The Chemical Engineering Journal, 14 (1977) 113 - 118 0 El sevier Sequoia S.A., Lausanne - Printed in the Netherlands
Rates of Induced Aeration in Agitated Vessels D. A. WHITE and J. U. DE VILLIERS Department
of Chemical
and Mineral Processing
Engineering,
The University,
Stellenbosch
(South Africa)
(Recei ved 9 Decemb er 1976; in final form 2 June 1977)
liquid and air to take place, thereby aerating the contents of the main tank. In this configconfiguration the rotor will absorb a given power and will draw in a given quantity Q of air per second. Q can be called the rate of aeration, aerat ion, but both and Q are important in design considerations. The correlation of power power in aerated stirred tanks has been considered elsewhere. Both Arbiter et al. [l] and Calderbank [2] report a correlation of the type
Abstract The paper describes describes a prelimin ary inv esti gation into aeration aeration rates in stirred stirred tank s as function of operat operat ing variables. A tentat ive corre correlat lat ion is proposed for a laboratory aer at or. This is affected affected by th e mode of aeration aeration hich in tu rn is a function of t he physi cal proper ies of th e liquid in th e tan k. The geom geom etry of t he aerat aerat or has an imp ortant effect effect on t he rat rat es at w hich air is sucked int the vessel.
INTRODUCTION
where PO is the power absorbed abs orbed with no aeration at given N and D, is the power absorbed with aeration and Q/ND3 = Ae is the aeration number. Typical results show that P/PO will drop rapidly from unity when Ae = 0 to P/P, P/ P, = 0.5 at Ae = 0.04. At higher values of the aeration number the drop in P/PO becomes less rapid. Other work [ 31 has shown that the power requirements in an aerated vessel are not so simple. simple. Recirculation of air within the impeller can make correlations for power power more complex. Thus P/PO can be lower than predicted by eqn. (1). However, there is a general trend that P/PO approaches constant asymptotic values at high aeration rates. Moreover, it is known [4] that in nonaerated vessels the power number Npo (Pa/ pN3D5) attains a constant value at an an impeller impeller Reynolds number Re in excess of 5 X lo*. The impeller Reynolds number Re is given by pN2D/p where I_( s the viscosity viscosi ty of the fluid in the vessel. From From these considerations it appears that th at at high Re and high Ae in an aerated vessel
Flotation Flotatio n machines, aerated fermenters and sewage digesters are widely used in the process industries. Many of these machines are self-aerated. Other machines employ direct aeration by means means of low pressure air blown into the aerated vessel. The subaerated unit consists of a rotor of diameter D spinning at a speed iV inside a stator assembly (Fig. 1). The rotor and stator are immersed at a mean depth below the surface of the fluid or slurry in the tank. tank. The rotation of th assembly causes a forced vortex to form inside the stator, which enables mixing of Air
in
ROTOR
NP = -
pN3D5
Fig. 1. Aeration of a stirred tank. 113
= constant
(2)
114
This conclusion is supported by Rind [ 51 for a series of commercial flotation machines. The aeration flow rate in these machines and similar equipment is also an important important parameter. However, less seems to be known about this than about the power requirements. Arbiter and Harris [6] suggest that optimal flotation performance is obtained in set of similar machines if the aeration number is held constant. It is apparent, however, that in a self-aerating machine the volume of air drawn into the rotor will itself depend on the operating parameters. Expressing this idea in terms of of dimensionless quantities, the aeration number will depend on the cell Froude and Reynolds numbers and in machines of different design geometrical size ratios will also appear in the correlation. To make some progress with this problem it is assumed that at high Reynolds Reynolds numbers the aeration number is only dependent on the Froude number, as is the case with the power number of a stirred vessel at high Re. It is the purpose of this paper to make some observations on obtaining aeration correlations with liquids in a laboratory aerator.
THE ROLE
OF THE
R O T O R -S -S T AT AT O R
IN
AERATION
It is the practice in some flotation plants to control aeration rates by blowing low pressure air through the machines as shown in Fig. 1. The role of this step is to aid the rotor overcome the main resistance to aeration, which is due to th thee hydrostatic head pgh of the fluid above it. Increasing the applied pressure A across the air inlet of the machine results in an increase in aeration rates and a reduction in the net hydrostatic head across the rotor. This reduced hydrostatic hydrostatic head h, is given by
h,=h-i?
