Thermodynamical Theory of Turbulence. 2. Determination of Constitutive Coefficients and Illustrative Examples

摘要

This part is concerned mainly with the determination of constitutive response coefficients as well as some simple illustrative examples. A system of simplified constitutive equations for incompressible viscous turbulent flow is obtained from the more general system of equations in Part I (ADA-206 455) through a judicious choice of retaining only those terms which appear to represent major features of the turbulent flow. Even for this simplified system of equations, identification of some of the constitutive coefficients presents a formidable task. This is especially true of those coefficients associated with the presence of the additional independent variables of the theory due to the manifestation of the alignment of eddies (on the microscopic scale), turbulent fluctuation and eddy density. Because of this difficulty, this study must be regarded partly as tentative. Most of the relevant coefficients in the constitutive equations are determined, or the nature of their functional forms are estimated, through consideration of 'cartoon-like' models on the microscopic level. These results are then used in conjunction with the macroscopic equations of motion to examine a number of simple solutions. These include the possibility of a flow processing a constant uniform velocity gradient and solutions pertaining to decay of flow anisotropy and plane turbulent channel flows. The predicted theoretical calculations are in general accord with experimental observations. Keywords: Channel flow, Incompressible viscous fluids. Reprints. (EDC)