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NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER
Bethesda, Md. 20034
PROGRESS IN FRICTIONAL DRAG REDUCTION
SUMMER 1970 TO SUMMER 1971
lab. v. Scheepsbouwkunde
TecItui.he KoyehooI
4
by Paul S. GranvilleAPPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
SHIP PERFORMANCE DEPARTMENT RESEARCH AND DEVELOPMENT REPORT
The Naval Ship Research and Development Center is a U. S. Navy center for laboratory effort directed at achieving Improved sea end air vehicles. It was formed tn March 1967 by merging the David Taylor Model Basin at Carderock, Maryland with the Marine Engineering Laboratory at Annapolis, Maryland. The Mine Defense Laboratory (now Naval Ship R & D Laboratory) Panama City, Florida became part of the Center In November 1967.
Naval Ship Research end Development Center Bethesda, Md. 20034
a
REPORT ORIGINATOR SYSTEMS DEVELOPMENT DEPARTMENT MATERIALS DEPARTMENT SHIP ACOUSTICS DEPARTMENTMAJOR NSRDC ORGANIZATIONAL COMPONENTS
NSRDC CONNANDER TECHNICAL DIRECTOR 01 OFFICER.IN.OIARGE ANNAPOLIS PROPULSION AND AUXILIARY SYSTEMS DEPARTMENT 27 IISRDL PANAMA CITY COANDING OFFICER -P1 TIOINICAL DIRECTOR P101 OCEAN TECHNOLOGY DEPARTMENT_2}...
INSHORE WARFARE AND TORPEDO DEFENSE DEPARTMENT AVIATION AND SURFACE EFFECTS MINE COUNTERMEASURES SHIP PERFORMANCE
DEPARTMENT DEPARTMENT DEPARTMENT (SHIPS)
COMPUTATION AND MATHEMATICS MINE COUNTERMEASURES STRUCTURES DEPARTMENT
17 DEPARTMENT DEPARTMENT (AIR) P;
29
CENTRAL INSTRUMENTATION
DEPARTMENT OF THE NAVY
NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER
BETHESDA, MD. 20034
PROGRESS IN FRICTIONAL DRAG REDUCTION
SUMMER 1970 TO SUMMER 1971
by
Paul S. Granville
Drag-Reduction Monitor for ORDI-IAC (Ordnance Systems Command Hydroballistics Advisory Committee)
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
TABLE OF CONTENTS
Page.
ABSTRACT 1
ADMINISTRATIVE INFORI4ATIPN 1
INTRODUCTION 1:
PROGRESS IN DRAG-REDUcTION--SUMMER 19.70 TO SUMMER 1971 .
FUNDAMENTAL ASPECTS ... 2 CORRELATION 2 DIFFUSION . . 3 DEGRADATION S
SUMMARY OF DRAG-REDUCTION RESEARCH IN LABORATORIES- -1971 3
DEFINITIONS 3
ADMIRALTY RESEARCH LABORATORY 3
ADVANCED TECHNOLOGY CENTER, INC. 4
UNIVERSITY OF ALBERTA 5
ARIZONA STATE UNIVERSITY
BROWN UNIVERSITY 6
COLORADO STATE 11NIVERSIY 6
HYDRONAUTICS, INC. . . 7
UNIVERSITY OF ILLINOIS ... 9
ISRAEL INSTITUTE OF TECHNOLOGY - .
. 9
UNIVERSITY OF LONDON
...
UNIVERSITY OF MICHIGAN .. . .... .. 10
UNIVERSITY OF MINNESOTA 10
UNIVERSITY OF MISSOURI-ROLLA _ii
NATIONAL PHYSICAL LABORATORY 12
NAVAL POSTGRADUATE SCHOOL .i.
NAVAL RESEARCH LABORATORY .. .
-...
.
13
NAVAL SKIP RESEARCH AND DEVELOPMENT CENTER . 14
OHIO STATE UNIVERSITY 16
UNIVERSITY OF OKLAHOMA ... 16
UNIVERSITY OF PARIS . .
17
PENNSYLVANIA STATE UNIVERSITY 18
UNIVERSITY OF SOUTHAMPTON ... 19 TEXAS MM UNIVERSITY ... 21
UNIVERSITY OF TOKYO - . . 21
UNIVERSITY COLLEGE OF WALES . . . .
BIBLIOGRAPHY--FRICTIONAL DRAG REDUCTION: SUMMER. 1970 TO
ABSTRACT
A summary of progress in the achievement of frictional drag reduction is presented in terms of highlights, laboratory activities, and bibliographic entries from the summer of 1970
to the summer of 1971.
ADMINISTRATIVE INFORMATION
The work described in this report was sponsored by the Naval Ordnance
Systems Command (Code 035B) and was funded under UR-123-Ol-03.
INTRODUCTION
One of the duties of the Drag-Reduction Monitor is to encourage
sci-entific and engineering developments in drag reduction. The purpose of this report is to disseminate current knowledge about drag reduction to
researchers and developers here and abroad. A brief summary of highlights
is given of progress in drag-reduction techniques from the summer of 1970 to the summer 1971. A summary is presented of drag-reduction work underway
in laboratories and other establishments. The statements are in response
to a letter of inquiry and are r.epeated almost verbatim. The bibliography lists the available published literature which appeared during the year
defined previously.
