Longitudinal dispersion in oblong aerated systems

Longitudinal dispersion in oblong aerated systems

Citation for published version (APA):

Ottengraf, S. P. P. (1980). Longitudinal dispersion in oblong aerated systems. Chemical Engineering Science,

35(3), 697-707. https://doi.org/10.1016/0009-2509%2880%2980020-0

DOI:

10.1016/0009-2509%2880%2980020-0

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Published: 01/01/1980

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Chemad Engineering Sconce Vol 35 pp 687-707

T Pergamon Press Ltd 1980 Pnnted ,n Great Bntam ooO9-2509/80/0301-0697/f,O200/0

LONGITUDINAL

DISPERSION

IN OBLONG

AERATED

SYSTEMS

S

P P OTTENGRAF

Laboratory for Physlcal Technology, Emdhoven Umverslty of Technology, P 0 Box 513, Emdhoven The Netherlands

(Recezved 12 March 1979 accepted 23 May 1979)

Abstract-A scale model study to the flow and mixmg phenomena has been carried out In oblong aeration basms, where a transversal clrculatmg flow of the bquid is introduced by dispersing an along one side of the basin A semi-empmcal correlation of dlmenslonless numbers has been developed, which 1s considered to give a reasonable prcdlctlon of the rate of longltudmal mlxmg Experiments carried out m commercial basms have shown to be m good agreement with the presented model

I INTRODUCTION

In btologtcal sewage treatment the solved and colloidal

pollutions are eliminated by micro-organisms, which are agglomerated m activated sludge floes To provide the organisms with oxygen, air can be dispersed m the aqueous suspension, or aeration 1s cart-ted out wtth rotatmg brushes or surface paddles As a result of these aeration processes, ctrculatmg flows, turbulence and mtxmg are introduced m the aeration basin [l-4] The mtxmg phenomena are necessary m order to keep the acttvated sludge m suspension, to distribute tt throughout the reactor-volume and for promotmg the physical mass transfer processes As a consequence, also longrtudmal mixing IS introduced m the system The advantages of a strong longltudmal mixing m a continuously operating waste water treatment plant are (1) the dlllutton effect on toxic materials or slugs of degradable orgamcs m the mfluent stream and (2) the provlslon for a more uniform physical environment for the blologlcal culture

On the other hand, longltudmal mlxmg IS generally detrimental to the degree of conversion of a contmuously operating process Aeration basins are usually of the order of 3 5-4 5 m deep, 4 O-9 5 m

wide and 30-100 m Iong Generally, an bubbles are introduced mto the hquld by means of perforated plates (e g the Inka system) or by porous tubes (e g the Brando1 system) These dlffusors generally are located along one side of the basin Residence time dlstrtbutlon measurements have shown a considerable amount of back mlxmg [3,4 ]

The obJectwe of this work is a further analysis of the

mlxmg mechanrsm and the clrculatmg flow A semt- emplrlcal correlatton has been developed, which IS considered reasonable to predict the rate of longt- tudmal mtxmg as a function of the extrmslc parameters of the system

2 FLOW PHENOMENA AND MIXING IN THE SCALE MODELS

2 1 Experimental set-up

A scale model mvestlgatlon has been set up for the analysis of flow and mlxmg phenomena

These models consisted of oblong basins with a rectangular cross-sectlon, and at a linear scale of 1 20, 1 10 and 1 5 with respect to the investigated com- mercial basins Air bubbles were contmuously dispersed m water by means of a hortzontal tube, provided with a single queue of equidistant perfora- tions Thts distance was varied from 0 5 cm to 2 0 cm, the diameter of the perforations being vat-ted between 0 3 and 1 Omm The aeration tube was situated along one side of the basin, thus mtroducmg an overall clrculatmg flow m a cross-sectlon of the basin by the hft of the an- bubbles (see Fig 1)

Since the longltudmal rate of mlxmg and the mlxmg mechanism were shown to be independent of the hydraulic load to the basin, all experiments were carried out without liquid feed The rate of longttudmal mlxmg was measured by mlectmg a pulse of a sodium chlonde solution at one end of the basin and determmmg the electrlcal conductlvlty as a function of time at the other end The longltudmal dlsperston coefficient was calculated by comparmg the measured response with the theoretical one [14] (see Ftg 2)

VC

~ = &$ _ exp

-(l - 2n)2

6 4F,

The influence on the clrculatmg flow and the longttudmal rate of mixing of the followmg extrmslc parameters has been investigated the superficial gas velocity vO, the height of submergence H* of the aeration tube and the geometrlcal parameters of the basin

2 2 The transversal cwculatmg flow

By the lift of the atr bubbles an overall transversal

clrculatmg flow IS introduced m the basin The streamline profile of this flow has been vlsuallsed m the (1 lO)-basin by suspendmg polystyrene particles (P,, = 1002 kg/m’) m the hquld (see photographs Ia and Ib)

698 S P P OITENGRAF

Rg 1 Schematlc diagram of a scale model of an oblong aeration basm

1

.’

