14th European Conference on Mixing Warszawa, 10-13 September 2012 COMPARISON OF POWER CONSUMPTION FOR MIXING PROCESS

USING THE NEW CONSTRUCTION OF MIXER WITH THE RECIPROCATING AND ROTATING AGITATOR

Marian Kordas, Stanisław Masiuk, Rafał Rakoczy

West Pomeranian University of Technology, Institute of Chemical Engineering and Environmental Protection Process, al. Piastów 42, 71-065 Szczecin, Poland

rrakoczy@zut.edu.pl Abstract. The main aim of this paper is to present experimental investigations of the influence of the new construction of agitator on the power consumption. The comparison of two kind of movement (rotational and reciprocating) of the non-typical agitator is discussed. Moreover, the synergic effect of reciprocating and rotational movement of this agitator is expressed in the form dimensionless correlation. Keywords: mixing; power consumption; rotational agitator; reciprocating agitator

1. INTRODUCTION The mixing process is very often occurred in the chemical engineering systems. This

process is the subject of many experimental investigations and theoretical considerations. The design of optimal mixer is still an open issue in industry. In many situations the correct knowledge of the power consumption is need for better design and operation of the agitated vessels. During recent years, the studies of power consumption for the impeller-vessels systems of different geometry have been carried out by many research workers. Karcz et al. [1,2], Kamieński and Wójtowicz [3]. Masiuk and Rakoczy [4], Zdghaffari et al. [5] determined the power characteristics for new types of impellers. The results of power consumption for the various types of mixers are collected in the papers [6,7].

An increase in transfer coefficients may be achieved by means of various techniques such as vibration, rotation, pulsation or oscillation in addition to other techniques. Practically, the selected geometrical configurations and the kind of agitator movement may successfully to reduce underside variations of state variables in the specific chemical engineering process. The high shear stress generated by a rotational agitator is the most desirable when the chemical process requires exactly destroyed of the mixed multiphase compact structure. On the contrary, the lower shear stress produces by a reciprocating agitator is particularly important for biochemical processes.

Unfortunately, many aspects of the mixing process are not still explained. One of them is analyzed in this paper where the mixing process characteristics of the new type of agitator are given. From the data available in a technical literature it is clear that the attention has not been focused on the experimental studies of power consumption under the action of this type agitator. The power characteristic for rotating or reciprocating agitators were reported in literature [8,9]. But investigations on power consumption studying the synergic effect of reciprocating and rotational movement of agitator are rare. There is, therefore, a need to

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3456investigate the influence of this problem. The combined effect of vibration and rotation on transfer processes are presented in Refs [10,11]

2. THEORETICAL BACKGROUND It should be noticed that the maximal power input to the mixed liquids may be

generalized by relationships between the adequate dimensionless numbers. Under convective conditions a relationships may be expected of the form ( )Po Ref= (1)

The dimensionless power number, Po, and the dimensionless Reynolds number, Re , are determined by 2Po p wρ= Δ (2) Re wd ρ η= (3) where: d – diameter, m; p – pressure, Pa; w – velocity, m·s-1; ρ – density, kg·m-3; η – liquid viscosity, Pa·s.

3. EXPERIMENTAL DETAILS

3.1. Experimental details The experimental apparatus used for these investigations is shown in Fig.1.

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Fig.1. Schematic diagram of experimental equipment: 1 – vessel, 2 – rod, 3 – bottom hub of

agitator, 4 – agitator, 5 – upper hub of agitator, 6 – rod, 7 – electric motor, 8 – inductive transducer, 9 – ring, 10 – case, 11 – circular cam, 12 – inverter, 13 – inductive bridge, 14 – ammeter, 15 – power pack, 16 – computer

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All experimental measurements are performed using a vertical cylindrical vessel of 0.55 m in diameter and 0.7 m in height. Water was used as the mixed liquids. All liquid properties in dimensionless numbers were evaluated in the mean liquid temperature. The main parts of the mixer are variable-speed drives and electrical instrumentation to measure power input to the mixed liquid.

The electrical method was used to measure the torque produced by the rotational agitator. Detailed description of the procedure for measuring power consumption is appeared in Ref. [12]. The power consumption for the reciprocating movement of the agitator was measured using the hardened steel ring mounted on the shaft. The shaft was articulated eccentrically to the flywheel. The inductive transducer in the ring was used to measure the inductive voltage proportionally to the power input to the mixed liquid. The amplitude of the reciprocating movement of the agitator was adjusted on the scale. The intensity of the mixing of the reciprocating agitator may be controlled changing the frequency of supply current.

The all experimental measurements of the power input to the mixed liquid was realized by using the new type of agitator. The single module of this agitator is presented in Fig.2.