PROGRESS IN DRAG-REDUCTION--SUMMER 1970 TO SUMMER 1971
Almost all the literature about turbulent drag reduction concerns
polymer additives. Activities cover the spectrum from fundamental inquiries
to engineering applications. The effort is international in scope and
in-terdisciplinary in range. Fluid dynainicists, physical chemists, mechanical engineers, chemical engineers, and others are involved. There still remain
scientific and technical questions.
FUNBAMENTAL ASPECTS
An acceptable explanation of the niechanism of drag reduction has yet to be agreed upon. Paterson and Abernathy (51) believe that the polymer additive affects the viscous property of the flui4 in not the usual way as in a rotating viscometer but in an irrotational manner such as occurs when
a long thr:ead is pulled. They allude to Lumley,ascribing the existenceof
such irrotational flows close to a wall for drag-reducing fluids. TiLis is
a laminar flow property which is plausible inasmuch as turbulent flow appears as an unsteady laminar flow to a polymer molecule,
Arunachalam, Fulford, and Bryson (2) and (11) postulate that drag reduction is due to free-hanging loops of adsorbed molecules which damp
turbulent eddies originating at the wall. On the other hand1 experimental
studies by Peyser, Little, and Singleterry (52) show that 'Polyox and poly-acrylamide molecules adsorb in thin films and lie relatively flat at the
interface with no large loops projecting into the solution. Also, the
composition of the surface and its polymer adsorption show no relatioü tO
the degree of drag reduction.
-CORRELATION
The concept of a logarithmic interactive velocity similarity line
by Virk (72) is proving more attractive. There are direct velocity surveys by Tsai (P-76 of TN 184) and TOmita(P-74a of TN 184). There is the
in-direct correlation with maximi.nn drag reductions (72). Granville (27) uses the interactive similarity law to. provide limitations to B correlations in
cases where the shear layer or pipe diameter is small. Granville (26) and
(28) obtains logarithmic relations for maximwn drag reduction for flat. plates and rotating disks, respectively.
*
DIFFUSION
In studies of injection from a slot, Latto and Shen (43) find it is desirable to keep the injection velocity low and tangential to the surface. Poreh and Hsu (85) consider the analytical and experimental aspects of
in-jection from a slot..
Wu (81) concludes that slot ejection is better suited for dilute solutions, and porous injection is better suited for concentrated solutions. Walters and Wells (74) and (75) in studies of porous injection find that the
polymer solution reduces the rate of turbulent diffusion.
DEGRADATION
Polymer additives represent a mix of molecular weights since the
polymerization process is not an exact chemical procedure. Paterson and Abernathy (51) find that mechanical degradation affects most readily
molecules of the highest molecular weight which unfortunately are the most
effective.
White (78) believes that degradation, although initiated by
turbu-lence, is primarily due to oxidation. Antioxidants then inhibit
degradation.
SUMMARY OF DRAG-REDUCTION RESEARCH IN LABORATORIES- -1971
DEF INITIONS Title of Project Principal Investigators Cc) Description of Project Results Publications
ADMIRALTY RESEARCH LABORATORY Teddington, Middlesex, England
Measurement of Turbulence Velocities in a Boundary Layer with Polymer
Additive.
A. Hobson and N. Hodson
Cc) The boundary layer is provided by a small gravity-fed water tunnel with
a Perspex working section. Neutrally buoyant particles are introduced upstreamof the measuring section and are illuminated in t1e measurement
plane by a laser beam. Particle motion is recorded on film,. A large
number of, measurements of U, V, W velocities have been made both with and without additives.
(d) Data arein the process of analysis. Mean turbulent-velocityfluctu-ations as a function of distance from the wall have been determined. Very marked differences arise when additive is present.
ADVANCED.TECHNOLOGY CENTER, INC.
(Formerly LTV Research Center), P.O. Box 6144, Dallas, Tex. 75222
1. (a) Diffusion of Additives
(b) C.S. Wells, Jr., and R.R. Walters
(cExperimental and analytical techniques are used to determine the factors which control friction reduction when a polymer solution is
diffused uniformly. from a surface.
(d)An experimental phasewascompleted, inwhich solutions of one additive, Polyox WSR-30l, were injected through a pOrous wall into
a turbulent pipe flow of water. The results showed an effect which - in somecases was detrimentalto.friction reduction over the area of
uniform injection, e g , where the additive reduced the diffusion rate near the wall, which in turn increased the viscosity in the
viscous sublayer. Concentration profile measurements enabled identification of the transitional sublayer as the boundary layer region requiring the presence of the polymer to sustain friction
reduction.; This information should be very helpfulin optimizing
the practical drag-reduction techniques that utilize uniform
diffusion from a surface.
Ce) (75)
2.. (a) High Shear Stress Effects on Polymer Drag Reduction
J.G. Spangler
An experimental rotating-disk facility is being used to investigate polymer-friction reduction under conditions of very high turbulent
shear stréssés for both smooth and rough surfaces.
Tests of a rough (600-grit sandpaper) surface were performed in a Polyox coagulent solution so that the onset of friction reduction
occurred before the onset of roughness effect. The results showed
the onset of roughness effect to be delayed due to the polymer.
