Numerical simulation of fluid dynamics in the stirred tank by the SSG Reynolds Stress Model

Abstract

The Speziale, Sarkar and Gatski Reynolds Stress Model (SSG RSM) is utilized to simulate the fluid dynamics in a full baffled stirred tank with a Rushton turbine impeller. Four levels of grid resolutions are chosen to determine an optimised number of grids for further simulations. CFD model data in terms of the flow field, trailing vortex, and the power number are compared with published experimental results. The comparison shows that the global fluid dynamics throughout the stirred tank and the local characteristics of trailing vortices near the blade tips can be captured by the SSG RSM. The predicted mean velocity components in axial, radial and tangential direction are also in good agreement with experiment data. The power number predicted is quite close to the designed value, which demonstrates that this model can accurately calculate the power number in the stirred tank. Therefore, the simulation by using a combination of SSG RSM and MRF impeller rotational model can accurately model turbulent fluid flow in the stirred tank, and it offers an alternative method for design and optimisation of stirred tanks.

Key words： stirred tank; fluid dynamics; numerical simulation; SSG Reynolds Stress Model; MRF

Acknowledgements

Financial support from the Major State Basic Research Development Program of China (973 Program, Grant No. 2005CB221205) was gratefully acknowledged. Ms. Qi would like to acknowledge financial support from the China Scholarship Council (CSC) during her stay at the University of Adelaide, Australia.

Nomenclature

B	sum of body force, N/m3
cµRs,σϵRS	constants in the SSG RSM
cs	constant in the SSG RSM
cϵ1,cϵ2	constants in the SSG RSM
Cs1,Cs2	Constants in the SSG RSM
Cr1~Cr5	constants in the SSG RSM
d	diameter of the impeller, m
D	diameter of Rushton turbine, m
F	external force, N/m3
H	height of the tank, m
Idef	default turbulent intensity of 5%, m2/s2
N	rotation speed, 1/s
Np	power number
p	pressure, Pa
R	diameter of the tank, m
T	inner diameter of the tank, m
Tq	total torque, N·m
u	turbulent velocity, m/s
U	average velocity, m/s
w	baffle width, m

Greek letters

δ	Kronecker delta, when i=j, δ=1; when i≠j, δ=0
e	turbulence dissipation rate, m2/s3
\kappa	turbulence kinetic energy per unit mass, m2/s2
µ	viscosity, Pa ·s
ξ	bulk viscosity, Pa ·s
r	density, kg/m3
{\varphi }_{ij}	pressure-strain correlation in the SSG model, kg · m /s3

Subscripts

i, j, k

Cartesian coordinate direction vector

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