Distribution of eddy viscosity and mixing length in a non-Newtonian flow of a solid particle-gas suspension

The present work concerns the study of the radial distribution of eddy viscosity and mixing length and their dependence upon the Reynolds number and the concentration of the solid phase in a non-Newtonian flow of a suspension of solid particles in a gas. The investigated systems have a pseudoplastic character and the deviation from Newtonian behaviour increases with an increase in the concentration of the dispersed phase. Relations are presented for the eddy viscosity and mixing length in the flow of pseudoplastic fluids. From the analysis of results it follows that the mixing length and eddy viscosity increases with an increase in the Reynolds number. In contrast, an increase in the concentration of the solid phase and consequently of the pseudoplasticity causes a decrease in the investigated quantities. The radial distribution of the mixing length and the eddy viscosity is characterized by a maximum, after which the investigated quantities vary only slightly. This enables the area of the core of the turbulent flow to be defined. E Non-dimensional eddy viscosity - K fluid consistency defined by Ostwald-De Waele's formula (power law) - K fluid consistency, eq. (12) - L mixing length - L _t non-dimensional mixing length - N ⁺ position parameter, eq. (3) - n power-law index - n ⁺ Reichardt's position parameter, eq. (4) - n slope of the dependence ln _w = fln (8w/D)] - R pipe radius - r radial distance from the pipe axis - Re=D W /µ Reynolds number - U ⁺ non-dimensional local mean axial velocity, eq. (2) - u ^* = w (/8)^0.5 friction velocity - non-dimensional local mean axial velocity - local mean axial velocity - u turbulence velocity component - mean axial velocity at pipe axis - w average velocity over cross-section of pipe - loading ratio of solid to air, i.e. ratio of mass flow rates of solids to air - Y _m ⁺ =Rⁿ u^2–n /K 8^n–1 non-dimensional distance of pipe centre from the wall - y distance from pipe wall - y ⁺ non-dimensional distance from pipe wall, eq. (5) - friction factor - µ _L laminar part of viscosity - µ _t eddy viscosity - density - shear stress - _w shear stress on the wall