(1a) Eccentric Mixing with a Maxblend Impeller

Various kinds of large impellers, such as FULLZONE (Kobelco Eco-Solutions Co., Ltd.), Super-Mix MR205 (Satake Chemical Equipment Mfg Co., Ltd.), Hi-F mixer (Soken Tecnix Co., Ltd.) and MAXBLEND (Sumitomo Heavy Industries Co., Ltd.), have been developed in Japan. Since these impellers have a high mixing performance over a wide range of viscosities, they are used in mixing, dispersion, reaction and polymerization processes. Recently, their use in the food and pharmaceutical industries is being considered. For agitation in the turbulent region, these large impellers are usually used with baffles to promote mixing. However, baffles often cause problems for washing and sterilization. Furthermore, in the laminar region, baffles are not effective for mixing, and in fact, they often obstruct mixing. Eccentric mixing is one of the traditional methods of promoting mixing in a vessel without baffles. An eccentrically located impeller generates a vertical flow, which contributes to mixing, without baffles. If a large impeller is used at an eccentric position, it is expected that the high performance of the large impeller can be combined with the advantages of an eccentric mixer. In this study, a MAXBLEND impeller was investigated as an example of a large impeller. The power consumption and mixing time of a MAXBLEND impeller were measured under various eccentric conditions. Furthermore, the mixing performance based on the power consumption of eccentric mixing with a MAXBLEND impeller was investigated.

When eccentric mixing is used industrially, we should be concerned about the horizontal load to an agitating shaft. It is expected that the average torque and horizontal load on agitating shaft are larger than in the concentric mixing without baffles. Since these values fluctuate with the rotation of the impeller, the instantaneous maximum value is still larger. The large, fluctuating torque and horizontal load can cause serious problems, such as the falling off of the impeller or the breakage of the shaft, motor, mechanical seal or gearbox. It is, therefore, important to understand the relation between these values and the impeller rotational speed when designing the mixing equipment and determining the operating conditions. In this study, the torque and horizontal load were measured in eccentric mixing using a MAXBLEND impeller, as an example of a large impeller, at various impeller rotational speeds and under various eccentric conditions in a turbulent state. The average torque and standard deviation, corresponding to the amplitude of fluctuation were calculated, and the cause of the fluctuation was investigated by FFT analysis.

Power consumption and mixing time of MAXBLEND eccentric mixing

The power consumption in neat glycerol was proportional to the square of the impeller rotational speed. It was presumed that the flow state was laminar. The change in power consumption with the eccentric length was small. The power consumption at L_E = 0.04 m was slightly larger than that of concentric mixing with baffles. The power consumption in water was smaller than that in glycerol, and it was proportional to the cube of the impeller rotational speed. This indicates that flow was in a turbulent state. When the eccentric length increased, the power consumption increased. The power consumption at L_E=0.04 m was almost the same as that of baffled mixing. In Figure 1, the relation between the impeller rotational speed and the power consumption was shown by the correlation of the Reynolds number, Re (= ρnd ²/μ) and power number, N_p ( = P/ρn ³d ⁵). In the laminar region, N_p of eccentric mixing decreased linearly with increasing Re on a logarithmic graph. The slope of N_p against Re was approximately −1. When L_E was large, N_p was large. The difference between N_p of eccentric mixing and N_p of concentric mixing with and without baffles was small. It was interesting that the power consumption at L_E = 0.04 m was larger than that of concentric mixing with baffles. In the turbulent region (Re > 2000), N_p at L_E = 0.01 and 0.02 m decreased linearly with increasing Re. This behavior was similar to that of concentric mixing without baffles. On the other hand, the values of N_p at L_E = 0.03 and 0.04 m were constant. This behavior was similar to that of concentric mixing with baffles. Since N_p at L_E = 0.03 and 0.04 m was independent of Re, it was presumed from the power consumption that a turbulent state was established throughout the whole of the vessel. In eccentric mixing, since a vortex, which was very large in concentric mixing without baffles, was not generated near the mixer shaft, it was presumed that the generation of a cylindrical rotating zone was inhibited. In this region, N_p of eccentric mixing was clearly larger than that of concentric mixing without baffles (L_E = 0). It was, thus, confirmed that a large amount of energy can be supplied to the mixing liquid in eccentric mixing.

The mixing time was considered a non-dimensional quantity, given by nθ_M. The relation between nθ_M and Re is shown in Figure 2. In the region where Re < 2000, when Re increased, nθ_M decreased. In this region, which was considered to be in a laminar or a transition state, the value of nθ_M of eccentric mixing was smaller than that of concentric mixing with and without baffles. The eccentric impeller generated asymmetrical flow, which promoted mixing. On the other hand, in the region where Re > 2000, the value of nθ_M was almost constant for each value of L_E. This was characteristic of a turbulent state. In this region, the value of nθ_M of eccentric mixing was clearly smaller than that of concentric mixing without baffles. The nθ_M at L_E = 0.01−0.03 m of eccentric mixing was larger than that of concentric mixing with baffles. However, the value of nθ_M at L_E = 0.04 m was almost the same as that of concentric mixing with baffles. Turbulent diffusion dominated nθ_M during mixing in a turbulent state. It was predicted that the turbulence intensity of eccentric mixing would be lower than that of concentric mixing with baffles.

Torque and horizontal load of MAXBLEND eccentric mixing

The torque of eccentric mixing was fluctuated periodically. When the eccentric length L_E, which was distance from the center of vessel to impeller shaft, increased, the average torque increased. FFT analysis showed that the frequency of torque was twice the impeller rotational speed, n, and that an amplitude of fluctuation became large by the increase in L_E. According to CFD, it was found that a large drag force was generated on the blade near the center of the vessel, and the torque had maximum peaks. In eccentric mixing with a MAXBLEND impeller, which has two blades, and since the blades approach the center of vessel twice during each rotation, the torque fluctuates with a frequency of 2 n [Hz]. In mixing with water, the average of torque, T_ave was almost proportional to the square of n. This is typical behavior in turbulent mixing. T_ave increased exponentially with L_E, and the gradients of each n were almost the same. When L_E increases, the speed of blade through the vessel center and working length of drag force increase. Therefore, the torque as a moment increased. The relation between the standard deviation of the torque, T_std, which corresponds to the amplitude of the torque fluctuation, increased with the increase in eccentric length. T_std, particularly increased greatly in larger eccentric length. When T_std was compared with T_ave, each T_std was 15% or less of T_ave at the same eccentric length and impeller rotational speed. In the design of a shaft diameter in an eccentric mixer using a MAXBLEND impeller, it is necessary to prepare larger torque than T_ave based on T_std.

The load in normal – direction (y) to the blade, F_y was fluctuating between plus and minus periodically, and their average was almost zero in both cases. The period of F_y was the same as the impeller rotational speed. The strain gauges for measuring F_y were affixed to the rotational shaft. The period of F_y means that forces in both, positive and negative directions, were loaded on the impeller during each rotation. This corresponded with the blade twice passing the center vessel wall during each rotation. The amplitude of F_y increased in proportion to the square of n. This may indicate that F_y is caused by an unbalanced load on the two blades of MAXBLEND. F_y increased exponentially with L_E, and the gradients of each n were almost the same.

Material strength analysis was performed based on measuring torque and horizontal load of MAXBLEND eccentric mixing. As a result, it was found that the horizontal load has a large influence on the principal stress and stress concentration in the agitating shaft, and that value and period of horizontal load are important for equipment design and estimation of fatigue strength.