However, it was also observed that a degradation of the friction reduction also occurred for smooth disks in the polymer solutiOn it
the same level of high shear stresses. This apparent second
UNIVERSITY OF ALBERTA
Department of Chemical an4 Petroleum
Engineering, Edmonton 7, Alberta,'
Canada .
-Drag Reduction Mechanisms F.A. Seyer
Cc) 1. Streak-photograph dtermination of velocity profile and turbulence
intensity in pipe flow. Verification of similarity laws. Laminar and turbulent entry flow of drag-reducing polymers.
Theoretical analysis of molecular deformation and orientationof
polymer solutions.
Cd) h The Prandtl-von Krinn similarity laws are applicable to drag
reducers, provided the flow is turbulent. Both the sublayer and buffer layer are substantially thickened.
The drag reduction asymptote of Virk et al is not unique
For
theconcentrated drag reducers the first turbulence appeared at Reynolds numbers of approximately 2100 but the intermittency increased very
slowly with Reynolds number
2 Dilute drag reducers (onset of drag reduction at NRe > 2100) have
contraction losses andentrylengths equivalent to Newtonian fluids.
Concentrated drag reducers differ markedly from Newtonian fluids Qualitatively it is possible to relate the deviations from Newtonian
behavior to the transitional nature of the flow.
3. A molecular model has been used to show how the. shear dependent relaxation time of the White-Metznei model can be fabricated from
linear viscOelastic measurements.
(e) la. Rollin, A., "Streak Velocity Measurethents in Turbulent Flow of Polymer Solutions," Ph.D. Thesis, University of Alberta., EdmontOn
(Jul 1971).
lb. Rol.lin, A. and Seyer, F.A., "Velocity Measurements in Turbulent
Flow
of Dilute Viscoelastic Solutions," to be presented at 21st Canadian Chemical Engineering Conference Montreal (Oct 1971).2 Seyer, F A and Cantania, P J , "Laminar and Turbulent Entry Flow of Polymer Solutions," submitted for publication (Jun 1971)
ARIZONA STATE UNIVERSITY .
College' of:Engineeririg Sciences, ' . :
Tempe, Ariz. '85281 - . . .
Response of Dilute Polymer Solutions d Wate tb Disturbances in Pipe
Flows
. .. .'N.S. Bernan . "
A laser Doppler velocimeter. has been used to measure velocities and
velocity distributions at various points downstream of disturbances
The disturbances resulted in various types of eddy flows at Reynolds
numbers less than transition. These eddy flows decayed downstream. The disturbances did not propagate from the waLl to the pipe certer as
fast in the dilute polymer solutions as in pure water. Therefore, the
decay was faster for pure water. Autocorrelation and probability
studies showed that there was a lack of random siñall eddies in the dilute polymer cases. The behavior of the dilute polymer solutions was attributed to thedifferences in the eddy sizes created by the
dis-turbance at the wall.
BROWN UNIVERSITY
Division of Engineering, Providence, R.I. 02912
(a) Mechanics of Dilute Polymer Solutions
(1,) R.I. Tanner
(c) The project was an investigation of the mechanical properties of dilute
(drag-reducing) solutions of polymers,
Cd) Some theoretical results on a new nonlinear-spring Rouselike molecule
-have been obtained. They wil.1 appear in the publication given in (e).
Tanner, R.I. and Stehrenberger, W., "Stresses in Dilute Solutions of
Bead/Nonlinear Spring Macromolecules I," Journal of Chemistry and Physics (about Aug 15, 1971).
COLORADO STATE UNIVERSITY
Department of Civil Engineering,
Fort Collins, Cob; 80521
Viscous Drag Reduction for Polymer Injection into Developing Boundary
Layers J.P. Tullis
The project has been an experimental program using . 12-inch-diameter
pipe, 200 feet in length, with flow velocities exceeding 60 feet per
second. A developing boundary layer is created by a 5-foot-diameter
settling chamber and a converging nozzle. Polymer is injected at the
wall several feet below the nozzle. The effect of the polymer on the wall friction, velocity profile, and turbulence is being studied as well
as the diffusion of the polymer in the developing boundary layer. Results so far have been a thórcigh evaluation of. developing shear
stress and boundary layers for flow without polymer. The length required to obtain a uniform wall shear stress has been determined.
The shape of the velocity profile and the. boundary layer thickness in the developing region have been measured. An analytical equation for predicting boundary layer growth has been developed and verified.
HYDRONAUTICS, INC.
PindeU School Road, Howard County,
Laurel, Md. 20810
1. (a) Hydrodynamics of Disperse Systems
(b) J. Wü and M.P. Tulin
-Cc) Studies 10 date have been aimed at imprpvirg 0th understanding. of
turbulent flow of dilute polymer solutions and at investigating the techniques and requirements for using additives for drag reduction
in external flows.
(4) 1. Ejector
Inclined, vertical, and shielded.slots along with a porous-type
ejector have been tested. The slot ejector wa fouiid to be better
suited for dilute solutions; the porous ejector, for concentrated
sOlutions. Compared to the vertical and the shielded slots, the
inclined slot was fOund to introduce less mix.ng between the ejected additive solution and the surrounding water.
