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AN ANALYSIS OF TWO-DIMENSIONAL LAMINAR AND TURBULENT COMPRESSIBLE MIXING
ARNOLD ENGINEERING DEVELOPMENT CENTER ARNOLD AFB TN
An analysis is presented to two-dimensional, isoenergetic, compressible mixing of a jet with a fluid at rest for both laminar and turbulent mixing. The analysis is primarily concerned with the development of theoretical expressions for the mixing similarity parameters. A general momentum equation is derived, which relates the similarity parameter to the mixing length and viscous shear stress. By using this general equation and Newtons viscous shear relation, a complete theoretical solution for the laminar mixing similarity parameter is derived, which does not involve a reference perturbation velocity factor. Prandtls mixing length theory for the apparent viscous shear relation is used to obtain the theoretical similarity parameter for turbulent mixing. Based on these similarity parameters, equations for the width of the corresponding mixing regions are derived. These results and the approximate theoretical velocity profile equation developed by Pai, Nash, and Korst represent a closed-form theoretical approximation of the type of mixing considered.
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