ML082530372
| ML082530372 | |
| Person / Time | |
|---|---|
| Site: | Vermont Yankee  |
| Issue date: | 07/23/2008 |
| From: | Patrick M, Tagg D, Wragg A Univ of Exeter |
| To: | NRC/SECY/RAS |
| SECY RAS | |
| References | |
| 06-849-03-LR, 50-271-LR, Entergy-Applicant-E4-22-VY, RAS M-337 | |
| Download: ML082530372 (7) | |
Text
/ 2 ~ks H-3392 HEAT AND MASS TRANSFER DOWNSTREAM OF ABRUPT NOZZLE EXPANSIONS: IN TURBULENT .FLOW .4S By D. J. TAGG, M. A. PATRICK, (ME.J.v.) and:A.. WRAGG At
Deartment of Chemical Engineering,
University of Exeter Axial local wall mass transfer distributions have been explojed downstream ofthenozle plane for 'cirlar Jets injected into axisymmetric circular ducts using the limiting electrolysis diffusion current technlque. ByW uing the Chilton-Colburn analogy the data for eak mass0transfer 1 rate were shown to be correlated along with indqendent heat transfer data by the equation Sh = 0.27R e _ SCO.' thus demonratng the. u ue of the t"ecie the modelling of redircuilating flow beat transfer Situatio.ns. Additionallyi, investigations of the relationship between mass transfer distribution and recirculation zone hydrodynamics have been made.
INTRODUCION (LDCT). Costellos made: use.of the copper deposition reaction for two, expansion :ratios ,.of 3: 4 and 3 :.8.
Significant enhancement of heat and mass transfer The, various large cathodes used, yielded only indirect rates generally occurs when fluids are transported information on the magnitude of, local transfer rates.
through sudden enlargements in pipe or duct .cross-Runchato employed, the .cathodic reduction of ferri-sections. The increased transfer rates arc associated with cyanide ions on nickel for an expansion ratio of 1 :2.
a region of flow separation and recirculation extendinga over a range of Schmidt number from 1400 to 2500.
-few duct diameters downstream of the plane--'of Although the measurements were mad with small enlargement. - ,. / "local". electrodes, the active cathode area within which The above situation arises frequently in engineering these were embedded only covered a part of the re-practice, notably in the process industries, and is of circulation zone. and thus there is. some doubt as to the special importance in the design and operation of high state of development of the mass transfer boundary throughput combustion systems. In this .case the total layer in -the region within which the results were heat-transfer is by a combination of radiation and obtained.
convection and in .high velocity separated flows the It should be noted that, in these previous studies, the.
contribution of forced convection can become appreci-abrupt changes. of section have sometimes been formed able. An important mass transfer application is found in using contoured nozzles, while in other cases simple the.design of entry sections for electrochemical reactors.
pipe expansions have been employed. Detailed differences in results between these situations may be expected due PREVIOUS WORK to the different velocity profiles and turbulence structures of the flow in the plane of expansion.
There have been a. number of in*vestigations of heat The present study has endeavoured to produce well-and mass transfer in ,xi-s_,n*nric pipe expansions in characterised conditions for the flow into the expansion.
recent years. Ede et ai'U zadez a comprehensive study section by the use of standard nozzle shapes which give of. heat transfer to water under conditions of constant flat inlet velocity profiles and fairly low initial turbulence heat flux with the upstream or the downstream levels. The LDCT has been employed to provide true-duct surfaces, or both, as active transfer area. Other local measurements of mass transfer within and near the workersO-4-s have made similar measurements using air recirculation region ofthe axisymmetric sudden expansion or water as the working fluid but with. only the down- .over a. wide range of expansion ratios. However, a stream section heated. Krall and Sparrow4 used orifice detailed description of the influence of initial flow nozzles, to -provide flow separation and worked over a structure on the flow development for a series of different range of equivalent large to small duct diameters (Did) inlet geometries is :outside the scope of this work and of 1.5. to 4. As an alternative to these studies employing will be left for a further investigation.
electrical. heating, Louise$ -used hot air together with
'watdr-cooled calorimeters along the duct wall, so approaching the constant temperature situation.
EXPERIMENTAL -
Mass transfer measurements for flow through axi-symmetric sudden expansions have employed two main The use of tle lim"iting "diifluii ciiicrent technique of techniques. Read, made measurements, for large. mass transfer measur'ement *iýaariktyrf (low situatios*
diameter ratios, using the sublimation of naphthalene in is well documented 0 '-. The ý% present' investigation-,
air, while other workers" 9 haye used the more accurate employed the c*tlhodic _reduction of, ferricyanide-ions,at electrochemnical "limiting diffusion current technique" nickel. electrodes. The elect0o1yte wa'snmade up to U)"NI 0046--9858J79/03'0176-06 $02.00;."
