Turbulent mixing with multiple second‐order chemical reactions

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Abstract
A molecular‐based statistical simulation program was developed to study the covariance terms involved in the mass balance equations for complex chemical reactions during mixing. Several closure theories were compared to the simulations and available experimental data. The simple closure by Brodkey and Lewalle was found to be an extension of Toor's analysis applied to two reactions. This closure does not satisfy the molar fluctuation balance equation and was found only to represent the high Reynolds number data of Li and Toor. This result led to examining other possible closures which were based on Damkoehler numbers, reaction rate constant ratios, and limiting forms of the covariance term. These closures also were inadequate. The second reaction's covariance term varied from the product of the average values for each component to the Brodkey and Lewalle value for the range of Reynolds numbers considered.