Polymer Ejection
A systematic drag-reduction study was conducted by.ejecting Polyox additive solutions into a pure water boundary layer over both smooth
and rough surfaces It was found that for the most effective
ejection, the slot-ejection angle should be small, the slot thickness
should be comparable with the thickness of the viscous sublayer, arid
the ejection rate should be comparable to the normal viscous sublayer
discharge A range of optimum concentration of the ejected solution was found to be 102 to l0 parts per million weight for the smooth plate and an order of magnitude greater for rough surfaces where a wall mixing due to roughness caused increased dilution of the
ejected solution.
Diffusion Process
The diffusion of drag-reducing polymer ejected from the wail into a turbulent boundary layer was measured with a laser-phototransistor
unit. The results indicated a suppressed turbulent diffusion of
polymer solution. Surface Containing
An expe]-iment was conduçte4 which involved ejecting the additive
solution through the inclined slot into pure water boundary layer over a smooth plate and terminating the ejection suddenly to observe
the period over which the drag reduction persisted. A prolonged
drag reduction following cessation of ejection was found.
(e) (60) and (81)Wu, J.. etal. t'Recent Drag Reduction Research at
HYDRONAIJTICS," Proceedings of Drag. Reduction Workshop, Office of Naval Research (iii press).
2. (a) Development and Trials of a Surface Ship Additive System (b) A. Goilan and M.P. Tulin .
The general aim of this research was to investigate the applicability of polymeric additives for reducing friction drag of a ship; in
particular, studying the varioUs physical parameters involved as well as the dispersion system effect on the drag
Experiments were carried out on a ship model 11.4 feet in length,
1.4 feet in girth, find towed at a maximum speed for 20 feet per second.
Two separate injection slots were arranged on the model The forward and the mid slots were located 40 and 70 inches, respectively, from the bow. A i-am scoop provided the required Water flows, which were
measured by a.pitot tube and were piped into a mixing chamber. A
concentrated premixed solution of FRA (concentration 1 percent) was
in-jected into the mixing chamber by air pressure. The polymer solution was injected from the mixing chamber through the slots located on the
model.
Continuous measurements of polymer concentrations at the model hull
were obtained. The ejected polymer solution contained a black dye,
having a concentration that varied with changes in polymer
concen-tration. Photoelectric pickups previously calibrated with this dye gave
a continuous polymer concentration readout as the solution was pulled through the pickups from slots in the model hull.
As expected higher drag reduction was obtained for higher model speeds. Optimal results were obtained for a combination of solution-injection rate of approximately 10 times the boundary sublayer and concentrations
in thô ra.nge between 1000 and 1300 parts per million. At lower
in-jection concentrations, as a result of the high rate of disperison, the
polyner was less effective. Higher concentration of flow rates was also less effective, presumably due to the high local head losses
created by the mixing action.
It should be noted that in the design of injection slots the diver:gence
of
the stream lines at the model hull should be taken into account. In this particular model, injection through the mid slot was moreeffective than injection through the forward slot (despite higher shear stresses at the bow) because of the high divergence of the stream
lines at the bow of the model. It seems that max-imi.nn drag reduction
can be obtained f polymeric additives are injected along the whole ship hull; however, in cases of small quantities of injection polymer, higher drag reduction can be obtained by injecting the polymer only
through parts of the slots.
In our experiments, a reduction of 11 percent of the total model drag
was measured. This corresponds to a reduction of about 35 percent of
the viscous drag.
However, we can predict from our experiments with the two slot that reduction of approximately 19 percent. of the total model drag at top
speed is probable. This should be obtainable through (1) optimization of the injection slot opening and (2) injection of the polymer-water
solution at the right, flux and concentration on the model hull.
UNIVERSITY OF ILLINOIS Department of Chemical
Engineering, Urbana, Ill. 61801 Wall Turbulence
T.J. Hanratty, G. Fortuna
Electrochemical techniques are being used to examine the effect of
drag-reducing polymers on the structure of turbulence in the viscous sub-.
layer.
The principal effect has been found to be an increase in the scale of
the flow oriented eddies.
Fortuna, G., "Effect of Drag Reducing Polymers on Flow Near a Wall,"
Ph.D. Thesis, University of Illinois, Urbana, Ill. (1971).
ISRAEL INSTITUTE OF TECHNOLOGY Department of Civil Engineering, Haifa, Israel
Drag Reduction and Diffusion in Flows of Dilute Polymer Solutions
M. Poreh
Cc) Theoretical and experimental study
Poreh, M. and Hsu, K.S., "Diffusion from a Line Source in a Turbulent Boundary Layer," to be published in the Journal of Hydronautics, Vol. 14.
Miloh, T. and Poreh, M., "The Resistance to Rotation of Free and
Enclosed Discs," Journal of Applied Mechanics, Paper 71, APM-21 (1971).
Ce) (56) and (85)
UNIVERSITY OF LONDON
Imperial College of Science Technology, Department of Mechanical Engineering,
London SW7, England
Calculation Procedure for Drag Reduction
D.B. Spalding
General computer program developed for solving the boundary-layer equations of turbulent flow with allowance for diffusion of
drag-reducing additive. Cd) See Ce)
Ce) (84)
UNIVERSITY OF MICHIGAN
Department of Engineering Mechanics, Ann Arbor, Mich. 48104
(a) Polymer Additive Flows
(b) W.P. Graebel .
