier-Stokes sub-filter model. The proposed model estimates a time-averaged resolved turbulent Schmidt number that is used in place of the constant value common to standard Reynolds-averaged Navier-Stokes approaches. This approach is assessed by grid refinement study in which different amounts of turbulence are resolved. Fuel concentration predictions show an improvement when compared with experimental measurements versus the multi-scale model without the adaptive approach. Nomenclature = heat capacity at constant pressure = generalized coefficient for numerical viscosity estimation = Smagorinsky constant = injector inner diameter