Pg
of immersion hR as well as on the rotational speed of the mechanism. Thus the aeration rate Q will be a function of N, g, and h, hence Ae (= Q/ND3) will be a function of the Froude number and a geometrical constant h,/D (hR = for self-aerating machines). A formulation of the Froude number in the following form has some advantages fi=-
N’D” (4)
It is possible to see how this definition can be used to determine the point of onset of aeration in a flotation machine, which occurs at a certain critical speed N,. At this particular speed the rotor will develop a pressure drop across the forced vortex. This pressure will depend on the speed of the rotor and its diameter as well as on the the density of the fluid in the vortex, which will be devoid of air bubbles at the point of onset of aeration. Dimensional considerations give V = kpN,2D2
(5)
When this vortex pressure drop is equal to the equivalent hydrostatic head pghR, a slight increase in rotor speed will cause aeration to occur. Equating the two pressures gives pgh,
=
pN 2D2
Thus the value of the Froude number Fr, at the onset of aeration is given by N2D2
F&=2-
&a
=-
(6)
and will be a constant constant for a given rotorstator system. Thus T hus simple considerations initially indicate that the correlation for the aeration number can be formally written (7) subject to the condition that Ae = 0 for Fr < Fr,-
Conversely if the depth of immersion of the impeller in a self-aerating machine were reduced, the aeration rate obtained in the unit would be correspondingly correspondingly increased. It is the practice in many plants to control pulp levels carefully where self-aeration units are employ-
In order to test some of the ideas developed in the previous section an experimental laboratory aerator was constructed. The
tion cell will depend on the equivalent depth
tion consisted of a stator and rotor as shown
EXPERIMENTAL
115 Airtight
seal
TABLE 1
Tap water 0.1% Teepol solution Glycerine solution no. 1 Glycerine solution no. 2
Viscosity
Surface tension (N m-l)
(N s m-l)
6.01 3.03 5.18 5.59
1.00 1.00 9.36 3.11
x 1o-3 x 1o-3 X 1O-3 x 1o-3
RESULTS
V-844
Fig. 2. Diagram of the experimental apparatus (dimensions in mill imetres).
in F ig. ig. 2. 2. The dimensions dimensions n th e sketch a re in millimetres. The sta tor was made f a Perspex tube and it was sealed to the top shaft with an airt ight ight seal. This was made f two eram ic pressu re seals which which were wa ter lubricated. The rotor t ur ned in two airt ight bearings which which were mount ed n either side f th seals, Sixteen evenly sp aced vertical slots were ut into th e bott bott m par t f th e sta tor, as shown, to allow for aeration. The rotor onsisted f an upper t apering shaft with with two rubber impellers from a peristaltic pump. Each had twelve vanes and was 56 mm X 30 mm in size. size. The The speed of t he sha t was measur ed with with a hand t achomete achometerr and the air low low rat was measu red with with a soap soap bubble meter m ade f a glass tu be 50 mm in diam eter with a tr ap downstream to prevent soap getting into the aerated tank. The assembly was driven by a variable speed drive via a rubber vee-belt. Fina lly th e pressur e f t he a ir inside th e sta tor stand pipe was measured. The stator and rotor were en closed closed in a large cylindrical cylindrical glass jar 290 mm in diameter and 430 mm high that contained liquid. Tap water, glycerine-water and TeepolTeepol-water water solut solut ions ions were used in th experimen ts . The dens ity of of the glyc glycerine erine solut solut ions ions was measu red to det ermine t he composition composition an d hen e th e solution viscosity. viscosity. The surface tensions of all fluids used in the experime experiments nts were measured using a thin plate hoop hoop at ta hed to an analytical analytical balance. balance. The hoop hoop was leaned between between experiment experiment s a nd sta nda rdized using pure benzene. benzene. The surfac tension tension measurements and th e cal ulated viscosities are shown in Table 1.
