## LSU Historical Dissertations and Theses

1987

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Chemical Engineering

#### Abstract

Solutions of conservation equations for the three-dimensional turbulent flowfield in agitated vessels were developed. Results showed that the Navier-Stokes equations with the nonisotropic k-$\varepsilon$ turbulence model described the three-dimensional velocity profiles and turbulence kinetic energy and its dissipation rate for the flowfield. The nonisotropic model considered the rotational effect on turbulence with a turbulent-Richardson-number term and accounted for the important baffling effects through the nonisotropy of the viscosity. The solutions were validated with the experimental data for velocities and turbulence parameters. An isotropic k-$\varepsilon$ turbulence model for rotational flow was also used. This modified isotropic k-$\varepsilon$ model proved to be inaccurate to describe the turbulent flow in turbine stirred tanks because it did not consider the baffling effects. We also compared this work with the similar studies by other investigators. These comparisons showed that the finite domain method and the nonisotropic k-$\varepsilon$ model were the appropriate ones to be used in studies of the three-dimensional turbulent flow in agitated vessels. The turbulent flowfield simulation used the Navier-Stokes equations and a turbulence model to form a closure system. We proposed and used two different k-$\varepsilon$ models for this purpose. The three-dimensional transport equations were discretized with the finite domain method. The power law scheme was used to approximate the convective transport and diffusive flux. The discretization equations were solved with the SIMPLE algorithm. In this solution procedure the Tri-Diagonal Matrix Algorithm with sweep method was used to solve each of the discretization equations. A general purpose computer FORTRAN code was developed to obtain solutions of these three-dimensional equations with the FPS-264 scientific computer.

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