Cc) An experimental investigation of pipe flow of fluids with po.nier
additives A laser-Doppler anemometer is utilized in measuring mean
velocities as well as turbulent fluctuations The equipment is being converted to two-component capabilities so that all pertinent Reynolds
stresses can be measured.
In addition, a theoretical study of the transition of pipe flow is
being conducted. . . .
No results differing from past suimnaries at this time.
Graebel, 1.P., The Stability of Pipe Flow: Pa.t I, Asymptotic Analysis for Small Wave-Numbers," J. of Fluid Mechanics, 43, pp. 279-290 (l970).
UNIVERSITY OF MINNESOTA
St. AnthOny Falls Hydraulic Laboratory, Minneapolis, Minn. 55414
1. (a) The Influence of Drag-Reducing Polymers on Surface Pressure
Fluctuations:on Rough Surfaces
(b) J. Kilien and J. Almo .
-(c.) Measurements were made of average drag- and surface-pressure
fluctuation spectra on a cylinder rotating in hater The effect of
a drag-reducing polymer additive in concentrations from 9 to
1000 wppm were measured on both smooth and rough surfaces. Drag was calculated from the average torque required. to drive the cylinder. Surface pressure fluctuations were measured by an .NSRDC surface hydrophone placed in the cylinder surface. .
Change in surface pressure intensity due to the addition of a drag-reducing polymer (Polyox 301) to the water or the addition of
roughness to the cylinder surface or both in combination was found
to correlate with changes in the friction factor...
Project Report 119, St. Anthony Falls Hydraulic Laboratory (in .
preparation).
2. (a) Injection of. Polymer Additives into Relatively Large-Scale Boundary
Layers .
(b) J.M. Wétzel .
(c) Concentrated solutions of Polyox WSR-301 have been injected
tangentially into the developing turbulent boundary layer of a.large
flow stream. Concentration and velocity profiles have been measured for various injection rates and distance downstream from the in-jection slot in boundary layers hat may be as much as 1 foot thick.
Local drag measurements were made with a surface-plate dynamometer
for various polymer-injection rates. Measured velocity profiles indicated that the mixing-length constant in the region near the wall was a function of concentration at the wall or local drag
reduction. The mixing length constant monotonically decreased from 0.4 to approximately 0.1, the latter being obtained with a wall concentration of 225 parts per million and a local drag reduction of
70 percent. Diffusion of the injected polymer in the boundary layer was found to decrease with increasing concentration and injection rates.
Report in preparation.
UNIVERSITY OF MISSOURI-ROLLA
Department of Chemical Engineering, Rolla, Mo. 65401
1. (a) Drag Reduction in Aqueous Detergent Systems
J.L. Zakin
The effects of concentration, aging, shear stress, and salt concen-tration on drag reduction of aqueous detergent solutions are being
studied.
2. (a) Drag Reduction in Solid-Liquid Flow
J.L. Zakin and G.K. Patterson
The effects of particle size, shape, and concentration on drag
reduction in solid liquid flows are being studied.
3. (a) Mechanical Degradation of Dilute Polymer
J.L. Zakin, G.K. Patterson, and J. Culter
The effect of concentration, molecular weight, shear stress, polymer type, and solvent on the rate of degradation of dilute polymer solutions and the effect of degradation on drag reduction
are being studied.
4. (a) Measurement of Solution Complex Viscosities at High Shear Strains
G.K. Patterson
An instrument has been developed which successfully measures Ti' and
ri" in the audiofrequency range (30-1500 cps) at strain amplitudes beyond the linear range. Improvements are being sought to increase
sensitivity to lower the viscosity limit from 50 to approximately
5 centipoise.
Shen, K.-S., "Measurement of Complex Viscosity in Solutions at
Finite Shear Strains," Ph.D. Thesis, University of Missouri-Rolla (1971).
NATIONAL PHYSICAL LABORATORY Ship Division, Feltham,
Middlesex, England
Basic Studies of Drag Reduction G.E. Gadd
Two review articlèshve been Written as well as an account made of
experiments on drag redUction by algae. (d) (24) and (29)
Gadd, G.E., "Friction Reduction with Dissolved Polymers," tobe
published in a volume of Encyclopedia of Polymer Science and Technology
(scheduled to appear Sep 1971).
NAVAL POSTGRADUATE SCHOOL
Department of Mechiiical Engineering., Monterey, Calif. 93940
(a) Flow of. Dilute Polymer Solutions about Bluff Bodies
(b)T. Sarpkaya
(c) Flow of aqueous solutions of Polyox WSR-301, with concentrations of 1.0 to 200 wppm, past circular cylinders was investigated in the
drag-transition region of Reynolds numbers Drag force, pressure
distri-bution, and separation angle were measured on cylinders with diameters
from 1/4 inch to 1 1/2 inches. Lift and drag forces acting on a
NACA-0Q24 hydrofoil mOdel were also measured.
