PROCESS STUDIES

INVESTIGATION OF HYDRODYNAMICS IN APPARTUS WITH AERATING DEVICES

Vo A. Zaitsev and T. P. Guseva UDC 532.5 541.12.012/.013

One way of intensifying processes in multiphase systems (gas--liquid, gas-liquld-solid) is the use of self-priming aerating devices in reactors. At present, reactors with self- priming devices designed by the Research Institute of Chemical Machinery (Nllkhimmash) (Fig~ i) are widely used in various branches of industry. Aerating devices type N-2 alone are widely used in the microbiological, chemical, and allied branches of industry for obtaining gas--liquid emulsions in semiproduets and dyes, in hydrating and chlorination processes, in prime organic analysis, in sewage treatment, etc.

The principal advantage of using such devices compared with bubbling devices, air lifts, and also mechanical mixing with supply of the gas to the mixer is the possibility of ensur- ing high specific circulation of badly soluble gas, its uniform dispersion and distribution throughout the entire space of the apparatus, and also the fact that a strongly developed interphase surface is created [1-5]. Yet the power required formixing andaeration is29-30% lower than whenother typesof mixing are used [1-3, 5].

However, the investigation of processes of hydrodynamics in t~e liquid phase, in parti- cular the regularities of the change of power requirements for the mixing of gas--liquid sys- tems, has not been treated sufficiently in the literature [1-9]. Moreover, in some cases the data of different authors are mutually contradictory. For instances some researchers use the methods of the theory of similarity for processing their experimental results, other authors derive theoretical dependences with the aid of criterial equations obtained by the methods of dimensional analysis. The equations presented in the literature do not make it possible to calculate the power required for the mixing of gas--liquid systems in dependence on the geometry of the aerating device, the properties of the system, the amount of sucked- in gas, the number of vanes of the aerator~ the effect of hydrodynamic factors, etc.

The present article submits the results of the calculation of the expended power of an aerating device of optimum design. As the optimum design of aerating devices we adopted the design type N-2. Zaitsev [i, 2] gave recommendations for the selection of the optimum ratios of the geometric dimensions of aerating devices: D/d = 2.5-4.0; H/d = 1.5-2.5; ho/d = 0.125; hin/d = 0.3; I/d = 0.25; ~ = 0.0125 d; ~I = 0.015 d, where D is the diameter of the apparatus~ m; d is the diameter of the aerator mixer, m; H is the depth at which the aerator mixer operates, m; h o is the height of the vane at the outlet from the mixer aerator, m; hin is the height of the vane at the inlet to the aerator mixer, m; ~ is the length of the vane, m;

is the optimum gap between the aerator mixer and the vaned guide stator, m; 81 is the op- timum gap between the outer diameter of the aerator mixer and the inner diameter of the stator, m. The outer diameter of the stator Dst is determined from the ratio Dst/d = 1.25.

Figure 2 shows the calculation diagram of the aerator mixer for determining the required power N. The power expended for setting in motion an elementary area df of an aerator vane is calculated by the following formula

~N -- ~ ~dfw3 (1 ) 2g

where ~ is a coefficient taking into account the increase of the jet of liquid in relation to the elementary area of the vane (for the aerator mixer calculated on the basis of constant cross section of the jet of liquid, ~ = i); g is the acceleration of gravity, m/see2; y is the specific force of gravity, N/m3; w = 2~xn is the circumferential speed of the elementary area, m/see; n is the rotational frequency of the mixer shaftj rps; x is the distance from the axis of rotation.

If we substitute the values of the circumferential speed and of the elementary area df = hdx (here h is the height of the mixer vane at the distance x, m) into formula (i), we obtain for one vane [4]

Translated from Khimicheskoe i Neftyanoe Mashinostroenie, No. I0, pp. 13-14, October, 1983.

0009-2355/83/0910-0429507.50 �9 1984 Plenum Publishing Corporation 429

L

~I I . . . . . . . . ~I !

