Drag reduction and shear degradation of dilute polymer solutions as measured by a rotating disk

DEPARTMENT OF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

BETHESDA, MD. 20034

DRAG REDUCTION AND SHEAR DEGRADATION OF DILUTE POLYMER SOLUTIONS AS MEASURED

BY A ROTATING DISK

by

T.T. Huang and N. Santelli

Approved for Public Release: Distribution Unlimited

TABLE OF CONTENTS

Page ABSTRACT

...

ADMINISTRATIVE INFORMATION .

... ...

)

i

INTRODUCTION 1

E:XPERIMENTAL APPARATUS AND PROCEDURE 3

DRAG-REDUCTION SATURATIÒN LINE FOR A ROTATING DSK 5

DETERMINATION OF DRAG-REDUCTION DOMAINS

SHEAR DEGRADATION MEASURED BY A ROTATING DISK 8

COMMENT ON ELLIS RESULTS lo

CONCLUSION 11

ACKNOWLEDGEMENTS

..

li

REFERENCES 23

LIST OF FIGURES

Figure 1 - Housed. Rotating Disks l2

Figure 2 - Effects of Housing Diameter and Gap on the Moment

Coefficients Of Rotating Disks in Water 14

Figure 3 - Drag Reduction Properties of Disks in a 10-Inch

Housing with Varying Gaps and Temperatures 15

Figure 4 - Sununary of Measured Drag-Reduction Saturation Lines, Compared with the Line Derived from New Similarity

Law 18

:Figure 5 Drag-Reduction Domains, Determined by Rotating Disks 19

Figure 6 - Typical Results of Shear-Degadation Values versus

Specific Energy Dissipatioñ at Varous Concentratjons 19.

Figure 7 - Shear-Degradation Value versus Specific-Energy

Dissipation for Polymer Concentrations Under and Well

Over Optimal Concentration 20

Figure 8 - Shear Degradation versus (E/)/(E/)05 for

Conceiitra-tion Slightly over Óptimai COncentration

...21

Figure 9 - Concentration versus Energy Dissipation to Cause

50-percent Degradation (PTR)/(PTR)0 = 0.5)

...

Figure 10 -Effects of Solvent Temperature and Shear Stress on

5

Shear-Degradation Value After Applying 10 Foot#

Pounds per Cubic Foot of Energy into Polymer Sälutions of 5 Parts Per Million .

. 22

LIST OF TABLES

Table 1 - Shear Resistance and Figure of Merit or Shear Resistance for Three Polymer Solutions Tested at 1500 Dynes per

Square Centimeter. 10

ii

A and B Constants defined in Equation (3) C Moment coefficient m C C m E

E.

min

(E/)

Concentration Optimal concentration NOTATION Energy dissipation

Minimum energy dissipation

Specific energy dissipation per unit voiwne

Specific energy dissipation at (PTR)/(PTR)0 = 0.5

2M Torque

(PTR) Percent torque reduction after shear

(PTR)0 Percent torque reduction of fresh solution

R Radius of disk Reynolds number r Radial distance T Elasped time u Local velocity u Volume

y Normal distance from wall Thickness of boundary layer Kinematic viscosity

p Mass density of solvent

Ta Average wall shear stress

Local wall shear stress

w Angular velocity

ABSTRACT

A saturated drag-reduction line for dilute polymer solutions is derived for a rotating disk from new velocity-similarity laws. The derived line is in good agreement with present and other experimental results. Drag reduction measured by a rotating disk is found to have three domains--oversaturated, optimal, and undersaturated. At a given boundary-layer

thickness and wall-shear stress, the drag-reduction increases with increasing concentration in the undersaturated domain, and the drag reduction does not increase with increasing con-centration in the oversaturated domain. The boundary between the two domains is the optimal drag reduction, which is

determined by the type of polymer and its concentration and a Reynolds number u R/v or u.ó/v, based on shear velocity and disk radius or boundary-layer thickness. Each drag-reduction domain has its distinct shear-degradation characteristic. The measured shear degradation for a given polymer solution

in optimal and undersaturated domains is found to depend

uopn the concentration, specific energy dissipation, wall-shear stress, and ambient temperature of the solvent. However, the polymer solution in the oversaturated domain may show no de-gradation in drag reduction, if the specific energy dissipated by the solution is not sufficiently large.

ADMINISTRATIVE INFORMATION

This work was authorized and funded by the ..Naval Ship Research and Development Center under its Independent Research Program, Task ZR0230101 and by the Naval Ship Systems Command under Subproject S-F354 21 003, Task

01710.