F -.

I ..

_{-THEORETICAL PATH} 5. *MODEL1 10 B H H' 40 50 32 cm &= 14cmk3 Eax= 26cmh

Fig 2 Measurement of the longtudmal dlsperslon coefficxnt

The polystyrene particles, having a diameter range of 120 up to 200 pm, were lllummated by intensive light sources located behind a narrow split perpendicular to the longltudmal axis of the basin This resulted m an lllummated cross-sectlon, m which the movement of the particles was observed from a dlrectlon per- pendicular to it By measuring the tTaJectorles of the lllummated particles during exposure time local fluid velocities could also be determined from the photographs (see Figs 3(a)-3(b))

From the photographs it was concluded that the clrculatmg flow generally has its centre m the middle of the cross-section However, m case the llqmd height H 1s stgmficantly less than the width B of the basm, the flow profile 1s no longer rotationally symmetric at high clrculatmg flow rates (see photograph Ib)

The clrculatmg flow can be characterlsed by the cn-culatmg flow rate and the time of clrculatlon T, This IS defined as the time a fluid element needs to cover a full circulation m a cross-section of the basm It has been measured by injecting a tracer pulse m the

periphery of the clrculatmg flow and determining Its concentration as a function of time m the plane of inJection (see Fig 4)

If there 1s only one predominant circulating flow, the clrculatlon time r, IS related to the flow rate qE per umt length of the basin according to

BH T, = ~

qe

The flow rate qc can also be compsred with the flow rate Qc calculated from the measured velocity profiles (see Fig 5) From Fig 5 it can be concluded that the flow rate qc calculated from the clrculatlon time 1s generally somewhat higher than QC

From the photographs it will be clear that this IS due to the fact that the effective area for clrculatlon IS somewhat smaller than the cross-sectional area B H However, it may be concluded that the transversal clrculatmg flow rate can reasonably well be estimated from the clrculatlon time T,, which can be measured very easily

Longltudmal dlspersron m oblong aerated systems 699 a -a- %2, - -- ---d,_ _ - n -I. 4 -3 =- . m l m # L p* ‘Q

Photograph Ia Streamline profile of the transversal clrculatmg flow (H=B=4Ocm,H*=30cm,o,=030cm/s,r,=47s)

2 3 Longztudrnal drsperslon coefic rent stagewtse backflow model [3-51 In the further

Tracer experiments have shown that the RTD of the analysis It will nevertheless be started from the mvestlgated basms can best be described by the contmuous backflow model From its more simple

-y _

I__LL__- “+m

Photograph Ib Streamhue profile of the transversal czrculatmg flow (H=30cm,B=40cm,W*=29cm,u0=019cm/~r,=48s)

700 S P P ~ITENGRAF * _:.a t 20 . . N CL) \ $” -,- 0 I ia. _{‘x, ’}

EL

I \ 0 \ *= -t- 25 so’, 76 \ _\ -10,. t ‘% -20..

---

0

::

2s/ 50

I--

r/’ -10 Ai+ -20 I

Fig 3(a) Velocity profile of the transversal clrculatmg flow (H=B=40cm,H*=20cm,v0=038cm/s,r,=62s) -!I_ H 0 25 /so 75 a+

nature this model lends itself better to a physlcal- mathematical descrlptlon m modelhng the up-scaling factors Moreover the contmuous backflow model and the stagewise backflow model converge at increasing Peclet numbers The correspondence between the two models has thoroughly been investigated by Roemer and Durbm [6 J The experimentally deter- mmed dependence of the longrtudmal dispersion

t

I

CONC 1 A

Fig 3(b) Velocity profile of the transversal clrculatmg flow (H=46cm,B=#cm, H* = 15cm,v0=038cm/s,r,=74s)

-TIME-

Fig 4 Determmatlon of the cwzulation time =C

coefficient E,, on the height of submergence H* of the aeration device for the (1 lO)-model 1s shown m Fig 6