Fig. i. Single-stage aerating device type N-2: i) mixer aerator; 2) starer; 3) diffuser; 4) dividing disk.

Fig. 2.

I_ -r l- ii

Calculatlon diagram of a vane of the aerator mlxer,

z~O y,~ -

o 20 40

/

6g Ng. l . ca l

Fig. 3. Correlation graph of the power for aerating devices types N-2 with different diameters of the aera- tor mixer: x ) diameter of the aerator mixer equal to 0.5 m; 0) 0.7 m; o) 0.9 m: ..... ) calculated value.

dN= ~ (2~t) z xanZhdx

2g

In view of the fact that Y/g = Qmi (here emi is the density of the mixture, kg/m3), we obtain for z vanes

dN = 124z ~ Pmiw~x3hdx. ( 2 )

If we substitute the height of the vane of the aerator mixer

h = h O § ( r e - - x ) ( ~ i n - - ~ ) r o - t i n

at the distance x from the axis of rotation into formula (2), we obtain

dN=124zr (ro--x) (hin--/b) ' ] xndx, ( 3 ) r o - - r i n

where re, rin are the outer and inner radii, respectively, of the mixer, m.

430

If we integrate Eq. (3) from x =rin to x = ro, we obtain a formula for determining the power required by the aerator mixer:

i~ (ro--X) (hin--'h-OJ] x~dx. N = 124z ~p pmin :~ /b-i" (4) r o-- rin J

ri~

The results of the investigations [4, 5] show that the power expended on the hydraulic resistances with developed turbulent flow of a homogeneous two-phase mixture is close to the power expended with flow of such a pure liquid whose density is equal to the mean density of the mixture. Since with intense mixing a gas is distributed uniformly throughout the entire volume [5] and since the size of the bubbles is small compared with the dimensions of the apparatus and the aerator mixer, the gas-liquid system in our case may be regarded as a homo- geneous mixture with mean density

Pmi= ~ ~ @ pl ( l - - T ) , (5)

where eg. QI are the densities of the gas and the liquid, respectively, kg/m~; ~ is the specific volumetric gas content of the liquid, ma/m a.

It is known that the density of the gas is much lower than the density of the liquid, therefore in the calculations the density of the gas may be neglected. Then Eq. (5) has the form

pro/= p/ (I--~). (6)

It should be noted that the specific volumetric gas content of the liquid [5] is equal to the product of the specific quantity of gas sucked in by the aerating device and the time the gas remains in the liquid, i.e.,

where Qg is the amount of gas sucked in by the aerating device (m3/sec) which is calculated by a formula given in [I]; V z is the working volume of liquid in the apparatus, m~; ~t is the time of surfacing (remaining) of the gas bubbles in the liquid, sec.

Taking into account that ~t = H/Vt, we obtain

= (~ /V~) ( H / ~ ) , (7 )

where V t is the surfacing speed of the gas bubbles, m/see.

If we substitute Eq. (6) into Eq. (4) and take into account dependence (7), we obtain the following theoretical dependence for calculating the power required by an aerating device with different geometric dimensions:

. to-- q n J n

(8)

The results of the investigations to determine the power required by aerating devices in apparatuses with a capacity from 0.001 to 125 m 3 and the data calculated by formula (8) are presented in Fig. 3.

Thus the suggested theoretical dependence (8) for determining the required power may be used in the calculation of apparatuses with any capacity, calculated by the suggested for- mula, have been introduced and are now operating successfully in different branches of indus- try.

LITERATURE CITED

i. V.A. Zaitsev, "Self-priming aerating devices of sewage treatment, their investigation and calculation," Trudy NIIkhimmasha, No. 66, 145-152 (1974).

2. V.A. Zaitsev, "Investigation of the operation of self-priming aerator mixers," Trudy NIIkhimmasha, No. 71D 55-60 (1975).

3. F. Strenk, Mixing and Apparatuses with Mixers [Russian translation], Khimiya, Moscow (1975).

4. k. Ya. Sokolov, (ed.), Fundamentals of the Calculatlon and Design of Machines and Appa- ratuses [in Russian], Mashlnostroenie, Moscow (1969).