Runs were carried out with these solutions usin g rota tion speeds varying from from 7 to 19 rev s-l an d for for imm ersion dept hs of of 89 184 mm. In one case a set of of ru ns was car car ried out out with a positive positive pr essure applied applied to th e air inlet to test the usefulness of the reduced hydrostatic head concept. concept. For each set of ru ns th e speed of the rotor was gradually increased until the point of onset of aer at ion ion was rea ched. The ritical speed NC was recorded recorded and th e onset Froude n umber Fr , was alculat alculat ed. Owing to an inst ability ability in the dr ive mecha mecha nism N C was somewha t diffi diffi ult to mea sur e. However However for the present set of data Fr, was reasonably onstan t with a mean of of 0.230 and a sta nda rd deviation f kO.022. It is concluded concluded th at th ese resu lts confirm confirm th e validity of of t he oncept oncept of a ritical Fr ude n umber r aera tion. The maximum experimental Froude number btained in these experiment experiment s was about about 2.0. 2.0. It was also alculated alculated tha t th e minimum Reynol Reynolds ds num ber u sed in in these test s was 1.6 X lo6 lo6 or water an d th e TeepolTeepol-wat wat er solut ions a nd 1.6 X 10’ for for t he more viscous viscous glycerine solution. Maximum Reynolds nu mber s were 5 X 10’ an d 5 X lo4 res pectively. Data indicate th at baffled baffled impellers may be expec expected ted to opera opera te in a regime where th e power power num ber is nst an t and indepenindependent of Reynolds Reynolds n um ber in in cond cond itions in which t he lat ter is in excess excess of 104. For these experiments it may therefore be expected tha t aera tion performa performa nce, like power power requ iremen ts, is un affec affected ted by fluid fluid friction. friction. The data for for ru ns with wat er are plott plott ed in Fig. 3 for for several diffe differen ren t values of hR /R r ne series f r un s with with assist ed aera tion. tion. In th e last case a positive positive pressur e was applied over the agitator. The data in Fig, 3 are plott plott ed with th e logarith logarith m of of Fr - Fr, a abscissa abscissa an log,, as rdinate:
116
lOg,o(
Fr FL-)---C
Fig. 3. Results for aeration in clear water: A, ordinary runs; assisted aeration.
(8) A reasonable straight-line correlation of the data was obtained with M = 0.0231 (Fr - I?+84
-0.5
- l , o
logro
(Fr- Fr,
Fig. 4. Results for aeration in solutions.
Fig. 4 correlates the data for increased increased aeration under conditions conditions of significant significant gas holdup as M = 0.0977 (Fr - Fr,)2.33
(9)
For all the clear water results it was noted that the height of the water in the tank remained steady st eady as the aeration rate increased. This indicated that there was little hold-up of bubbles within the tank and that these rapidly rose to the surface. surface . No measurements of bubble sizes were were made in the present pres ent series of experiments experiments but a comparison between the results for water on the one hand and for the glycerine-water and Teepol-water solutions on the other showed that at higher Froude numbers much finer bubbles were produced in aeration of the mixtures. For the glycerine and Teepol solutions very fine bubbles were noted in the tank, and the fluid became quite opaque. The level of the fluid in the tank rose quite noticeably and a froth level built up on the top of the liquid. It is obvious that considerable considerab le hold-up of gas was occurring within the liquid. Under these conditions it was was noted that there was considerable increase in aeration rates compared with the water data for the same Froude number. These results are shown in Fig. 4. The data do not not correlate as well as the water results but some of the data at lower Froude numbers correlate with water results (Fig. 4, line A). A). It was was qualitatively noted that these particular runs did did not show appreciable appreciable air hold-up and that the aeration process was similar to the results for water, Line B in
(10)
It is clear that that the production of fine bubbles and the inhibition of coalescence coalescence within the bulk of the fluid are the reasons for the appearance of significant hold-up in the bulk of the tank itself. Both the added viscosity and the increased increased effect of surfactan& brought about by adding either glycerine or Teepol to t o the water will clearly retard the motion of fine bubbles. This concept is clear and obvious. However it does not account for the increase increase observed in in aeration rates under these conditions. The answer to this question lies within the rotorstator assembly itself. Within the confines of this assembly assembly there is a powerful centrifugal force. Liquid and water are mixed and the air bubbles flow through the stator with the liquid; the rotation of the agitator also acts to mix the liquid itself. A centrifugal force field is similar in its effect on bubbles in a liquid to other field forces such as gravity. In a gravity field bubbles will move upwards against the force and in a rotating system a bubble will move inwards inwards against the centrifugal acceleration. In the rotor-&&or rotor- &&or system of an aerated vessel the flow of liquid outwards from the rotating shaft will counter the tendency for bubbles to move inward. The bubble size produced in the rotor is important. The smaller the bubble diameter the greater will be the effect of the liquid viscosity on it. A small bubble will consequently consequently move out of the stator more
