EFFECT OF IMPELLER TYPE AND ROTATIONAL SPEED ON FLOW BEHAVIOR IN FULLY BAFFLED MIXING TANK

1. Mech. Eng. Dept, College of Engineering, al-Mustansiriya University, Baghdad, Iraq. 2. Mech. Eng. Dept, College of Engineering, al-Mustansiriya University, Baghdad, Iraq. 3. School of Science & Engineering, Teesside University, Middlesbrough, TS1 3BA, UK. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History


The CFD Model and Simulation
The CFD modeling of mixing problem, consist of three steps which are per-processing, equation solving and postprocessing. In first part the problem geometry should be built and meshed. In the second step the partial differential equations describing the flow (Continuity and Navier-Stokes) are discretized on the mesh and solved simultaneously. The boundary and initial conditions should be introduced to the CFD. The turbulence model selected which is describing the effect of turbulence on the bulk flow properties of the fluid. Finally, the obtained results should be analyzed.
The CFD involves the numerical solution of conservation equations. In the present study, the simultaneous solution of continuity and Reynolds-averaged Navier -Stokes (RANS) equations together with the RNG of K-ε turbulent model were carried out using the finite control volume with cylindrical coordinates. The following equations were used in the model:

Continuity Equation:-
The net flow of mass across the boundary of a control volume is zero in steady state flow: , is mass velocity.
Equation (1) can be written relative to cylindrical coordinates as follows: The subscripts z, r and ө are representing to the axial, radial and tangential components respectively. The u , v and w are the components for the time mean velocity in z, r and ө directions respectively, and uʹ, vʹ and wʹ be the corresponding velocities of fluctuation. The continuity equation can be written as conservation of mass equation with the following form: (Joseph 1997), (Ronald 1984)

Momentum Equations:-
The general momentum equations in terms of shear stress τ governing the fluid motion for three dimensions for cylindrical coordinate are [9]: The previous equations of mass conservation and momentum can be combined to form of one general form (Versteeg 1995) For the continuity and momentum the ψz, ψr, and ψө are the total diffusion fluxes defined by:

The k-ε Turbulence Model:-
Jones and Launder had proposed the following equations for both the turbulence kinetic energy (k) and for energy dissipation (ε) [10], for turbulence kinetic energy (k) For energy dissipation rate (ε) 1198 Where G refers to the generation term and is given by [37]: The turbulent kinetic energy (k) and the dissipation rate of the turbulent energy (ε) are chosen as the two properties in order to determine the turbulent viscosity μ t Where: Cµ is a constant. It is assumed that at a high Reynolds number, (ε) value to be Proportional to l k 2 3 , the above equation becomes:- The quantities σk,t , C1 , C2 , σε,t and Cμ that appear in the k-ε model and μt equations, are the universal k-ε model constants, whose values are reproduced in table (2) .

Model Stirred Tank Configuration:-
A schematic diagram of the tank and the impeller is shown in Fig. 1. The system consists of a flat bottomed cylindrical vessel, the diameter (Dt = 0.3 m) of which equals the height of the liquid (H=Dt). Four baffles having width, W=Dt/10 are spaced equally around the vessel. The shaft of the impeller is concentric with the axis of the vessel. The Impeller diameter, Di, equivalent to Dt /3. The distance between the tank bottom and the impeller position C is set to C= Dt /3. The rotational speed of the impeller, N, is ranging from 60 rpm to 135 rpm increasing step 15 rpm, leading to a tip speed, Vtip, ranging 0.314 m/s to 1.05 m/s. The working fluid is water with density, ρ, of 1000 kg/m3 and viscosity, μ, of 1×10-3 Pa.s. The mixing tank as showed Fig.1 was design in depends on the standard configuration as follow: [1], (Georgy 1991). The two types of impellers: Chemineer S-4 and pitched blade impeller as shown in Fig.2, the specification of the impellers are show in table (3). 1199

The Numerical Solution Setup
In the present study, mixing in 21.2 liter of water agitated by three types of impellers. The impellers rotation speeds were ranging from 60 to 135 rpm. The mixing tank model was divided in to 58244 nodes as shown in Fig.3. The MFR method was applied for modeling the impeller rotation. Also the continuity and Navier-Stokes equations together with the RNG version of the K-Ɛ were used to describe the equation of motion (13).

Results and Discussions
The impellers rotation speed has a great effect on fluid motion in mixing processes. Consequently, the efficiency of settling process for the solid material is affected by the changing of impeller rotation speed. Also, the concentration of chemical additives would become more homogeneous when the optimum impeller rotation speed has been correctly selected. The average velocity of fluid is in varied with the radius of the tank. Thus, two poor mixing zones are generated at center of the bottom of the vessel also at the free surface of fluid. The same behavior of fluid is repeated in Sec.30º, and Sec60º but the average velocity of fluid decreases when the fluid motion toward the upper zone of the vessel due there are no baffles existed at those sections. At Sec. 90 degree it is easy to note that the fluid motion is identical with the fluid flow at Sec.0 degree.
In Z-R plane as shown in Fig. 5 at height 0.01m from the bottom of the tank the fluid flow generates a low velocity zone at the center of plane , this zone about 0.085m in diameter. At height 0.1m the fluid velocity is highly fluctuated due to the high influence of impeller pumping capacity as well as the effect of circulation fluid which decrease the velocity of pumped fluid which produces the eddy as explained earlier. The low velocity mixing zone is located between the impeller zone and the tank wall having an annulus shape of inner diameter about 0.038m and 0.24m in outer diameter. The fluid velocity is increased near the baffles with impeller rotation direction is clockwise, resulting in part of the fluid flow toward the upper zone of tank and the rest return to impeller zone with high velocity. The fluid flow changes from highly fluctuated to more moderate motion at height of 0.2m which reflects the effect of rotational motion of impeller. The effect of baffles is quite clear by producing poor mixing zones located between them. The velocity increases as height increased until reached 0.3m height at which the eddies length scale become small and circulated toward the shaft of impeller due to the effect of pumping from impeller.  jets. The small jet is circulated downward to the bottom of tank and then returns to the impeller zone so produces an eddy in the zone below the impeller. The center of eddy is located at radius of 0.103 m from the tank center and 0.064m from the bottom of tank. A Poor or weak mixing region is existed at the center of tank below the impeller.
The second jet of the fluid will be circulated in upward direction, so generate an eddy which is located at same radial direction with lower one but with height of 0.134m from the bottom of tank. The flow pattern will be same at 30º and 60ºplans except the reduction in the fluid flow velocity at the upper zone especially at 30º plan and velocity of fluid near the wall of tank increases in the upward direction. The fluid flow behavior in 90º plan is similar to that observed at 0º plan.

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The mixing time depend on both the fluid flow pattern and fluid velocity, hence the Chemineer impeller produce fluid flow with high velocity and shorter paths than that generates with Pitched Blade impeller thus the mixing equipped with Chemineer impeller is less in time than with Pitched Blade impeller as Shows in Fig. 16.