INTRODUCT ION

Although considerable experimental information has been accumulated concerning drag reduction by fresh, dilute polymer solutions, little effort has been made to study the degradation of drag-reduction effectiveness after

flow shearing and mechanical agitation. Ellis1 reported that drag-reduction. effectiveness, measured in a capillary pipe, did not change after flow

shear-ing. However, the drag-reduction effectiveness in a 9/16-in.-.ID pipe was

completely lost acter the, saine shear treatment.. Ellis, Ting, and Nadolink2

demonstrated some of the qualitative effects of storage and shear history on the drag-reduction effectiveness of polymer solutions in a capillary-tube rheometer. However, satisfactoty xplanations of the previously described observations have not yet been given.

The drag-reduction properties of a given diluted polymer solution may be classified according to three domains.

Undersaturated, where the drag-reduction effectiveness increases with increasing concentration;

Oversaturated, where the drag reduction reaches its maximum value, and the drag-reduction effectiveness cannot be increased by increas-ing concentration:; and

Optimal, which is the boundary between Domains (1) and (2). Rotating disks of various diameters and rotational speed were used to determine the optimal drag-reduction boundary as a function of concen-tration wall-sheer stress, and solvent temperature. It has been found that the concentrations on this optimal drag-reduction boundary for POLYOX WSR-30l, MAGNIFLOC 835A, an4 SEPARAN AP-30 sOlutions are all proportional to a

Reynolds number with wall.-s1ear velocity as characteristic velocity and with disk radius as characteristic length.

This

relationship also holds for the pipe-flow data of Huang and Santelli,3 of the polymer solutions in each

drag-reduct-ion domain. The distinctive characteristics were suited

quan-titatively in rotating-disk experiments and are reportéd below.

'Ellis, H.D., "Effects of Shear Treatment on Drag-Reducing Polymer S lutions and Fibre Suspensions," Nature, Vol. 226 (25 Apr 1970).

2Ellis, A.T. et al., "Some Effects f Storage and Shear History on the Friction-Reduction Properties of Dilute Polymer Solutions," NAVY-American Institute of Aeronautics and Astronauctics, Antisubmarine Warfare, Marine Systems, Propulsion Meeting, AXAA Paper 70-532 (4-6 May 1970).

3Huang, T.T. and N. Santelli, '1Drag Reduction and Degradation of Poly-mer Solutions in Turbulent Pipe Flow," NSRDC Report 3677, (Aug 1971).

The apparatus used in this study consisted of a disk rotating in a housing. Two disks of 5- and 6-in, diameter and of 1/16-in, thickness and two cylindrical housings of 5-in, and 10-in. ID, with upper and lower plates, were built for this study. The gap between the two end plates was varied

from 1/2 to 6 in. for the 10-in, housing but was fixed at 1 in. for the 6-in, housing. The 10-in, housing had a temperature-control system. Each disk was suspended midway between the end plates and was driven by an

elec-tric motor connected by a shaft through the upper plate. The motor had a constant speed control and was mounted by means of a strain gage, Bendix Corporation, flexural pivot to a support stand. The complete setup, in-cluding digital readout equipment to measure the torque of the disk, is shown in Figure 1.

The average sheer stress of the disk is defined as

where

T =

a

EXPERIMENTAL APPARATUS AND PROCEDURE

R Jo

_Tr2dr

_{3 2M}

_3cm

22

- -

pwR

J'R2d

4R3

87r

o C -m 3 2M 1/2 (p W2R5) (1)

w is the angular velocity of the disk R is the radius of the disk

2M is torque experienced by both sides of the disk p is mass density of the fluid

r is the radial distance from the disk center

By recording the time history of the torque 2M, one can calculate the energy input per unit volume of the polymer solution E, which is approximately equal to the specific energy dissipation per unit volume of the solution, given by

E

IL IL

T

(2M) wdt

(2)

-where T is the elasped time during a given run, and IL is the total volume of solution in the disk apparatus Thus, the rotating disk readily gives the shear degradation of polymer solution in terms of the decrease in torque reduction and the shear history in ternis of the specific energy dissipation. As an experimental technique to study polymer degradation, the rotating-disk apparatus is far more convenient than a pipe-flow apparatus. In order to evaluate the rotating disk apparatus, measurements in pure water were made of the moment coéfficient C = 2M/(p w2R5/2) asa function of Reynolds num-ber R = w2R/v for 5- and 6-in, disks rotating, in 6- and 10-in, housings with various gaps. The results are plotted in Figure 2. At R > 5 X 10g,

the data follow the laminar free-disk line. A graduated transition appears to exist between R = 2.5 X l0 and 5 X lOs, At R > 5 X l0 all the curves

n

.4

are approximately parallel to the turbulent lines of a free disk (Goldstein and Von Krmn5) and of an enclosed disk where the gap is several times the boundary layer thickness (Schultz and Grunow6). The measured Cm falls be-tween the theoretical predictions for free and enclosed disks. As shown in Figure 2, C decreases with decreasi.ng gap and increasing ratio of disk-to housing diameter. Nevertheless, the curvès of Cm

parallel tb each other at large Reynolds numbers. -rotating disk at aU conditions tested were fully

The tor4ue in this apparatus was measured 3 percent, and the rotational speed was read with

cent.

at various conditions are Thus, the flows on the

turbulent at R > 5 X l0.

- n

with an accuracy within an accuracy within 1

per-4Goldstein,.S.,, -"OntheResistance to the Rotatiön of a Disk Immersed in a Fluid," Proceedings of Cambridge Philosophical Society( england), Vol 31, Part .2, p.232 (Apr 1935). .

VÖfl irmgn, T.., "Uber Laminare and Turbulente :Reibung," Vol. -1 pp.. 233-252 (1921), National Advisory Committee for Aeronautics TM 1092, see

Zeitshrift fur A-r.gewandte Mathematik and Mechanik (Berlin) Work 11, pp. 7.0-97.. 6Schultz-Grtmow ., "Der Reihungwiderstand Rotierender Scheiben in

Gehausen," Vo-l. .15, pp. 191-204 (1935).

DRAG-REDUCTION SATURATION LINE FORA ROTATINGDISK

The drag-reduction ef-féctiveness and shear-degradation characteristics of polymer solutions are believed to be closely related to the drag-reductión saturätion line, which is the boundary line between the under- and over-saturated drag-reduction dOmains. When drag reduction is saturated, the logarithmic velocity-similarity law hàs two distinct constants A and B, which are different from thos for Newtonian fluids; A and B are dterinined from the inner velocity similarity law

uy

=

A logI +

B

U V

where

u is the local velocity

UT _{is T w/p}

T _{is the local wall-shear stress}

y is the normal distance from the wail p i.s the mass density of the fluid

y isthe kiñematic viscosity of the fluid

When the same constánts A and B, derived from pipe-flow èxperiment, are applied tò théGoldstein4 analysis, one can derive a saturáted' drag-reduction

line for rotating disks.

According to Goldstein,4 the moment coefficient Cm = 2M/(p2R5/2) and Rèynolds numbér of the rotating disk R = ¿R/v-havethè following

.re-làtionship.

(R)/Ç)

5

loge (8 A2. e'')]

For zerodrag reduction,A is 2.5, and B is 5.5. However,during saturated drag reduction, Huang and Santelli3 determined that A = 13, and B = 20.2 from their own gross pipe-flow data and the velocity-profile

(3)

[lo e

measurements of'ti,7 and Seyer and Metzner.8 If 'A 13, and B = 20.2 are used in Equation.. (3), the drag-reduction saturation line for rotating disk

is

tk]

Then, för the same R

13 1° 4.93 (5)

lO.5 loge

tj1"Ç)

47.4 (7)

The subscripts p and s represent the polymer-solvent system and the solvent (water) alone, respectively;

i/VE:

versus RP'Ç was determined experiment-ally for both water alone and various concentrations of the polymer solution to determine

l/VE]

_-

i/p'Ç]5

at constant values of

RYE.

Since the thickness of the boundary layer on the disk is much smaller than gap onthe measured values of

i/p'Ç]

_Eiiyç]5

is expected to constant and is assumed to be independent of the housirjg effect.

Figures 3a through 3f show th measured

fl/çj

-

l/yç5

RV'Ç fòr- various disk configurations 'and for various concentrations

POLYOX SR-30l (a polyethylene oxide polymer of Union Carbide Corporation), MAGNIFLQC 835A (an. anionic charged polyacrimide polymer of American Cyanamid Co.), and SEPARAN AP-30 ( a polyacr.imide copolymer of the Dow Chemical Co.). All solutions were prepared by the same procedure. The dry polymer powders were dissolved in distilled water 'at a ratio of 1000 ppm one day before each

experiment a4 were diluted to the desirçd concentration prior to test.

7Tsai, F., 'The Turbulent Boundary Layer in the Flow of Dilute

Solut-ions

of

Linear Macromolecules," PhD Theisis, University of Minnesota (1968).

8Seyer, F.A. and Metzner, "Turbulence Phenomena in Drag Reducing Systems," American Institute of Chemical Engineers Journal, Vol. 15, No. 3, pp. 426-434

(1969).

6 ' '

For zero drag reducton of A. = and B = 5.5, Equation (3) becomes

i

_{2.5 loge - 1.85 (6)}

the

be a

versus of

Two solution temperatures, 70 and 120 F, were studied. As shown in Figure 4 on the saturated drag-reduction line, the temperature effect on the drag-reduction effectiveness of a fresh polymer solution is satisfact-orily absorbed into the kinematic viscosity of the solvent, which appears,

in the forni of

RP"Ç,

where R= w2R/'. However, the present rotating disks

are too small for use in studying the drag-reduction characteristics in the undersaturated domain because they reach saturated drag reduction at rather low polymer concentrations. This information can best be obtained in a pipe-flow facility.3

The summary of measured drag-reduction saturation lines for rotating disks at six different conditions is shown in Figure 4. The present group of data, the result from the Hoyt and Fabula9 45.7-cm free disk, and the curve from Gilbert and Ripken1° 49.9-cm enclosed disk agree well with the derived saturation line Equation (7). Thus, the new velocity-similarity laws for saturated drag-reduction appear to be valid not only for internal

(pipe) flow but also for external (rotating) flow. Figure 4 also shows that the effects of housing diameter and gap on the results of

_[i/YE

-[l/y']

versus

RP'Ç are indeed small.

m _P

Three (Over-, under-, and optimally saturated) drag-reduction domains are defined experimentally in the next section with reference to the satur-ated drag-reduction line.

DETERMINATION 0F DRAG-REDUCTION DOMAINS

As shown in Figure 3, the drag reduction may change from an under-to over-saturated domain when the solution concentration is increased, and

the value of RVÇ is kept constant.

Similarly, the drag reduction may shift from an over- to an under-saturated domain when RYÇ is increased, and concentration is maintained at the same value. An optimal concentration may then be defined so that the drag reduction will be optimal for c =

oversaturated for c > Em and undersaturated for c< The optimal

9Hoyt, J.W. and A.G. Fabula, "The Effect of Additives on Fluid Friction," Published in Fifth Symposium on Naval Hydrodynamics, Edited by J.K. Lunde and S.W. Doroff, Office of Naval Research, U.S. Department of Navy ACR112

(1964).

10Gilbert, C.G. and J.F. Ripkin, "Drag Reduction on a Rotating Disk Using a Polymer Additive," Symposium on Viscous Drag Reduction, Edited by C.S. Wells, p. 256. Plenum Press, New York (1969).

concentration 'at a given'R1.V'Ç can be estimated from datagven in Figure 3. It should be rioted that RYÇi.s equal to _Y81T/3 R and is approx-imately equal to 5.5 provided the boundary-iayer thièkness is assumed to he

0.526 R (R)"5 (Schlichtihg)»

The experimentaldeterthinatjon of optimal drag-reduction lines in terms

of _{versüs Rd}

VÇ7/v

_{for the three polymer solutions tested is shown in} Figure 5. To the right of this line is the under-saturated domain, and _to the left Of the liné is thé oversaturated domain. _{It is important to know} in which domain the apparatus for measuring drag reduction is operated befóre the study of sher degradation of polymer solutiOns can be made. As shown in Figure 5 at a given YTa/pIV the value of is higher for 'arger disks. Thus, at â given concentration and wall shear, the drag reduction maybe 'oversaturated for a small disk but may be undersaturatéd for a large disk.

SHEAR DEGRADATION MEASURED BY A ROTATING DISK

The rotating disk suspended. in the two housings with various gaps was used to determine the shear degradation of the diluted polymer solutions. The ,disk torque was continuously recorded after the disk had, beefl brought upto speed to give an initial average shear stress _{Ta = 1500 dyn/,cm.} The shear degradation characterized by (PTR)/(PTR)0 could then be computed, where

(PTR) was the percent of torque reduction after' shear treatment1 and (PTR)Q was the percent of torque reduction of the fresh solution. The specific

- energy dissipation could be computed from Equation (2).

Typical results "of shear degradation versus specific energy dissipation at various concentrations of POLYOX WSR-301 are shown n Figure 6. The'

corresponding drag-reduction characteristics of the fresh solutions' 'are'

given 'in Figure ,3a. The average shear stress Of _{Ta =}

isob

dyri/cin2 is at

RJ/E =7.5

x'Io.

SinceRp'E

= J(8 iî/3 R VTa/P/VI R'VT/P/\.' is 2.6 X lO4

for Ta = 1500 dyn/cm2.' Entering R VTa/PR = 2.6 X into Figure 5' ¿ne

finds that the ptimaí concentration

m

is 3.4 ppm for the case of POLYOX

WSR-3Ól. As can be seen from Figure 6, the shear degradation is measured almost immediately after shear treatment fOr c =1 and. 2.5 ppm. These

con-cenratjons

t T 1500 dy1/cm aré in the undersaturated domain (c<

11Schlichting, 'H'., "Boúndary-Layer'Theory," Sixth Edition, p. 607, McGraw Hill Book Company, New 'York (1968).

as measured by the 5-in, disk. Zero shear degradation is observed for 200 ppm, which is in the oversaturated domain (c » Within the range test-ed the specific energy dissipattest-ed by the 200-ppm solution is not large enough to reduce the drag-reduction effectiveness. The shear degradation is not noted until sufficient energy is dissipated for concentrations of 5, 10,

and 20 ppm. Those concentrations are slightly above optimum.

Other data on shear-degradation values versus specific energy dis-dipation for concentrations under and well over optimal concentration are shown in Figure 7. Zero shear degradation was noted for SEPARAN AP-30 and MAGNIFLOC 835A at 20 ppm, which is well over the optimal concentration level. For concentrations less than optimal, the shear degradation approximately obeys a power law of the form

(PTR)

(E

(PTR)

o min

if E > EinS Where Emin is the minimum energy dissipation required to cause noticeable degradation of the polymer solutions, and n is a constant ranging from 3 to 5, depending upon the type of polymer, concentration, and temperature.

The effect of temperature on shear degradation can also be seen in Figure 7. At a given concentration, the resistance to shear degradation decreases with increasing temperature for the three polymers tested.

Figure 8 shows shear degradation plotted against e = (E/.)/(E/.)0 for concentrations slightly more than optimal concentration, where (E/i.)05 is the specific energy dissipation at (PTR)/(PTR)0 = 0.5. The data is well fitted by the similarity relationship

(PTh)

(PTR)0 1 + e

The values of (E/y)05 for various conditions are shown in Figure 9. The value of (E/y)05 for a given polymer increases approximately linearly with

increasing concentration c.

9

We may definèa shear-resistance measure (SRM as (E/v- 5/C in foot-pounds percuhic foöt per parts per.million, which is simp the siöpe of a given Une shown in Figure 9. We may further define a figure .of.merit (FOM) ior shear resistance by taking the MAGNIFLOC 835A at 70 F as loo percent. The tabulated results qr the three polymers are given in Table .1. It is

onc1uded that the MAGNIFLOC.835A has the strongest resistance to shear áegradat,on. The resistance to shear degradation is dropped an order of iagni'tude when:the solvent temperature is increased from 70 to 120 F.

The effect of shear stress Ta 011 the shear degradation was also

tudied.. The shear degradation was measured with the Specific er,ergy dis-$ipation equal to 1,O ft-Ïb/(ft)3 for various average shear stresses Ta

I'he effects of Ta Ofl shear degradation of the two 5-ppm polymer solutions

at 70 to 120 F are shown in Figure 10. The shear degradation increases älmost linearly with increasing shear stress, when the specific energy dis-sipation is kept constant.

TABLE i - SHEAR RESISTANCE AND FIGURE OF MERIT FOR SHEAR RESISTANCE 'FOR THREE POLYMER SOLUTIONS TESTED AT

1500 DYNES PER SQUARE CENTIMETER

SR is resistance to shear degradation in ft-.lb/(ft3 ppm).

**FOM is figure: of merit for shear resistance of polymer solutions.

COMMENT ON ELLIS RESULTS

Ellis1 performed a shear treatment of concentrated fresh polymer lution of 1000 ppm by recircu1atng it through an impeller pump for 1 hr. The drag re4uction was measured in a small pipe '(lD 0l15 cm) and in. a large pipe (1D 1.45 cm) at 10 ppm. As can be seei from Figure 1 of Ref-erence 1, the optimal concentration (em) is about 3 ppm for the small pipe and is about 30 ppm' for the large pipe. Thus, it isnöt surprising that. the small-pipe data showed zero shear degradation after the shear treatment

lo 70F 120F

F0M*

SR* FOM** MAGMIFLOC:835A SEPARAN' POLYOX WSR-301 1Q5

i:.3

X

loo

66 4. 6.4 X

1.3 x io3

20

0.4

11

since the apparatus is in the oversaturated drag-reduction domain.

However,

the large-pipe data indicated serious shear degradation after the saine

shear tréatlment.

In this pipe, lo ppm is below its

CONCLUSION

The derived rotating-disk saturated, drag-reduction line compares

favorably with the present rotating-disk data and that. at others.

9,10

Thus, the new velocity similarity laws appear to be valid not only for

in-ternal (pipe) flow3 but also for exin-ternal (rotating-disk) flow.

It is

expected these laws will hold also for flat plates, although no experimental

data are available yet.

The boundary between the over- and under-saturated, drag-reduction

lines is the optimal drag reduction. .

The values of the optimal concentration

m

estimated from the present and other data, are found to increase with

incrêasing disk diameter and average wall shear.

Shear degradation, measured by a rOtating, disk in each drag-reduction

domain, has its distinct characteristics.

Zero shear degradation is noticed

if the drag reduction js initially in the oversaturated domain and still

remains in this domain after shear treatment.

For concentrations slightly

higher than the optimal concentration, the rate of degradatiOn of drag-reduction

.effectiveness is initially small and increases withincreasing shear

treat-ment.

For concentrations less than the optimal concentration,. serious shear

dégradation is measured after shear treatment.

The shear degradation as

measured by percent of torque reduction of the rotating disk after and

be-fore the flow shearing follows a simple power law.

High-temperaturé and wall-shear stress are found to weaken the

re-sistance to shear degradation of the three polymer solutions tested.

The

MAGNIFLOC 835A solution has the strongest resistance to shear degradation,

the POLYOX WSR-30l solution has the lowest resistance to shear degradation,

and SEPARAN AP-30 performs in between the two but rather close tO the

MAGNIFLOC solution.

ACKNOWLEDGEMENTS

The subject of shear degradation of polymer solutions was brought

LLI4

I

L

r'

Figure 1 - Housed Rotating Disks

u.

-f

Figure la - The 5-Inch Rotating Disk in the 6-Inch Housing

e.

.

o

O

[o

i

0.04 0.03 0.02 It)

0Ml

0.009 N 0.008 0,007 ii 0.006 0E 0.005 0.004 0.003 0.002

-LAMINAR WITH

X

-HOUSING. C = 2.67/R/2

V

-(SCHULTZGRUNOW)6 GAP LAMINAR C

= 387/2

DISK ClAM HOUSI NG DIAM DISK DI AM INCH ES

06

04

>(5

A

_EL

X-A

TURBULENCE GOLDSTEIN4

iijÇ= 1.97 log (R,/)

+ 0.03 (A = 197. B = 6.53) GOLDSTEIN4

iiJÇ

= 2.50Iog (R/) - 185

(A = 250. B = 5.5)

VON KARMN

Cm = 0.146/R

TURBULENCE WITH HOUSING C

= 0.0622IR (SCHULTZGRUNOw)6. I I i I i I I I 106

Figure 2 - Effects of Housing Diameter and Gap on the Moment Coefficients

of Rotating Disks in Watcr

HOUSING DIAM INCHES GAP I NCH ES lo 35 10

i

lo 3.5 10

i

lo

0.5 lo 3.5 6 1

7

Figure 3 -. Drag Reduction Properties of Disks in à 10-Inch Housing With Varying Gaps and Temperatures

CO o L 7 6 LLJ 4 L .1 o iO

RJÇ

Figure 3a -. A 5-Inch Disk with a 1-Inch Gap at 70 F

106

= 1500 dyn/cm2 c POLYOX MAGNIFLOC SEPARAN

(ppm) WSR-301 835A

AÑÓ-G.

£

L

V 15 106

Rj

Figure 3b .- A 5-Inch Disk with a 3.5-Inch Gap at 70 F

1.0

0

2.5 0

s .

10

₄

MAGNIFLOC 835A Ò

£

V = moocIynicrn V V V VV

Figure 3d - A 5-Inch Disk with a 3.5-Inch Gap at 120 F

16

106

Rn\fm

Figure 3c - A 5-Inch Disk with a 1-Inch Gap at 120 F

7 POLYOX (ppm) WSA-301

_.1

O 2.5 0

q

5 10 50 V 4

o-E3

i

L

o

g1

n. 5 4 3 2 MAGNI FLOC 835A

4

"u

£

V 17

Figure 3e - A 5-Inch Disk in 10-Inch Housing with a 3.5-Inch Gap at 70 F

POL VOX

WSR-3Ó1

10

RJÇ

Figure 3f - A 6-Inch Disk with 3.5-Inch Gap at 120 F

i

o

2 DISK HOUSING

'DIAM

DIAM

INCHES INCHES 5

s

5:

6 6

Virk,etaI2

[v']

p GAP INCHES

92 log, (R\fm) - 405

4/

F

TEMPERATURE

F. 5 ppm '1:0 ppm

_{DISK DIAM'}

HOUSING DiÄM

(HOYT& F'ABULA)9'Cm - 110 ppm

/

HOYT AND FABLJ LA9 (GUAR. GUM, 621 ppm)

GILBEAT AND RIPKEN10

(GUAR:GUM', 500 ppm) _{PRESENT STUDY}

_[1/'ím]'p

-[1/[rn]

'1.0.53 lOg (R,i\ím' 47.4

"

-GAP

Compared with the

100. 1.0 i .70 10 3.5 .7°

lo

1 120 3;5 120 10 3.5 70 10 3.5, 120 o I

i

i'

1.1111!

Ii

io4

RnVm

Figure 4 - Summary of Measured Drag-Reduction Saturation Lines,

g X 100 80 60 40 20 10 1000 800 600 400 200 100 80 60 20 lo 8 6 4 2 OVERSTURATEP DRAGREDUCTION

ÒOMAIN IS AT TÑE LEFT OF THE

OPTIMAL DRAG-REDUCTION LINE

-

'I

/

-

//

=AF

/

/

UNDERSATURATED DRAG-REDUCTION DOMAIN

O POLYOXWSR-301,PRESENTSTUÔY POLYOX WSR-301. HOYT AND FABULA9

D MAGNIFLOC 835A. PRESENT STUDY A SEPARAN AP-3D. PRESENT STUDY

E/V IN FT-LB /(FT)3

Figure 6 - Typical Results of Shear-Degradation Values versus Specific Energy Dissipation

at Various Concentrations

19

Figure 5 - Drag-Reduction Domains, Determined by Rotating Disks - POLYOX WSR.301

-

INITIAL = 1500 dyn/cm2

-

TEMPERATURE = 70 F DISKDIAM=5IN. 10-IN. HOUSING V 0.0388 FT3

I I I

I-I Jill

I I- I I i

I iii

I I 111111 I I

II liii

I I I 11111

o

DISK CÓNCENTRATION TEMPERATURE DIAM POLYMER (ppm) F C/Cm INCHES V(FT3): POI VOX WSR-301 5 70 1 5 0.0388 O 5 120 <1 5 0.0388 X 5 120 <1 6 0.0388 SEPARAN AP-30 5 70 <1 5 0.106

V

20 70 >1 5 0.106 MAGNIFLOC835A 5 70 <1 6 0.0388 5 120 <1 5 0.0388 O 5 70 <1 5 0.0388 V. 20 70 > 1 5 0.106 20 70 >1 5 0.0388 5 70 <1 5 0.106 5 120 <1 5 0.106

V V

'

y

V

V O V G V

vZv c

c O O

o-

'a.

-- o.& .

-4A

i

I

i

I I I i I

i

I: I I I i: EN IN FT-LB/(FT)3

Figure 7 - Shear-Degradation Value versus Specific-Energy Dissipation for Pòlymer

Concentrations Under and Well Over Optimal Concentration

io5 X o 200 I- I- 3-100 80

V

V V ... .

O---60 40 20 10 I .11

i

t

I

100 Q. X 80 o o 60 40 20 10 O POLYOX WSR.301 C u V

POLYMER CONCENTRATION TEMPERATURE

(ppm) (F)

MAGNI FLOC 835A MAGNIFLOC 835A SEPARAN AP.30 5 10 20 5 lo 10 70 70 70 70 _(c/c.,«-l) 70 70 21 835A 100(PTR) ibO (PTR)Q 1+e

X.

D

III

I

1111111

I

I

1.11111-III

I I I

111111

- I I I I I I I 0.1 e = 10 DISK

DIAM CONCENTRATION TEMPERATURE

(FT3) POLYMER INCHES (ppm) F O POLYOX 5 10 70 0.0388 WSR301 D 5 20 70 0.0388 5 10 120 0:0388 5 20 120 0.0388 X 6 20 120 0.106 V 5 10- 70 0.0184 5 20 70 0.0184 MAGNIFLOC 5 20 120 0.0388 0.1 -

i

10 -=(E/M)/(E/V)05 -.

Figuré 8 - Shear-Degrádatión versus (E/-)/(E/)0 for Concentrations Slightly over Optimal Concentration

200 100 90 80 70

x

60 50 40 30 20 10 200

Q.-26 24 22 20 18 16 14 12 X 10 w 6 4 2 CONCENTRATION IN ppm

Figure 9 - Concentration versus Energy Dissipation to Cause 50-Percent Degradation (PTR)/(PTR)0 = 0.5) 120 110 100

-

90 X N 80 10 60 X 50 I-40 I.-30 20 10 o 0 400 800 1200 1600 in dyn/cm2

Figure 10 - Effects of Solvent Temperature and Shear Stress on Shear-Degradation Value After

5

Applying 10 Foot-Pounds per Cubic Foot of Energy into Polymer Solutions of

5 Parts per Million

22 POLYMER DISK DIAM INCHES TEMPERATURE F '(FT)3 sR FT-Lb/ FT3Ippm G SEPARAN AP-30 5 70 0.106 5 70 0.0388 1.9 X 10 MAGNIFLOCB3SA 5 70 0.106 + 5 70 0.0388 14 0 1O O 5 120 0.0388 76X104 X POLYOX WSR.301 5 70 0.106 1.4 X io O 5 70 .0388 1.4 X 5 70 0.0184 1.4 X 6 120 0.0388 o 5 120 0.0388 1.5 X 10 V 5 120 0.106 POLYMER TEMPERATURE POLYOX WSR.301 70 POLYOX WSR.301 120 o MAGNIFLOC 835A 70 o MAGNIFLOC 835A 120 10 15 20 25

= o.o388 Fr3.5.IN. DISK

II

I

III

I I I I I I

REFERENCES

Ellis, H.D., "Effects of Shear Treatment on Drag-Reducing Polymer Solutions and Fibre Suspensions," Nature, Vol. 226 (25 Apr 1970).

Ellis, A.T. et al., "Some Effects of Storage and Shear History on the Friction-Reduction Properties of Dilute Polymer Solutions," NAVY-American Institute of Aeronautics and Astronautics, Antisubmarine Warfare, Marine Systems, Propulsion Meeting, AIM Paper 70-532 (4-6 May 1970).

Huang, T.T. and N. Santelli, "Drag Reduction and Degradation of Polymer Solutions in Turbulent Pipe Flow," NSRDC Report 3677 (Aug 1971).

Goldstein, S., "On the Resistance to the Rotation of a Disk Im-mersed in a Fluid," Proceedings of Cambridge Philosophical Society (England), Vol. 31, Part 2, p. 232 (Apr 1935).

von Kármgn, T., "Uber Laminare and Turbulente Reibung," Vol. 1

pp. 233-252 (1921); National Advisory Committee for Aeronautics N 1092; see Zeitshrift fur Argewandte Mathematik and Mechanik (Berlin) Work 11, pp. 70-97.

Schultz-Grunow, "Der Reibungwiderstand Rotierender Scheiben in Gehausen," Vol. 15, pp. 191-204 (1935).

Tsai, F., "The Turbulent Boundary Layer in the Flow of Dilute Solutions of Linear Macromolecules," PhD Theisis, University of Minnesota

(1968).

Seyer, F.A. and Metzner, "Turbulence Phenomena in Drag Reducing Systems," American Institute of Chemical Engineers Journal, Vol. 15, No. 3, pp. 426-434 (1969).

Hoyt, J.W. and A.G. Fabula, "The Effect of Additives on Fluid Friction," Published in Fifth Symposium on Naval Hydrodynamics, Edited by J.K. Lunder and S.W. Doroff, Office of Naval Research, U.S. Department of

Navy ACR112 (1964).

Gilbert, C.G. and J.F. Ripkin, "Drag Reduction on a Rotating Disk Using a Polymer Additive," Symposium on Viscous Drag Reduction, Edited by C.S. Wells, p. 256. Plenum Press, New York (1969).

Schlichting, H., "Boundary-Layer Theory," Sixth Edition, p. 607, McGraw Hill Book Company, New York (1968).

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1N0V651473

FORM I (PAGE 1) _UNCLASSIFIED

DOCUMENT CONTROL DATA - R & D

Sicuri!; cftps.sil.catiorr of title, incd;u t ,ihsfri,ç I arid ,r,drxi,,j,' ..nnota(ir,n nr,r.I ht entered when lite ,,vcrull rrp.cfl i. r lassiiied)

OcGINA uNU AC IIVIT'r' (('.r!pt.ra)e author)

Naval Ship Research and Developnlrnt Center

Bethesda, Maryland 20034

20.REPORT SECURITY CL cr'rc Ir a rlor.c

UNCLASSIFIED

2h. GROUP

3 REPORT ÎITLE

DRAG REDUCTION AND SHEAR DEGRADATION OF DILUTE POLYMER SOLUTIONS AS MEASURED BY A ROTATING DISK

4 DESCRIPTIVE NOTES(Type of report and inclusive dares)

5. AUTHORISI(First name, middle initial, last name)

T.T. Huang and N. San,.telli

6. REPORT DATE

September 1972

78. TOTAL NO.OF PAGES

29 76. NO.0E PEES 11 88. CONTRACTOR GRANTNO b. PROJECT NO. Task ZR0230101 Subproject S-F354 e. _{¿1 UU,)}i tsr _ias

r

i d

96. ORIGINATOR'S REPORT NUMBER(S)

3678

Sb. OTHER REPORT NO(S)(Any other numbers that may be assigned

thi.rporl)

IO. DISTRIBUTION STATEMENT

Approved for Public Release: Distribution Unlimited

il. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Naval Ship Systems Command

13

ABST.RAÂlVsaturated _{drag-reduction line for dilute polymer solutions is derived for a} rotating disk from new velocity-similarity laws. The derived line is in good agree-ment with present and other experiagree-mental results. Drag reduction measured by a rotating disk is found to have three domains--oversaturated, optimal and

under-saturated. At a given boundary-layer thickness and wall-shear stress, the

drag-reduction increases with increasing concentration in the undersaturated domain, and the drag reduction does not increase with increasing concentration in the

over-saturated domain. The boundary between the two domains is the optimal drag

reduction, which is determined by the type of polymer and its concentration and a Reynolds number uR/v or ud/\),based on shear velocity and disk radius or boundary-layer thickness. Each drag-reduction domain has its distinct

shear-degradation characteristic. The measured shear degradation for a given polymer

solution in optimal and undersaturated domains is found to depend upon the con-centration, specific energy dissipation, wall-shear stress, and ambient temperature

of the solvent. However, the polymer solution in the oversaturated domain may

show no degradation in drag reduction, if the specific energy dissipated by the solution is not sufficiently large.

UNCLASSIF ¡FI)

SecurLty Ctasi(ication

14

KKV WORDS LINK A LINK e LINE C

ROLE WI ROLE WI ROLE

sr

I)rag Reduction of dilute polymer solution

Shear Degradation of diluted polymer solutions Rotating Disks measuring drag reduction and

shear degradation

Polymer Solutions used in measuring drag reduction and shear degradation

/

1N0V151473

(BACK)

UNCLASSIFIED