@ Institulion of C.hcmical Engineers , --
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OFFERED by. aQnLicenseeIrvenor IDENTIFIED o 1n3L Witness/Panel. E C- t ActonTaken: , R REJECTED WITHDRAWN Pfoortr/cler * *.---
- in NaOH with an equimolar K3Fe(CN)6 /K 4Fe(C]N)G -from a reservoir using a centrifugal pump which mixture of concentration 0.005MN. Under limit ing circulated the fluid through a rotameter bank and control current conditions the mass-transfer coefficient was gi,ven valve system to the test section and back to the reservoir.
by the simple expression Precautions taker, to prevent -deterioration of the (1) electrolyte during the test programme included the K = idzF,4cb exclusion of ultra-violet light and the use of a nitrogen Figure 1 shows the main electrode assembly wh ich blanket over the liquid in the reservoir to prevent was manufactured from a 50 cm, long piece of 5.22 cm oxidation. Regular checks on the concentration of the i.d. nickel tube split longitudinally to provide separ 'ate ferricyanide ion in solution were made using a spectro-anode and cathode portions with an area ratio of photometer.
approximately 2: 1. The smaller segment forming cathode was electrically insulated from the anode means of a neoprene gasket and the whole arrangern carefully clamped together to form the downstre portion of an axisymmetric sudden expansion..
Local cathodes I Main cathode
\ 4one bAnode
\Nozzle block Figure 1. Schematic cell assembly.
One theoretical disadvantage of this arrangement is Figure 3. Instrumentation.
that the system is not symmetrical about the centre line since mass transfer" boundary layers of different The simple electrical circuit shown in Figure 3 was characteristics will develop- on the anode and cathode used to obtain the values of limiting current corre-surfaces. However, due to the very thin layers obtained sponding to the particular mass transfer rate for a given with the high Schmidt numbers involved, interaction. flow condition. Periodic checks were made to test the with thermain flow will. be small and, in the absence of validity of the assumption of diffusion control but for swirl, errors due to .disturbances at the cathode/anode all runs limiting currents were obtained with the applied boundary will be negligible. potential between anode and cathode at 0.8 V. In The cathode segment was fitted with "point" electrodes obtaining local .mass transfer rates, the main cathode at intervals of 12.2 mm and in a staggered formation. surface was held at the.same potential as the "point" These were formed by epoxy-cementing 1 mm diameter electrodes, relative to the anode, using a stabilised nickel wires into 1.4 mm rd42.eter holes drilled at power supply. The fluctuatingcurrent from a given small intervals along the length of :-t =athode. and machining electrode was converted to a fluctuating voltage using the protrusions flush with the inside wall. This method a simple solid-state amplifier. This voltage was then provided sufficient thickness ef electrical insulation to time-averaged using a resistance capacitance network give local mass transfer ".zL+/--* .-.in a large active area and the result read on a multi-range voltmeter.*
without significantly disptm- .n-he developed concen- Throughout the series of experiments the temperature tration layer on the main electrodeP. was maintained at 20 + 1 *C for which the corresponding The abrupt expansion was formed, by inserting, into physical properties of the electrolyte were the main tube, a perspex nozzle block with the nozzle contours shaped to a standard ASME long-radius p--.1.02gcm"-, /A= 1.05x 10- 2 gcm-'s- 1, profile. A series of interchangeable nozzle inserts gave .= 7.09 x 10-- cm 2 s-'
expansion ratios of 2, 3, 4, 6 and 10. As shown in giving Sc 1450. The Reynolds. number, based on the Figure 2, electrolyte was supplied to the test section downstream duct diameter D, was varied over the range Aspprooch A" Electrode PVC exit 1900 to 23 000. Prior to each set of runs, the electrode Flow nozzle Redu cItio.i no1z.C section jI section surfaces were polished with progressively finer grades of straightentr I.q-5 emery paper ind finally degreased with carbon tetra-chloride. It has been suggested14 that this provides 'an equivalcnt pre-treatrnent to that of adjusting the potential to give hydrogen evolution at the surface. In the present work, no noticeable influence on the results was found when using electrodes activated in either of these ways.
