Multi-dimensional analysis of turbulence models for immiscible liquid-liquid mixing in stirred tank based on numerical simulation

ABSTRACT

The Reynolds Averaged Navier-Stokes (RANS) simulation was employed to predict a turbulent flow of liquid-liquid two-phase system in standard stirred tank. The results calculated by the standard k-ε model and the Renormalization Group (RNG) k-ε model were compared to Particle Image Velocimetry (PIV) data from the literature. The constants of the transports equations were corrected, which could reflect the time-averaged strian rate of the main flow. Multi-dimensional investigation revealed the flaws of RNG k-ε model compared to standard k-ε model in predicting the liquid-liquid two-phase mixing process, which has great guidance for the selection of the turbulence models.

KEYWORDS:

• Standard k-ε model
• RNG k-ε model
• liquid-liquid system
• turbulence
• stirred tank

Nomenclature

A	=	Constant
D	=	Impeller diameter, m
F	=	Forces of LLP interactions
N	=	Impeller agitation speed, rpm
We	=	Impeller Weber number
d32	=	Sauter mean diameter, m
g	=	Gravity
k	=	Turbulence kinetic energy, m2·s−2
p	=	Pressure
u	=	Velocity
x	=	Volume fraction
xsim	=	Simulation data
xexp	=	Experimental data
αd,av	=	Average dispersed phase volume fraction
γ	=	Constant
ε	=	Turbulence dissipation rate, m2·s−3
μ	=	Viscosity, kg·m−1·s−1
μt	=	Turbulent viscosity, kg·m−1·s−1
ρ	=	Density, kg·m−3
ρc	=	Continuous phase density, kg/m3
σ	=	Interfacial tension, N/m
τ	=	Stress tensor
LLP	=	Liquid-liquid two-phase
rv	=	Radial velocity
tv	=	Tangential velocity
ST	=	Stirred tank
sts	=	Stirred tanks
Vin	=	Agitation speed of the rotor region
Vs	=	Agitation speed of outside region
Vr	=	Agitation speed of impeller
P	=	Working pressure
g	=	Acceleration of gravity
T	=	Working condition temperature
Pq	=	The relative pressure