11
rapidly than a larger one. Thus in i n a glycerinewater or Teepol-water mixture the inhibition inhibi tion of bubble coalescence brought about by either an increased viscosity or the presence of surfactants surfactant s will result in the formation of smaller bubble than would be found in the aeration of pure water under the same conditions. The result of this is the production of finer bubble which is less affected by centrifugal force and a consequent increase in aeration rate. In addition additio n to affecting h/D it is obvious that the design and geometrical geometrical configuration configuration of the rotor-stator unit will have an important bearing on the rates rates of aeration within the tank itself. Qualitative work was also carried out on the change in aeration rates caused by varying the geometry of the stator. In these runs the impeller depth was kept constant at a value h of 0.106 m. In the first series of runs alternate slits in the rotor were covered covered with masking tape. The results are given in Fig. 5. The aeration curve with the normal impeller is given by A in the figure; with half the slits slit s blocked off the aeration rate drops markedly, markedly, as the results show (Fig. 5, curve B). A second alteration was made to the stator: baffles about 5 mm wide were stuck inside midway between all the vertical vertical slits. The The idea behind this innovation innovation was to catch bubbles bubble s and force them out. However, the insertion of baffles causes cau ses dead areas to form on the inside surface of the rotor and this further reduced the aeration rate to the experimental values given in Fig. 5,
curve C. In addition, additio n, the bubbles were physically observed to be much finer with the baffles inserted. Thus the geometrical design of an impeller has an important bearing on the performance of an aeration machine.
CONCLUSIONS
The following conclusions are suggested sugges ted by this present work. (1) Aeration in a flotation or similar machine will begin once the Froude number has exceeded a critical value. (2) A correlation has been proposed which fits the data for aeration in water with varying Froude numbers and with varying varying depth of immersion of the rotor. (3) Increasing the viscosity of the solution or introducing surfactants can lead to an increase in aeration rate. Correlation of aeration under these circumstances circumstances is not as accurate. It is clear that this paper represents only an initial initia l statement on a complex problem and more work will be necessary. There are two aspects that need further study. Firstly the runs with the present apparatus should be extended to the study of aeration in slurries with and without the addition of trace amounts of surfactants surfactan ts and secondly work should be carried out using larger aeration machines.
ACKNOWLEDGMENTS
We are grateful to Mr. P. van Reenen who constructed constructed the apparatus and to Mr. P. Smit who helped with some of the experimental work.
NOMENCLATURE
Ae Fr J%
hrt Fig. 5. 5. Aerat Aerat ion ion in clear clear wat er with various rotor geometries.
Q/ND3, aeration number rotor diameter, N2D2/ghR, Froude number critical Froude number gravitation constant, m K2 mean rotor immersion depth, m A /pg, corrected rotor immersion h depth constant
118
(Q/ND3) (D/ha)1/2, modified aeration number rotor rotation speed, rev s-l critical rotation speed for the onset of aeration, rev scell power number during NP P/pN3D5, aeration NPO Po/pN3D5, cell power number without aeration cell power drawn, W cell power drawn without aeration, PO rate of aeration, m3 s-l ND'/p , cell Reynolds number Re Greek
symbols
pressure rise across the air inlet manifold, N rnd2
P
fluid viscosity fluid density
REFERENCES N. Arbiter, Arbiter, C. C. Harris and J. Staninger, Trans. Sot. Min. Eng. AIME, 229 (1964) 70. P. H. Calderbank, Trans. Inst. Chem. Eng., 36
(1958) 443. K. Vant’riet, J. M. Boom and J. M. Smith, Trans. Inst. Chem. Eng., 54 (1976) 124. J. H. Ruston, E. W. Costich Costi ch and H. J. Everett, Chem. Eng. Prog., 46 (1950) 395; 467. P. Kind, J. S. Afr. Inst. Min. Metall.. 76 (1976) 345 362. N. Arbiter Arbiter and C. C. Harris, Harris, Trans. Sot. Min. Eng. AZME, 244 (1969) 115.