431

5. K.G. Fadoseev, Processes and Apparatuses of BiotechnoloEy in the Chemical and Pharmaceu- tical Industry [in Russian], Meditsina, Moscow (1969).

6. A.G. Kasatkin, V. V. Kafarov, and M. N. Panfilov, "Investigation of the process of mixing with mechanical mixers in the system gas-liquid," Trudy MKhTI im. D. I. Mende- leeva, No. 24, 413-427 (1957).

7. R.D. Soifer and V. V. Kafarov, "Power expenditure on mixing in gas-~iquid systems," Khim. Neft. Mashinostr., No. 10, 15-19 (1965).

8. E.A. Vasil'tsov and V. G. Ushakov, "Optimum design of turbine-prlmed aerators for the biological treatment of sewage in aerated streams," Trudy Nllkhimmasha, No. 66, ii0- 115 (1974).

9. Yu. S. Zheltukhin and V. N. Ivanets, "Investigation of the effectiveness of self-prim- ing mixers," Trudy Kazansk. Politekhn. Inst., No. 81, 51-55 (1975).

INVESTIGATION OF THE HYDRODYNAMIC CHARACTERISTICS OF A HEAT AND MASS

TRANSFER APPARATUS WITH 100-m s VOLUME

V. A. Burenko, Z. A. Shishkin, V. A. Sabanin, V. V. Krikis, and K. I. Popov

UDC 66.021.3 532.5.001.5

The results of the investigations of physical models of heat and mass exchange apparatuses of different designs, represented in the form of empirical, semiempirical, and criterial equations, cannot be fully utilized in the calculations of industrial apparatuses with large unit power in consequence of the scale factor which, in the opinion of many authors, depends on the hydrodynamic conditions in the apparatus [1-3].

Investigations of the hydrodynamic conditions in pilot-plant and industrial apparatuses are usually impeded not only by the laboriousness and costliness of experiments but also by the lack of instruments for measuring the hydrodynamic characteristics in gas--liquid streams. To ensure that it will be possible to investigate directly the hydrodyamics in industrial apparatuses, staff members of the Irkutsk Research Institute of Chemical Machinery (Irkutsk- Nllkhimmash) designed instruments for measuring parameters such as the gas content ~, specific volumetric surface of phase contact a, the speed of the liquid phase w Z and of the gas phase Wg, and hydrodynamic tests were carried out with a fermentor of lO0-m s volume for the bio- synthesis of lysine.

The fermentor (Fig. 1) is a vertical cylindrical heat and mass transfer apparatus of 3600 mm diameter, 8500 nun high; the filling coefficient is 0.75. For inducing directional internal circulation and removal of the heat of the biochemical reaction, four coils are provided inside the apparatus. The disperser is a distributing disk mounted on the bottom of the apparatus with holes of 5 mm diameter and a free section for the passage of air equal to 7.2%. For more uniform distribution of the hydrodynamic characteristics of the gas-- liquid stream, the apparatus is divided into horizontal sections by six contact disks that have a conical peripheral and a flat central part. The free section of the disks amounts to 14.4%, the diameter of the holes is 5 mm. The working liquid is water.

At the time the apparatus was tested we measured the local values of gas content, the specific volumetric phase contact surface, and the linear speed of the liquid phase, both over the height and the cross section of the apparatus with flow rates of air of 2100, 4200, and 6050 m3/h. To eliminate random errors exceeding the accuracy of measurement of the parameters, not less than four measurements were carried out at each point in steady-state regime with subsequent calculation of the arithmetic mean of the parameter to be determined. The mean integral values of the hydrodynamic characteristics were calculated by the formula

H 2

xav HR t 0 0

Translated from Khimicheskoe i Neftyanoe Mashinostroenie, No. i0, pp. 15-16, October, 1983.

432 0009-2355/83/0910-0432507.50 �9 1984 Plenum Publishing Corporation