Cd) The polymer additive was found to alter only those force coefficients
having a Reynolds-nimiber transition region. Two distinct types of cylinder-drag transition were observed: (1) At high concentrations, transition from a sub- to a trans-critical flow occurred at the same
free-stream velocit independent of body diameter; and (2) at low
concentrations and/or molecular weights, tripping from a sub- to a super-critical flow occurred at a Well-defined flow condition which was a function of the free-stream velocity, body diameter, and turbulent
pipe-flow friction reduction.. In all cases, transition occurred
earlier than that in the pure solvent The polymer had a destabilizing
effect on the boundary-layer flow.
(e) (62)
Sarpkaya, T and Rainey, P G , "Stagnation Point Flow of a Second Order Viscoelastic Fluid," (to appear in Acta Mechanica).
$arpkaya,T., "Flow of Dilute Polymer Solutions About Bluff Bodies," Proceedings of the Canadian Congress of Applied Mechanics (17-21 May 1971).
NAVAL RESEARCH LABORATORY, Surface Chemistry Branch, Washington,. D.C. 20390
Drag Reduction Studies in Aqueous and Nonaqueous Solvents
R.C. Little,. R.J. Hansen, and P. Peyser
Experimental and' theoretical investigations are being made of the
drag-reducing ability of polymers and association colloids in aqueous and
nonaqueous environments.
Cd) 1. Theoretical work conducted at this laboratory indicates that polymer
solutions exhibit unusual behavior in transient laminar shear
gradients. This behavior may in some measure be responsible for the
drag reduction phenomenon.. Specifically, Stokes first problem has been solved fOr a liquid described by the convected Maxwell. con-stitutive equation. The results have been combined with a
quail-tatively correct mathematical model, for the turbulent boundary
layer, and the following predictions have been made: (1) for sufficiently small liquid velocities, polymer concentrations, an4 molecular weights, the turbulent flow behavior of a polymer solution
is essentially Newtonian, (2) a maximum drag reduction as)rmptote (that is, an upper bound on the amount by which drag may be reduced at a given flow velocity) exists for a given polymer additive.
2. Eariy'turbulence' has for the first time beeriobserved in the flow of dilute polymer solutions in tubes larger than capillary size. The onset wall shear stress for' this phenomenon has been measured in tubes of 0.553 and 0.660 centimeters. Polyethylene oxide samples of
two o1 hts were dispersed in. water-glycerine mixtures ranging from 0.0261 to 0.160 poise. The onset wall shear stress was
'fOund to increase linearly with solvent viscosity, fi,rst decreasing
then inceasing with increasing polymer concentration. An
explanation for eatly turbulence, incorporating both molecular and
continuum views, has been offered on the basis of these results. '3. A simplified equation resul'ting from a rearrangement of Virk's
uni-versal drag-reduction relation has been shown' to adequately
describe the drag reduction of aqueous solutions of polyethylene oxide condensates over a wide range of molecular weight and
concen-tration. Virk's intrinsic concentration was found to be an inverse
function of molecular weight.
4. A viscoelastic dispersion of 0.2 percent lithium phenylstearate in
aircraft.hydraulic fluid-base stock maintained a drag-reduction level of 25 to 40' percent for 600 hours of continuous shear at 200 F in a hydraulic-system mockup. The life of the dispersion is sensitive,
hOwever, to the presence of such reactants as carbon dioxide, oxygen, and water, and care must be taken to exclude these substances from
the system.
5. A sample of an asbestos disperison obtained from England was tested
for' drag reduction (DR) as' a functiOn of temperature from 19 to 90 C in a rotating-disk apparatus Significant drag reduction (40 percent
max) was observed, and the data could be represented by a common
curve from 10 to 70C as a plot of percent DR versus Reynolds number.
At 90 C, the dispersion appeared to coagulate. A new dispersion made up by dispersing long asbestos fibers (U.S. source) in Aeoresol
01 showed greater DR (50 percent max) than the English sample. These data could also 'be plotted as percent DR versus Re at' all
temperatures from 10 to 90 C. The asbestos dispersions showed less degradation under shear than Polyox FRA. Maximum DR. was obtained at approximately 300 parts per million.
(52) and (83)
NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER
Bethesda., Md. 20034
(a) Heat Transfer in Dilute Polymer Solutions (b) R.G. Howard
Cc) Characterize both fresh and aged Polyox WSR 01 and Polyhall M295 with respect to heat-transfer reduction and drag reduction.
(d) Aged Polyox WSR 301 was less effective than fresh Polyox WSR 301 be-cause the average contour chain length was less (measured by Waters Associates). Fresh Polyox WSR 301 and fresh Polyhall M295 were
approximately equal in effectiveness.
(a) Turbulent Flow Drag Reduction by Dilute Poly(Ethylene Oxide) Solutions in Capillary Tubes
-1. M. Felsen and T.G. Smith (U. of Md.)
