(56e) Studies on Ionic Mass and Momentum Transfer with Coaxially Placed Twisted Tape-Disc Assembly as Turbulence Promoter in Circular Conduits

ABSTRACT

Augmentation in transfer processes reduces the equipment sizes, increasing throughputs and operating costs. Various techniques hitherto adopted to obtain enhancements are by the use of

A. i) surface promoters ii) insert promoters iii) swirl generators iv) different geometric

shaped conduits and (v) additives

B. Vibration of the reacting surface

C. Pulsation or rotation of fluid

D. Application of two or three phase flow, and

E. Application of magnetic and electric fields etc.

Among the above, insert promoters are employed with advantages of easy fabrication, operation and maintenance. In recent years efforts are also diverted towards the use of combination of the promoter system. In case of insert promoters the flow fields vary with the shape of the promoter and they are generally complex and are not easily amenable to mathematical analysis. In such cases one has to resort to obtain accurate experimental data, analyze the data in terms of dimensionless groups and appropriately relate them. Twisted tapes and discs are useful insert promoters. In earlier investigations where twisted tapes as swirl generators, discs and string of discs (1,2,3,4,5,6) were employed as promoters, significant augmentation in heat and mass transfer rates were reported.

Studies on the effect of co-axially placed twisted tape-disc assembly in circular conduits on mass transfer rates in forced convection flow of electrolyte have not been reported. Present investigation is therefore undertaken. The study deals with the evaluation of mass transfer rates at the outer wall of the tube flow of electrochemical cell, through limiting current technique, in presence of co-axially placed twisted tape-disc assembly as turbulent promoters in circular conduits. Simultaneously pressure drop measurements are also conducted to obtain the energy consumption.

Diffusion controlled reduction reaction has been chosen for the present study. The mass transfer coefficients are evaluated from the measured limiting currents and the concentrations of the reacting species.

The study covers a wide range of geometric parameters such as pitch of the tape (TP), length of the tape ((TL) , width of the tape (TW) , diameter of the disc (Dd), tape-disc distance (h) and the flow rate of the electrolyte.

The results of the present study reveal that the mass transfer coefficient increases with increase in velocity, diameter of the disc (Dd), length of the tape (TL), width of the tape (TW) and decreases with increase in pitch of the tape (TP) and tape-disc distance(h). Within the range of variables covered in the present study, the augmentations achieved in mass transfer coefficients are 3 to 5 fold over those in case of tube flow in absence of promoter.

The pressure drop data are separately analyzed and pumping power requirements due to the presence of promoter are discussed .

The test section is divided into two different regions depending upon the placement of the promoting elements. The two regions namely are 1) tape-disc region and 2) region down stream to disc.

Tape disc region is an important region as it is the significant part of the test section in which the turbulence is prominent thereby transfer rates. The region down stream to disc is termed as down stream region. In this region the turbulence developed in the tape-disc region is transported and slowly decays along the test section. Transfer rates normally decline rapidly in this region.

The data on momentum transfer were analyzed with R(h+) and roughness Reynolds number (Re+)

The following correlations were developed for momentum transfer

Tape-disc region

R(h+)=3.573 (Re+)0.068 (f1)0.050 (f2)-0.033 (f3)0.012 (f4)0.228 (f5)-0.037

Downstream region of disc in tape-disc assembly

R(h+)=4.632(Re+)0.037 (f1)0.060 (f2)-0.029 (f3)0.005 (f4)0.255 (f5)-0.034

Where f1=TL/d, f2=TW/d, f3=TP/d, f4=h/d,and f5=Dd/d are dimensionless groups,

R(h+)=2.5ln[2h/d)]+Ö(2/f) +3.75

R(h+) is roughness momentum transfer function

Re+ is roughness Reynolds number defined by the following equation

Re+ = (h /d).Re.Ö(f/2 )

where h is distance between tape and disc, d is diameter of tube and f is friction factor.

The data on mass transfer were analyzed with roughness mass transfer function g(h+) and roughness Reynolds number (Re+) in the lines proposed by Dawson and Trass(7).

g(h+), roughness mass transfer function,

= (St/Sto)+R(h+)

Re+, roughness Reynolds number,

= (h/d).Re.Ö(f/2)

R(h+), roughness momentum transfer function,

= 2.5ln (2h/d)+Ö(2/f)+3.75

The following correlations were developed for mass transfer

Tape-disc region

g(h+) = 343.95 (Re+)-0.176 (f1)0.244 (f2)-0.001 (f3)-0.033 (f4)0.402 (f5)0.016 Sc-0.345

Region downstream to disc

g(h+) = 532.48 (Re+)-0.166 (f1)0.254 (f2)-0.014 (f3)-0.022 (f4)0.398 (f5)0.014 Sc-0.424

Where f1=TL/d, f2=TW/d, f3=TP/d, f4=h/d,and f5=Dd/d are dimensionless groups and

Sc is Schmidt number

The data obtained and correlations developed furnish useful information for the design of more efficient electrolytic cells.

Dimensionless Groups:

g(h+) = Roughness mass transfer function = (St/Sto)+R(h+)

JD = Mass Transfer Factor (kL/V).SC2/3

Re = Reynolds number = d.V.r./m

Re+ = Roughness Reynolds number == (h/d).Re.Ö(f/2)

R (h+) = Roughness momentum transfer function = 2.5ln (2h/d)+Ö(2/f)+3.75

St = Stanton number = kL/V

Sto = Stanton number for the conduit with no turbulence promoter

Sc = Schmidt number m/rDL

Sh = Sherwood number kL d/DL

Nomenclature :

d = Diameter of test section, m

DL = Diffusivity of reacting ion, m2/sec

Dd = Disc diameter, m

f = Friction factor = Dp d gc /2LV2 r , for circular conduits

g = Acceleration due to gravity, m/sec2

gc = Gravitational constant.

h = Distance between tape and disc, m

kL = Mass Transfer coefficient, m/s

L = Length of Test section, m

TP = Pitch of tape, m/turn

TW = Width of tape, m

TL = Length of tape, m

V = Average velocity, m/s

Greek letters:

f1 = (TL/d) = Dimensionless group

f2 = (TW/d) = Dimensionless group

f3 = (TP/d) = Dimensionless group

f4 = (h/d) = Dimensionless group

f5 = (Dd/d) = Dimensionless group

r = Density of fluid, Kg/m3

m = Viscosity of fluid, Kg/m .sec

n = Kinematic viscosity, m2/s

References:

1. Algifiri,A.H. and Bhardwaj, R.K.

Int.J.Heat Transfer 128 ,1637 (1985)

2. Evans,L.B. and Churchill,S.W.

Chem.Engg.Progr.Symp. Series 59,36(1963)

3. Venkateswarlu,P.

Studies on Ionic mass transfer with coaxially placed discs on a rod as turbulence promoters

Ph.D. Thesis, Andhra University, Visakhapatnam, India. (1987)

4. Royds,R.

Heat Transmission by Radiation , conduction and convection.

I Edition , Constable and co.,London. (1921)

5. Koch,R.

VDI-FORSH Hft,Series B,24,1-44(1958)

6. Sujatha, V.

Studies on ionic mass transfer with co-axially placed helical tapes on a rod in homogeneous fluid and fluidized beds.

Ph.D., Thesis , Andhra University, Visakhapatnam, (1991).

7. Dawson, David A. and Trass,Olev

Mass Transfer at rough surfaces

Int. J. of Heat and Mass Transfer, Vol.15,pp.1317-1336 (1971)