From the observed data it appears that

E,,,. )H* 2’3

and that for this particular geometry the gas velocity u0 hardly influences E,, (We shall revert to this influence m more detail m section 3 ) The dependence of E,, on

H* stems from the influence which H* has on the crrculatmg flow rate qE Figure 7 shows the measured relatlonshlp for the (1 1 O)-model

The relation between E,,, and T, 1s given m Fig 8 In these experiments the clrculatlon time z, has been changed by varying both the gas velocity o0 and the height of submergence H*

From the experImenta results It can be seen that for a given geometrical size of the cross-section of the basin, the influence of 11~ and H* on the longltudmal dispersion coeffictent can mtegrally be fully described by =e Furthermore, Fig 8 shows that m the larger basms at low values of the clrculatlon time 5, the longl- tudmal dlsperslon coefficient tends to a constant value

Lon@udmal dlsperslon m oblong aerated systems 701

t 3 TURBULENT _{ENERGY DISSIPATION} DIFFUSION AND

(C%&, ,’

I __

When the clrculatmg flow of the fluid 1s fully ,

I turbulent, mtxmg processes m the fluld are considered r, ’ _, to be governed by e(m2/s3), the mean rate of energy 4’ * +

dlsslpatlon per unit mass of the fluld These dlffuslon , processes take place m the longltudmal as well as m the I _{transversal direction In the transversal direction the} i

* + turbulence field 1s superposed on the mean clrculatmg

200. - I ’ ** flow, and therefore mlxmg m a cross-sectlon of the

‘* *

q,+

/ basin 1s very rapid The longltudrnal turbulent

,;*

‘c dlffuslon IS the Integral effect from all eddies, which

,’ contribute to a transport of mass rn this dIrection

Although the turbulent eddy spectrum extends to a

1.

:

very small scale, the maJorlty of the transport of mass IS

200 440 m

-qc

i-w -

Fig 5 Comparison of the crrculatmg Bow rates Q, and q< determmed from the velocxty profile and the circulation time

respectwely

From visual observations It could be established that this phenomenon 1s due to a disturbance of the clrculatmg flow At high clrculatmg flow rates air bubbles are dragged along with the liquid flow Rlsmg m the vlcmlty of the opposite side-wall of the basin, see Fig 9, they suppress the clrculatmg flow

done by the larger eddies [S] At the small eddy scale, referred to as the Kolmogorov microscale or “inner scale”, velocity fluctuations are smoothed out by viscosity effects To support turbulent motion, energy has to be supphed contmuously to the system to make up for these viscous losses

Via a wide range of eddies with decreasing length scales this energy 1s transferred to be eventually dissipated mto heat Let the eddies which contribute to the Iongltudmal dlffuslve transport have a size A and a velocity ulr then the rate of transfer of energy of these

0;: eddies to smaller eddies 1s proportional to -Y

This energy IS eventually dissipated at a rate E, which should be equal to the supply rate m the steady state Hence [lo]

A vortex has also been formed at this side-wall as a result of the liquid stowage m this region, which results in dragging air bubbles mto the liquid Both effects finally suppress a further increase m the clrculatmg flow rate and with that of E, In some cases even a decrease m E,, has been observed at increased gas velocities 4 E_- A.

(1)

40 _{H B Vo} cm cm cm* l 46 40 36 04640 82 I lb4040 38 / E.X (CnSISl 4 I . c 1 I I I I I I 1 1 I I I I 1 1 6 B 10 20 40 00 -H&n)-

702 S P P OTTENGRAF 600 I 400 qc Wl+, I 200 100 ll6

vo

cm cm cm,,

0’

046 40 38 Q

1

6 8 10 20 40 P - l&In) -

Fig 7 The clrculatmg flow rate (I, as a function of the height of submergence H*

With the foregomg premises the turbulent dlffuslon volumetric air flow rate Q, and the hydrostatrc coefficient 1s given by [7-91 pressure drop Ap,,, of the bubbles If liquid

E _(Ix = a, &If3 x413 ₍₂₎ stowage m the vlcmlty of the bubble street IS relatively _{1 ow, Ahyar 1s given by} where CI~ 1s a constant

E can be calculated from the knowledge on the APhydr = PC g H*

n B

n*vo

‘*

cm 2 050 : sz “v’=:’ 1, *78 81 78 var 046 40 v.r 82 b rs35 33 var war *20 20 19 var I I I - Zc(~~-- I 2 4 8 0 10 20 40

Longltudmal dlsperslon In oblong aerated systems 703

Fig 9 SuppressIon of the clrculatmg flow at high flow rates

and for E it follows that

Substltutmg eqn (3) m eqn (2) yields

H*

=ug g _

H (3)

E,, = a, (% g T)li3 24’3 (4) The experlmental dependence of E,, on u,, for several geometrlcal sizes of the bdsm 1s shown m Fig 10 Up to gas velocities of about 0 5cm/s the relation between

E,, and I+, IS m accordance with eqn (4)

As pointed out before, a further increase m v,, has experimentally shown to suppress the clrculatmg flow rate, as a result of which the longltudmal dlffuslon co- efficient becomes constant From the experimental results presented m Fig 10 it can furthermore be concluded that the nozzle diameter of the aeration

tube-and consequently the bubble diameter-has hardly any Influence, even while thts diameter has been varied by a factor 3-4 The same conclusion can be drawn from the experiments carried out m the two mvestlgated commercial basms the Inka and the Brando1 systems The nozzle diameter of the aeration devices m both systems differs about a factor 25 [13] We shall revert to these experiments below

It may be expected that the mfluence of the size d of the eddies on E,, must be given by a function containing the geometrical parameters It 1s evident that this function has to be determined experlmentally Since the turbulent dlffusron coefficient 1s strongly related to the transversal clrculatmg flow, the hydraulic radius RH = ____ 2BH

2H + B of the cross- section can be expected to play a role m this function By means of trial and error It was concluded that the relation

2413 = & H*‘f3

with

n=+lforBlH n=-lforB<H

described the influence of the geometry of the basin on

E,, m eqn (4) reasonably well

For the several scale models this function changes m Its magnitude about a factor 10, depending upon the basin utlhsed Figure 11 shows a plot of E,,

(uo g g)y3 according to eqn (4) as a function of that geometrical factor for the (1 5)-model with the

704 S P P OITENGRAF

B

z

ratio as a parameter Down to values of a = 10 a

decrease m the a ratlo results m a lmear decrease m

E PX

However, below this value a further decrease in a increases E,, It 1s suprlsmg to note-and this has been verified m lots of experiments-that the pomts return reasonably well to the orlgmal linear path, d the reciprocal value of the a ratio 1s substituted m the geometrical factor for values of a r: 1

The correlation thus obtained, which describes the longltudmal dlffuslon coefficient, 1s

&, = a2

with n = + 1 lfB2H

n= -1 IfBSH

Equation (5) can be transformed mto an equation of dlmenslonless numbers

pe* = a3 Fr* -‘f3

($\“3

(;I”

(6)

00%~ where Pe* = -

E (modified Peclet number) Fr* - gR’

vo2 (modified Froude number) A plot of the observed data m the several models IS shown m Fig 12 The seml-empn-lcal correlation seems good, with a3 = constant at an average of 20

Under normal condltlons, where B u H N H*, It can be concluded from the slope of Fig 12 and eqns (4)-(6), that the macroscale ;1 of the eddies contrlbutmg to the longtudmal dlffuslonal transport must be about 008 of the linear size of the cross- section This value corresponds quite well with the values encountered m other turbulent systems, like fully developed turbulent pipe flow [ 111 and m mechamcally agitated systems [ 12 ]

The correlation given m eqn (6) holds as long as the transversal clrculatmg flow 1s not suppressed by the phenomenon mentioned m 2 3 Exceeding the critical gas velocity at which E,, remains about constant, the path of Pe* IS as shown by the dotted lines m Fig 13 for the (1 lO)-model and the commercral Inka basin

Some observed data are given m Table 1

In Table 1 the observed data have also been given for a commercial Brando1 basin, where the aeration devices are located nearly at the bottom

These data are plotted m Fig 14 (It should be borne

ff* n=+r . n=--1

-

R,& (X)”

Cm%-

1 2 3 4 8

Fig 11 Determmatlon of the influence of the geometrical factor on the rate of longltudmal mixmg m the (1 5)-basin

B

Longltudmal dispersion m oblong aerated systems 705 I IF B>, u= I II *,1 R 4 I)0 100 50 . 4.0 -

(m$y&)”

10’

Fag 12 Plot of the observed data I” the several scale models according to eqn (6) n-+

n=-

In mmd that m this figure the two axes have been expanded by a factor 10 ) It can be concluded that m the Brando1 system the critical gas velocity IS not exceeded and that the seml-emplrlcal relation satisfies quite well

Accordingly, eqn (6) IS consldered to give a reasonable prediction of the rate of the longltudmal mixmg m oblong basins, where a transversal clrculatmg flow of the hquld IS introduced by

dispersing air along one side of the basin However, the determmatlon of the pomt at which suppression of the cn-culatmg flow sets m is a subJect for further study

Acknowledgements-The author would hke to express has thanks to Ir J H A M Rubbens, Ir N H Gerardu and Ir G J M Verbruggen for their contrlbutlon durmg the last year of their course of engmeermg The many fruitful dIscussIons with Prof Dr K Rletema of the same laboratory are also gratefully acknowledged \b=h PZ= E .X

#’

/

d

20- W- _{J+MOOELl 10} OCOMYERCIAL INKA BASIN

Fig 13 Plot of the observed data m the (1 IO)-basm and the commercial Inka basm exceeding the cntzcal gas velocity (The dotted hnes show the expected path at constant E., )

706 S P P O~ENGRAF al, a2, a3 B

E

Izx 002 H It!* L

A&,,

jl

~0% pe* = ~ E ax 1 - I COMMERCIAL SRANDOL BASIN

Fig 14 Plot of the observed data in the commercial Brando1 basm accordmg to eqn (6)

NOTATION

constants

breadth of the basm, m longltudmal dlsperslon

m2/s

Fourier number

modified Froude number

coefficient,

liquid height in the basin, m

height of submergence of the aeration device, m

length of the basin, m

exponent either ( + 1) or (- 1) hydrostatic pressure drop, N/m2 modified Peclet number

clrculatmg flow rate per unit length of the basin, calculated from the cn-cu- lation time z,, m2/s

cn-culatmg flow rate per unit length of the basin, calculated from the measured velocity profiles, m2/s

QS

ar flow rate, m”/s

RH hydraulic radius of the cross-section, m

u. superficial gas velocity, m/s

6, average circulating flow velocity, m/s u1 velocity scale of turbulent eddies, m/s y volume of the contmuous phase, m3

Greek symbols

E rate of energy dlsslpatlon per unit mass of fluid, mZ/s3

R length scale of turbulent eddIes, m pC density of the contmuous phase, kg/m3 P,, density of the dispersed phase, kg/m3

7, circulation time, s

Table 1

REFERENCES

[l] ArdernE andL0ckettT.J Sot Chem Ind 191433523 [2] Murphy K L and Tlmpany P L, J Sanlt Eng Dru

ASCE SAS 1967 93 1

[3] Ottengraf S P P and Rtetema K. J Water Pollut

Corm- Fed 1969 37 R282

[4] Ottengraf S P P, De Ingenreur, Chap 39, (1971) (In Dutch)

Basm (1 IO)-mode1 Inka basin Brando1 basm

L (m) 240 2400 2400 H (ml 040

I

3 40 340 305 340 B (m) 040

I

400 _I 400 H* (m) 0 38 _I 073 3 20 2 85 3 20 vo (cm/s) 030 128 247 4 36 038 095 1 25 1 50 028 028 055 E,, (cm’b) 29 31 38 35 234 235 220 232 583 854 797

Longltudmal dispersion m oblong aerated systems 707

[S] Ottengraf S P P, Paper presented at Symp Chem [lo

React Engng and the treatment of mdustrcal sewage, Cl1

Ziirlch 1973 Cl2

[6] Roemer M H and Durbm L D, I &E C Fun& 1967 6 120

[7] Mlyauchl T, Mitsutake H and Harase I, A I Ch E J [l3 1 1966 12 508

[S] Tennekes H and Lumley J L, A Frrsr Course VI

Turbulence MIT Press, CambrIdge, Massachussetts [I4 1972

[9] Levlch V G , Physrcochemzcal Hydrodymanrcs Prentice

Hall, Englewood Cl& New Jersey 1962

Taylor G J , Proc R Sot (Land ) SertesA 1935 151421

Hmze J 0, Turbulence McGraw-Hdl, New York 1975 Llepe F Mockel H 0 and Wmkler H, Chem Techn

1971 23 231

Pallasch 0 and Trlebel W, Lehr- und Handbuch der

Abwassertrchmh II Wdhelm Ernst & Sohn, Berhn-

Mumch (1969)

Carslaw H S and Jaeger J C, Conductton of Heat zn