Poly(Ethylene oxide) coagulant and WSR-N-3000 solutions were
sub-jécted to high shear stresses in glass capillary tubes and in glass capillary tubes coated with monomolecular layers having various surface-free energies. Drag-reduction was investigated as a
function of Reynolds number and concentration up to and through the
onset of degradation. '
-Drag reduction in glass capillary tubes (0.016-inch diameter) coated with fluorocarbons, hydrocarbons, and silicone as well as uncoated was measured, employing a 0.5 wppm concentration of poly(ethylene
oxide) coagulant solution in water. Drag reductions as high as
50 percent were measured. All coated tubes gave equal drag reduction until the onset of degradation. The maximum Reynolds number, or stability before the onset of degradation, Was obtained
with the uncoated glass tube. The experimentalevidence showed an
increase in the maximum Reynolds number at the onset of degradation with increasing surface free energy of the tube coatings. Conse-quently, it is hypothesized that drag reduction increases with
in-creasing surface-free energy at equal Reynolds numbers at the onset of degradation..
A possible explanation of the drag-reduction mechanism is presented, emphasizing the importance of surface viscosity and Gibbs elasticity of an adsorbed or hydrogen bond-associated polymer film rather than the mechanism of turbulence suppression by individual polymer
molecules. It is hypothesized that a wall-associated polymer film,
exhibiting optimum surface rheology characteristics, acts to inhibit turbulence in the wall region and thus to stabilize flow and retard
the onset of degradation.
(e) (16)
Felsen, I.M., "Turbulent Flow Drag-Reduction by Dilute
Poly-(ethylene oxide) Solutions in Capillary Tubes," Ph.D. Thesis,
Depart-ment of Chemical Engineering, University of Maryland, College Park,
Md. (1971).
3. (a) Drag Reduction and Degradation of Dilute Polymer Solutions in
Turbu-lent Pipe Flow (b) T.T. Huang
(c) Drag reduction caused by dilute polyethylene oxide (Polyox WSR-30l) and ainionic charged polyacrylimide (Magnifloc 835A) polymer solutions
was studied experimentally in 1.918- and 0.455-centimeter ID smooth
pipes. A three-layer mean-velocity profile model was used to
analyze the measured data.
(d) Drag reduction caused by dilute Polyox WSR-301 and Magnifloc 835A
solutions was measured in this study and was compared with other
results for high drag-reducing polymer solutions. The following conclusions can be drawn for internal, e.g., pipe flow of homogenous
polymer solutions.
The three-layer mean-velocity profile during drag reduction,
measured by Seyer and Metzner and Tsai is consistent with the present
gross-flow measurements. The three layers consist of
A viscous sublayer;
A strongly interactive layer, characterized by a smaller von
Krmn constant; and
A weakly interactive layer, characterized by a parallel upward
shift of a semilogarithinically-plotted velocity profile. The
gross flow can be divided into three regimes
Without drag reduction, following a Newtonian fluid-friction law; With drag reduction, dependent upon the entire characteristics of the polymer-solvent system, characterized by the presence of
the three layers; and
A saturate, limiting the maximum possible drag reduction, with the strongly interactive layer dominating the entire interactive
layer. The slopes of the present measured gross-flow curves
during high drag reduction are found to be parallel to the
correspond-ing slopes of the saturated drag-reduction line. However, these
slopes deviated progressively from those of the saturated line and became closer to those of the solvent curves with decreasing drag
reduction. Drag reduction at a given concentration in terms of + (= F/uT) -
(VS/UT),
which corresponds to the traditional iB, increases linearly with log(uT/uT*)
where V and V are the mean velocity of the solution and solvent
alone,
u is the friction velocity, and
u is the onset friction velocity.
Then V'levels off and finallydrops at
higher
u. The
Magnifloc solutions are superior in shear degradation resistance but inferiorin drag
reduction,
compared with the Polyox solutions at correspond-ing conditions The present measured onset of drag reduction depends upon polymer concentration and is seriously affected by sheardegradation.
Ce) (86)
OHIO STATE UNIVERSITY
Department of Chemical' Engineering,
Columbus, Ohio 43210
Visual Studies of the,Flow in the Sublayer of Drag-Reducing Polymer
and Soap Solutipns,
H.C. Hershey.
Visual studies of the wall area during turbulent flow, using
high-speed photography and tracer particles Also the flow around a probe will be photographed, using both a solvent and a drag-reducing
solution.
-Cd) A series of aluminum discaps has been studied in toluene. It has
been found that a minimum concentration for stabIlity exists below which the associatiOn colloid may be broken down either by high
shear or by aging or by a combination. Above this concentration, the association colloid may be broken down by high shear but it
reforms upon standing.:
UNIVERSITY OF OKLAHOMA
School of Aerospace and. Mechanical Engineering, Norman, Okla. 73069
Aerodynamic Skin-Friction Reduction
E.F. Blick
Turbulent skin friction reduction on airfoils coated with
poly-urethane foam and 'polyvinyl chloride skin.
Drag reductionsof asinuch as 30 percent were measured on anNACA 0009 airfoil tested in a wind tunnel at Reynolds numbers between
3XlO5and3XlO6.
Boyce, M.P. and Blick, E.F., "Skin Friction Drag and Velocity Profile Measurements in Two-Phase Flow," Paper 71-FE-32, American Society of Mechanical Engineers Conference on Fluids Engineering
-UNIVERSITY OF PARIS
Aerodynamics Laboratory, Orsay, France
(a) Determination of Viscoelastic Properties of Dilute Polymer Solutions by Dynamic Pressure Measurements
(b)D.H Fruman and C. LOieaü
(c) Actual measurements of pitot tube-defectpressures in viscoelastic
fluids are made in a small towing tank specially built for this purpose Measurement of defect is made directly by means of a
differential pressure transducer connected to two pitot tubes. One is immersed in the solvent; the other, in the solution. This set up permits very high accuracy in the measurements.