Fig.2. The sketch of module of new type of agitator: 1 – horizontal blade, 2 -vertical blade

The construction of this agitator is allowed to change its geometry during work (see

Fig.3).

a) b) c)

Fig.3. The variation of geometry configuration of the new type of agitator

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3.2. Definition of dimensionless numbers The dimensionless groups (Eqs 2-3) should be adopted to the description of the mixing

process realized by using the rotational or reciprocating movement of agitator. In the definition of the dimensionless Reynolds number should be used the maximal velocity of the blades edge for the rotational agitator and the maximal displacement velocity of the agitator in the reciprocating movement. The diameter of agitator is calculated basing on the comparison of active surface of agitator with substitute diameter to the total active surface of the all elements of the real agitator

Taking into consideration the above assumptions the dimensionless Reynolds and power numbers may be defined as follows (see Table 1). Table 1. The definition of dimensionless Reynolds number

Movement Dimensionless number Definition Numbe

r of Eq.

rotational Reynolds

Rero ro row d ρ η=

where: ro row n dπ= ; 016rod F π= (4)

Power 2Poro ro rop wρ= Δ

where: ro row n dπ= ; ro ro rop P w SΔ = (5)

reciprocating Reynolds

Rere re rew d ρ η=

where: 2rew A fπ ϕ= ; 132red F π= (6)

Power 2Pore re rep wρ= Δ

where: 2rew A fπ ϕ= ; ro ro rop P w SΔ = (7)

Remarks: − 0F is the surface of horizontal blades; 1F is the surface of vertical blades − 2 4ro roS dπ= ; 2 4re reS dπ=

− ( )2 2 2reD d Dϕ = −

− n – rotational speed of agitator, s-1; A – amplitude, m; f – frequency, s-1

4. RESULTS AND DISCUSSION

The dependence of maximal power consumption on the dimensionless Reynolds number is correlated by a well-known relationship. In order to establish the effect of the Reynolds number for the rotational movement of the new type agitator (see Fig. 3) on the maximal mixing power consumption the experimental data obtained in this work are graphically presented in coordinates (Poro, Rero) in log-log system in Fig.4.

The experimental results presented in Fig.4 suggest that the power number versus the Reynolds number may be described by the following relation ( )Po 120 for Re 42000,78000ro ro= ∈ (8)

The relationship between the dimensionless Reynolds and power number for the reciprocating movement of agitator is presented in Fig. 5. In the present report, the power input to mixed liquid is described by the similar relationship between the power number and the reciprocating Reynolds number, that it is proposed in Ref.[12] ( ) ( )1 0.13Po 450000Re 1 0.15Re for Re 135000,720000re re re re

− −= + ∈ (9)

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Fig.4. Power characteristic for the rotational movement of new type of agitator

Fig.5. Power characteristic for the reciprocating movement of new type of agitator

It should be noticed that the synergic effect of rotational and reciprocating movements on

the power number may be defined as follows ( )Po Re ,Rero ref= (10) where Po is resultant power number.

In order to adequately resume all experimental together in a single diagram, it is necessary to choose a three dimensional plot. The resultant power number, Po, is plotted versus Rere and Rero. The comprehensive data representation is shown in Fig.6.

Fig. 6. Comprehensive representation of power consumption in dependence of Rere and Rero

In order to establish the synergic effect of rotational and reciprocating movements on the

power number in the tested set-up, we propose the following relationship 5 4Po 123.5 8.57 10 Re 2.45 10 Rere ro

− −= + ⋅ − ⋅ (11)

The proposed form of Eq.(11), which is shown in Fig.6 correlates data with the approximation coefficient equal to 0.7 (standard deviation of approximation is equal to 18.91).

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5. CONCLUSION Several important conclusions could be drawn from the material presented in this report:

1. The new type of agitator may be successfully applied as the reciprocating and rotational agitator. It is shown that the reciprocating movement of the agitator has the significantly lower of the power consumption than the rotational movement.

2. The influence of the mixing intensity on the dimensionless power number presented in Fig.6 may be very helpful to predict the production costs which are obviously an important element of the economic analyze.

3. It should be noticed that in the selection of the suitable kind of movement (rotational, reciprocating or synergic effect of rotational and reciprocating movements) of the non-typical agitator for the homogenization process is not sufficient taken into consideration only the power consumption. For the comparison of the effectiveness of agitator should be applied the density of mixing energy that it is defined as the product of the power consumption and the mixing time. Therefore, additional investigations of the combined effect of vibration and rotation on transfer processes on mixing process should be carried out in the future.

ACKNOWLEDGEMENT

This work was supported by the Polish Ministry of Science and Higher Education from sources for science in the years 2012-2013 under Inventus Plus project

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