VALIDATING THE GALERKIN LEAST-SQUARES FINITE ELEMENT METHODS IN PREDICTING MIXING FLOWS IN STIRRED TANK REACTORS

INTRODUCTION A novel approach for computer aided modeling and optimizing mixing process has been developed using Galerkin least-squares finite element technology. Computer aided mixing modeling and analysis involves Lagrangian and Eulerian analysis for relative fluid stretching, and energy dissipation concepts for laminar and turbulent flows. High quality, conservative, accurate, fluid velocity, and continuity solutions are required for determining mixing quality.

[1]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[2]  P. Bandyopadhyay,et al.  Mean and turbulence characteristics of three-dimensional wall jets , 1975 .

[3]  L. Franca,et al.  Stabilized Finite Element Methods , 1993 .

[4]  Thomas J. R. Hughes,et al.  Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations†‡ , 1987 .

[5]  Richard H. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer , 1984 .

[6]  Fernando J. Muzzio,et al.  Characterization of flow and mixing in an SMX static mixer , 2002 .

[7]  Fernando J. Muzzio,et al.  Extensive validation of computed laminar flow in a stirred tank with three Rushton turbines , 2001 .

[8]  A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations , 1986 .

[9]  Thomas J. R. Hughes,et al.  A simple scheme for developing ‘upwind’ finite elements , 1978 .

[10]  Claes Johnson,et al.  On the convergence of a finite element method for a nonlinear hyperbolic conservation law , 1987 .

[11]  F. Shakib Finite element analysis of the compressible Euler and Navier-Stokes equations , 1989 .

[12]  K. J. Bittorf,et al.  Three-dimensional wall jets: Axial flow in a stirred tank , 2001 .

[13]  T. Coakley,et al.  Turbulence Modeling Validation, Testing, and Development , 1997 .

[14]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[15]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems , 1986 .

[16]  Thomas J. R. Hughes,et al.  A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems , 1986 .

[17]  T. Hughes,et al.  Stabilized finite element methods. I: Application to the advective-diffusive model , 1992 .

[18]  Suzanne M. Kresta,et al.  Internal annular wall jets: Radial flow in a stirred tank , 2001 .

[19]  P. Spalart A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .