the shear rate distribution, the pumping capacity and the

mixing time of the Super blend mixer are calculated from the simulated hydrodynamics. In this work, the Super blend coaxial mixer is found as a good alternative for tough mixing applications.

Barbot et al. [19] studied the effect of NaN3  addition on both volumetric oxygen mass transfer coefficient and rheology of activated sludge suspensions in a bioreactor equipped with a double helical ribbons impeller.

Yu et al. [20] studied mixing performance in high solid anaerobic digester with A-310 impeller and helical ribbon. A mathematical model was constructed to assess flow fields. A systematic comparison for the interrelationship of power number, flow number and Reynolds number was simulated in a digester with less than 5% and 10% total solids. The simulation results suggested a great potential for using the helical ribbon mixer in the mixing of high solids digester. Driss et al. [21] studied CFD simulation the laminar flow in stirred tanks generated by double helical ribbons and double helical screw ribbons impellers. They interested for a Newtonian fluid.

The literature review proves that the double helical ribbons impellers are always used for the mixing operation and par- ticularly for the highly viscous liquid. As a consequence, it appears important to study these impellers and to make a comparison through a CFD simulation. Although these im- pellers have been widely used in the industry, information regarding their mixing performance is scarce, especially for non-Newtonian fluids.

In this new work, we are interested to compare the flow re- sults of the double helical ribbons impeller with the simple ribbon in a stirred vessel. The study is performed for shear thinning fluids, operating in the laminar and transitional regimes, which are typical conditions of polymerization reactions. The effect of impeller rotational speed, fluid rheology, impeller size, impeller clearance from the tank bottom on the flow fields and power consumption have been investigated. The geometric arrangement and the parame-

Figure 1. Agitation system: a) double helical ribbons; b) simple heli- cal ribbon.

the effect of impeller (double helical ribbons) clearance from the tank bottom was tested, by three other geometries (c/D = 0.03, 0.26, 0.5).

3. Flow equations

We assume that the flow is fully periodic, making it possible to use a Lagrangian viewpoint to simulate a steady three- dimensional flow in the mixer. In this rotating frame of reference, the impeller remains fixed and the vessel rotates in the opposite direction (the observer is moving with the impeller). The corresponding flow equations are:

2(V gradV + ω(ωR ) + 2ωV ) +

(1)

gradp − p (2η(γ˙)γ˙) = 0

p V = 0 (2)

ters investigated in the present paper are not numerically 1 T

analyzed elsewhere.

2. Mixer configurations

The mixing configuration consists of a cylindrical unbaffled tank with a flat bottom (Figure 1), the liquid level H is equal to the diameter vessel D, with D = 300 mm. The blade width (b) presents a ratio of 0.1*D. Two types of impellers with the same diameter shaft ds/D = 0.05 were used: a simple and double helical ribbons. The effect of impeller (double helical ribbons) size was investigated, at this end, four geometrical configurations were realized, which are h/D = 0.5, 0.62, 0.76 and 0.9, respectively. Also,

In Equation (1):  γ˙ = 2 [gradV + (gradV )  ] is the rate of

strain tonsor, ω(ωR ) the centrifugal acceleration, 2ωV the

Coriolis acceleration, R the radial coordinate and ω the angular velocity.