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Mixing of two miscible liquids with high viscosity and density difference in semi-batch and batch reactors - CFD simulations and experiments
The mixing behavior of two liquids with different viscosities and different densities is investigated experimentally in a glass SBR and BR as well as by CFD simulation. With a torque method, the mixture viscosity ηm(t) of ethanol and glycerol is measured as a function of time. From mη (t) it is determined the mixing time tm at which the mixture viscosity begins to remain constant. In addition the mixing time tm is measured directly by a decolorisation method using the iodine sodium thiosulfate reaction. The dynamic mixing behavior of the ethanol and glycerol mixtures in a SBR and a BR is analysed by video visualisation of the flow field with a light cut procedure. In a BR a pan cake effect of an ethanol layer is observed. The definition of mixing, the scales of mixing, some important mixing characteristics and overview of types of stirrers as well as some essentials of computational fluid dynamics (CFD) are discussed within the theoretical background given in this work. For a quantitative description of the measured dynamic mixing behaviour of ethanol and glycerol, a CFD simulation is carried out by using the Ansys CFX-10 tool. The used models are an isothermal, multiphase, multicomponent, modified algebraic slip model and the following submodels: A homogeneous standard free surface flow model for air/liquid interface, a sliding mesh model and a laminar buoyant flow model for the liquid mixture. With Ansys ICEM CFD 5.1 an unstructured mesh with tetrahedron cells is used. It is found that the computational time of simulation (CPU time) can be reduced from 20 to 2 days if the number of tetrahedron cells will be reduced from 600,000 to 26,000. Then the cell size increases from 0.001 m to 0.015 m, without remarkable change in the calculated results. From the CFD simulations with a half geometry in a SBR, it is found that the mesh refinement at the interface between the mixture phase and the air changes from 0.015 m to 0.00375 m gives a sharper interface and better resolution. When the dosage time for ethanol increases from 1 s to 5 s and the inlet tube diameter increases from 0.023 m to 0.05 m, the mixing time increases with a factor of 2. When the velocity of the anchor impeller increases from 25 rpm to 400 rpm, then the mixing time decreases with a factor of 6. The stirrer velocity has a greater effect on the secondary axial flow than on the primary tangential flow. When the width of the horizontal blade of the anchor impeller increases from 0.012 m to 0.015 m the mixing time decreases with a factor of 2. The effect of different mixture ratios of glycerol and ethanol on the flow field is studied in a BR. It is predicted from the CFD simulation of the flow field that pure ethanol shows mainly axial flow with no circulations in the domain between the shaft and anchor impeller. A secondary flow with an axial circulation is predicted behind (down stream) the rotating anchor impeller in the case of the mixing of pure glycerol or of ethanol/glycerol. From the CFD simulations with a full geometry it is derived a new method to determine the mixing time tm, by calculation the ethanol mass fraction in a SBR and a BR at nine different positions as a function of time. The mixing time and a homogeneous mixture are obtained when the ethanol mass fractions are constant at all nine positions. It is found that the ethanol mass fraction near the stirrer reaches a constant value earlier than that near the shaft of the stirrer. The new developed modified algebraic slip model (MASM) which includes the ethanol droplets break up dp(t) as a function of time t by modeling with a validated step function, gives the real mixing behaviour, i.e. ηm(t) and mixing times tm in a good agreement with the experimental results in a SBR and a BR. Also the prolongation of the mixing time tm by a factor of 1.5 caused by the pan cake effect is predicted by the MASM. The often used algebraic slip model (ASM) and transport model (TRM) give an unrealistic prediction of the experimental mixing behavior in the case of ethanol and glycerol.
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