A further electrochenical experiment was carried out in order to investigate the length of the recirculation Figýure 2. Shcrnatic flow circuit. zone. This involved the use of a specia.l "sandwich" Trans lWheniil., Vol. 57, 1979
'3
Flow direction 2 *tTterential Cathodes l-SmimlSmmin mplf ier 1 12 A e output Figure4. Detail of sandwich electrode.
Ko
¢IM S-_
wall electrode (Figure 4) similar to that of Son &
Hanratty"5 which could be positioned at various distances downstream of the plane of enlargement by means of a sliding tube arrangement. 'The sandwich electrode was sensitive to the flow direction adjacent to. the wall in .-2 t1hat the "upstream" electrode of the pair always gave the higher reading, thus clearly indicating- the mean local flow direction. The reattachment point was indicated when the differential output of the electrode pair dropped to zero. In addition, a I mm diameter nickel wire wasset into the wall in the manner described previously at an identical downstream distance to the sandwich electrode. Operating this electrode as a cathode under diffusion control conditions, it was possible to investigate the axial distribution of mass transfer to a 0 3 4 5 .6 7 small active zone surrounded by an inert surface. In this case, the growth of the concentration boundary layer starts at the leading edge of the test electrode and due to its small size this does not result in the establish-ment of a fully developed profile. Runchalg has reported FIgure 5. Mass transfer distributions: 1: 3 expansion ratio.
that the mass transfer distribution is influenced strongly
- 21 700 .0 16900 0 10125 by the boundary conditions, i.e. whether the electrode
- 8150 0 4940 v 3375 is surrounded by an active or an inert surface. U 1985 ReD values
-"RESULTS .AND DISCUSSION Local M4ass Transfer Profiles Figures 5 and 6 show examples of the de'ailed variation of mass transfer coefficient along the duct wall down- K stream of the plane of enlargement for the I : 3 and I : 10 1002 expansion ratios, Included on each of the graphs, for comparison purposes, are asymptotic values for fully developed mass transfer in turbulent pipe-flow as predicted by the Dittus-Boelter equation:
Sh = O.O23ReDnas SO" (2)
For all the expansions tested, the mass transfer rate incrcased to a maximum value within a few duct diameters of the plane of enlargement and then decayed slowly toward.N the predicted fully developed value. These mass transfer profiles are very similar to those obtained by other work-ers", 2, 3,I and confirm that the region prior to the peak in the transfer rate is also subject to mass Figwrc 6. Mass transfer distributions: I : 10 Expansion ratio.
transfer in excess of that expected for fully developed A 5880 -S 4930 = 3375 Re,)vales flow. A 1985 ýO 1545 L _ 79 5 v Trans IChemE, Vol. 57, .1979
£'nrl..~.~£ *~t~lN3I tI~. £ i7 1)7 i" t~t1L~
Peak Transfer Rates results and those of Krall and Sparrow for heat transfer In Figure 7, the ratio of the measured peak Stanton plotted as peak Sherwood/Nusselt number against the number to the fully developed value is plotted as a nozzle Reynolds number. A one-third power- on the function of Reynolds number for each nozzle arrange- Schinidt/Prandtl number is seen to reduce both sets of ment. This illustrates the increase in mass'transfer rate datato a single line, in accord with the Chilton-Colburn at constant Reynolds number ReD for increasing analogy, the equation being expansion ratio corresponding to the higher jet velocities S/i = 0.27Reý;067 SCO-33 (3) involved. It can also be seen that the relative mass transfer enhancement increases with decrease in Reynolds The good agreement. between these two sets of data for number. such widely differing fluid property numbers illustrates the applicability of the LDCT approach to heat-transfer modelling. However, it I;s interesting to note that if the o01*10 1:6 1 present data are plotted alone they are better fitted by a
.13: 0.6 power on ReN, this value agreeing with that suggested st._lox 20 12.
V by Spaldinge for separated flows.
Stf.d. A 10
,'Relation of Peak Transfer Position to S* r~eiln~ntinn 7nn* T~rnnth 5 Se*-o -.- . The positions at Which the peak transfer rates occur in
-A. Figures 5.. 6, and. the rest of the data are in good agree-ment with those determined by Runchal and by Krall and Sparrow, though somewhat shorter than those obtained by Ede, where the nozzle to peak distance was
%:W 6z 2 approximately equal to the product of the expansion 103 2M103 5,403 I°' _ 2404 54e ratio and downstream diameter. In the present work the ReD location of the peak can be seen to remain sensibly Figure 7. Ratio of peak to fully developed Stanto.n number as constant for the higher expansion ratios at a given a function of Rej. Reynolds number and to drift upstream as the Reynolds number is increased.
II In order.to apply electrochemical modelling techniques toheat transfer situations, account must be taken of the wide difference in property number which may be involved. The mass transfer experiments are characterised .I "1 Output from sandwich electrode I
by high Schmidt numbers while. in heat transfer il'. I applications the Prandtl number may be of the order of I I
. - ~t. -
unity. The analogy between heat and mass transfer is .WI I 2 3 ' 4 often expressed through relationships such as the .1I-Chilton-ýColburn equation in which the property I I iI I
numbers are raised to a two-thirds power. Previous III' experimental work 1 ,1' has confirmed this value for forced convection systems -similar to that in the present8 study, though more recrat wo_-: by Shaw and Hanrattyi Figure 9. Output from sandwich electrode. 1 :3 Expansion suggests a different value. FAgure 8 shows the present ratio, ReD 110000.
A typical output from -the sandwich electrode for the 1: 3 expansion is. given as Figure 9. Results of the 0 determination of the length of the recirculation zone Correlation of peak from such readings are shown in-Figure 10 for the range transfer rates of expansion ratios and a Reynolds-number dependency can be seen to exist. The recirculation zone length is l0? markedly greater than the distance from nozzle to peak transfer position which is also indicated on Figure 10.
Examination or Figure 9 reveals a further interesting o' Present (Scv145ý_ feature, namely the existence of a second stagnation o Krall-Sparrow6 7 point closer to the plane of enlargement. This provides ShSc=O-M27iR : firm evidence for the existence of a secondary,. smaller recirculatiun zone immediately downstream of the I. A ....
. . I N
JI renlargement as has been suggested by A-bot and Klein as a result of flow visualisation studies on a two-dimensional step'9 . A single mass transfer profile ReN obtained with the local electrode surrounded by inert Figure 8. Correlation of peak transrer rates. surface has been included for comparison in Figure 11 Trans lChentE, Vol. 57, 1979
180 TAGG, PATRICK AND WRAGG much greater. 'Asymptotic conditions are reached very much sooner after the peak with the inert surroundings, but the shapes of the profiles prior to this are similar 4
enough to refute the suggestion of Runchal that the boundary conditions 'strongly affect the location of the peak (at least for high values of Sc).
The results of the determination of recirculation zone length and the position of the mass transfer peak. for both sets of boundary conditions are fully presented in the Table. The slightly greater distance between the 3[
D nozzle and the peak transfer position in the developed mass transfer case may be a result of unavoidable slight differences in. the cell geometry and inlet conditions for the two experiments. From this Table, however, it is 2 very clear that for all expansion .ratios and Reynolds numbers the peak transfer position does not coincide with the end of the recirculation zone, as was widely suggested in earlier work, but lies well within it.
1[ 0 1:10 ... position of Table. Tabulation ofrpeak trmasfer positions and recirculation A 1:6 peak transfer zone lengths 1:4 recirculation Peak point Peak developed 1:3 zone length Recirculation mass transfer mass transfer A
Did Re . zone xlD xlD x/D I
2 1984 2.50 i.25 1.5 0 4 8 12 M6 20 24 3858 2875 1.375 1.5 6270 3.0-3.125 1.375 1.5 Reb (,o-3) 10126 3.0 1.50 1.5 15912 2.875--3.00 1.50 1.5 Figure 10. Comparison of peak mass transfer rate location 22180 2.875 1.50 1.5 and recirculation zone length.
3 1984 3.75 2.0 -2.25 with a profile obtained with an electrode surrounded by 3858 3.75 2.0 2.25 active surface. The former exhibits a distinct minimum 6270 3.625 2.0 2.25 10126 .3.5 2.0 2.125 in the transfer rate which is shown up by the more 15430 3.25-3.375 1.875 2.125' detailed exploration, readings being taken at intervals 21340 3.25--3.375 1.875 2.125 of 0.125D rather than 0.25D as in the active surface case.
The peaks are seen to be nearly coincident although the 4 1984 3.875-4.10 2.25 2.5 3858 3.875 2.25 2.5 magnitude of that for th',e inert surround is of course 6269 3.75-3.875 2.25. 2.5 10125 3.75 2.125 2.5 14950 3.625 2.0 2.375 20010 3.5 1.875 2.375
.3P 6 1984 4.0-4.125 2.375 2.625 3858 4.0 2.375 2.5 6269 3.75-3.875 2.25 2.5 K 10125 3.75 2.125 2.25 xlo2 1.5430 3.5 2.0 2.25 cm s Inert surround 10 3375 " 3.75--3.875 2.25 2.5 4940 3.75 2.25 2.5 6270 - 2.125 -
.- 2 10'ýýActive Furthermore, recent numerical modelling workO. 1 surround shortly to be published in fuller form23 confirms this and demonstrates the relationship of the peak transfer posit.ion to the flow structure, notably the turbulence I I intensity near the wall.
0 a I 2 3 " 4 CONCLUSIONS Figure II. Mlustration of the effect of boundary conditions on A comprehensive set of mass transfer distribution data the rnass transfer distribution, Did = 2, Re,) = 1985 has been obtained for a. range of sudden expansions.
Trans 1(:hemE, Vol. 57, 1979
HEAT AND MASS TRANSFER IN TLIRBULENT FLOW 181 '-"
Comparison with independent heat transfer data has 4. Zemanick, P. P. and. Dougal, R. S., 1970, J Jlcat 7, uafcr, 92: 53.
confirmed the usefulness of the Chilton-Colburn 5. Emerson. W. H., 1966. NEL Report (No 256).
analogy for this flow situation. 6. Louise, K. D., Gas Council Midlands Research Station, The location of t.e peak Wall .iiass transfer rate Privatecommunication.
corresponds neither to the "eye" of the recirculation 7. Read, G. P., Gas Council Midlands Research Station, zone (i.e. the centre of the recirculation vortex).nor to Privatecommunication.
- 8. Costello, J., 1969, PhD Thesis (University of Aston).
the point of flow reattachment. 9. Runchal, A. K., 1971, Int J Heat & Mass Transfer, 14: 781.
- 10. Mizushina, T., 1971, Adv Heat Transfer, 8: 87.
- 11. Wragg,A. A., 1977, The Chemical Engineer (Jan), 39.
SYMBOLS USED 12. Lin, C. S., Denton, E. B., Gaskill, H. S. and Putnam, G. L.,
1951, Ind & Eng Chem, 43: 2136.
A electrode area (cm') 13. Furuta, T., Okazaki, M. and Toei, IL, 1974, J Chem Eng cb bulk ferricyanide ion concentration (tool dm-3) Japan,7; 350.
d nozzle diameter, upstream (cm) 14. Hubbard, D. N. and Lightfoot, E. N., 1966, Ind& Eng Chem D duct diameter, downstream (cm) Funda, 5: 370.
- diffusion coefficient (cm' s-1) 15. Son, L. S. and Hanratty, T. L. 1969,1 iFluid Mech, 35: 353.
- 16. Spalding, D. B., 1967, J'FluidMech, 27: 97.
F Faraday number (C mol- 1) 17. Jenkins, J. D., Mackley, N. V. and Gay, B., 1976, Letters in itl limiting electrolysis current (A) Heat and Mass Transfer, 3: 105.
K mass transfer coefficient (cm s-1) 18. Shaw, D. A. and Hanratty, T. J., 1977, AlChE Journal,23:
. 28.
V mean fluid velocity (cm s-1) x distance downstream from enlargement (cm) 19. Abbot, D..E. and Kline, S. J., 1962, J Basic Eng 84: 317.
- 20. Patrkik, M. A., Tagg, D. J., Vallis, E. A. and Wragg, A. A.,
z number of electrons exchanged (-) 1977, Paper to AIChE, 70th Meeting, New York, p fluid viscosity (g s-1 cm- 1) November.
p fluid density (g cm-) 21. Vallis, E. A., 1975, PhD Thesis (University of Exeter).
- 22. Tagg, D. J., 1978, PhD Thesis (University of Exeter).
- 23. Patrick, M. A., Tagg, D. J. and Wragg, A. A., to be published.
Dimensionless groups ReN = dVp/lp ReD = DVph&
St = K/V Sh = KD/1 Sc =.pp.g ADDRESS REFERENCES Correspondence in connection with this paper should be addressed to Dr M. A. Patrick, Department of Chemical *...
- 1. Ede, A. J., Hislop, C. I. and Morris, R., 1956, Proc IMechh, Engineering, University. or Exeter, North Park Road, Exeter 170: 113.
- 2. Ed,.-, A. J., Morris, R. and Birch, E. S., 1962, NEL Report FX44QF.
(No 73).
- 3. Krall, K. M.*and Sparrow, E. M., 1966, J Heat Transfer, The manuscript of this paper was received 3 July 1978.
88: 131. The revised manuscript was received 15 January 1979.
Trans IC'hie*mE, Vol. 57, 1979