Statistical Constraints on Scalar Correlations

Models for the scalar probability density function (pdf) have to be developed to achieve closure of turbulent transport equations for mixing and reacting flows. The best statistical bounds on a number of moments for tvvoand three-species flows have been derived and used to construct and test a delta function "typical eddy" pdf model. If has been proven that for two species a rational pdf composed only of delta functions can always be constructed at any point within the statistically valid moment space. The delta function model and a canonical pdf model have been directly compared to experimental pdf measurements and both models show good agreement for higher-order moments, but the delta function model is simpler to construct and is recommended for closure of the transport equations for mixing flows.