Cd) The first results obtained by this device show the existence of a
cutoff gradient at the nose of the pitot tube of the order of magnitude of the inverse of the first relaxation time tomputed by
means of the Rouse or Zimm theories By the utilization of different
probes with identical geometry but with different internal to
ex-- ternal diameter ratios, it is shown that the differences in the
cut-off gradients tend to a limit value when this ratio tends to zero..
For this limit value very simple theories based on potential flow permit a correlation of results obtained for different geometrical
shapes of the probes It is shown that a second relaxation time can be computed froi.these experiments to a very high accuracy.
(e) Fruinan, D., Loiseau, G., Sulmont, P., "Effets viscoiastiques dans
les mesures des pressions statiques et d'arrt," Comication
prsente au Comit Hdrotechnique deFriñe (20 Mar 1970).
2. (a) Static-Pressure Measurements in Dilute Polymer Solutions with Lift Reduction
(b) D.H. Fruman, G. Loiseau, and P. Sulmont
Cc) Study of the influence of dilute polymer solutions on static pressure
measurements on geometrical simple bodies Influence of this
solution on lift reduction The device described in 1(a) is used
for this research program.
(d) Measurements made on circular cylinders show that elastic effects
are present not only at the nose of the body but that they affect a
wide part of the upstream face. At the rear part of the body pressure measurements are very similar to those obtained in the
supercritical regime for the same bodies in Newtonian fluids.
(e) (23)
Fruman, D., G. Loiseau, P. Sulmont, les mesires des pressions statiques presnte au Comit Technique de la France (10 Mar 1970).
3. (a) Drag Reduction and Degradation (b) D.H. Fruman and G. Norgeot
17
"Effets viscolastiques dans et d'arrt," Communication
The main feature of this Work is to define for a very effective polymer (Polyox WSR 301) the condition of the onset of the
de-gradation in pipe flow.
For a low enough Reynolds number and given fluid and pipe diameter, a region is observed with constant local friction factor A, limited by two other regions--upstream an abnormally long entrance region
and downstream a region where the friction factor grows. If the
Reynolds number increases fOr a given fluid and a given pipe
diameter, the length of the entrance region decreases, and the down-stream region where A grows is shifted updown-stream The region of the
constant frict-ion factor decreases and sometimes disappears com-pletely.
(21), (19), (22)
PENNSYLVANIA STATE UNIVERSITY
Department Of Aerospace Engineering, University Park, Pa. 16802
1. (a) Theoretical Investigations of Turbulent Flow of Non-Newtonian Media
J.L. Lumley
Attempt to understand dynamical behavior of dilute polymer solutions
in turbulent flow on basis of constitutive relations.
Quantitative prediction and explanátiön of threshold phenOmenôn;
explanation of.apparent slip phenomenon. Sübniitted for publication, Physics of Fluids:
"Applicability of the Oldroyd Constitutive Equation to Flow of
Dilute Polymer Solutions"
"A Centerline Bernoulli Equation for Q.asi-Stea4y Dilute Polymer
Flow"
Proceedings of Convegno sulla Teoria della Turbolenzo, Instituto Nazionaledi Alta Maternatics, Roma (Apr1971):
"On the Solution of Equations Describing Small-Scale Deformation" Proceedings of Turbomachinery Symposium, Pennsylvania State
Uttiversity (Aug 1970) :
"Discussion of 'Non-Newtonian Effects on Flow Generated Cavitation and on Cavitation in a Pressure Field."
2. (a) Large Disturbance Stability of Non-Newtonian Flows (b) P. Kundu and J. Lwnley
(ç) Analysis by energy method of stability of simple shears of various non-Newtonian fluids.
Successful reformulation of energy method to encompass second-order fluids.
"Stability of a Plane Couette Flow of a Second-Order Fluid."
3. (a) Computation of Polymer Flows
(b) T. Gatski and J. Lumley
Cc) Direct numerical computation of simple laminar flows of polymer
solutions, modeled by Oldroyd constitutive relation. Cd) None as yet.
Ce) None as yet.
4. (a) Light Scattering in Strained Polymer Solutions
B. Khajeh-Nouri and J. Lumley
Attempt to measure light scattering by polymer molecules in an
irrotational strain-rate field. None as yet.
None as yet.
5. (a) Turbulence Measurements in Polymer Solutions by Laser-Doppler Velocimeter
W.K. George and J. Lumley
Attempt to measure velocity spectra in homogeneous turbulence of
dilute polymer solution by use of laser-Doppler velocimeter.
Successful analysis and experimental verification of all sources of
ambiguity in Doppler signal.
George, W.K., "An Analysis of the Laser-Doppler Velocimeter and Its
Application to the Measurement of Turbulence," Ph.D. Thesis,
Department of Mechanics, The Johns Hopkins University, Md. (May 1971).
George, W.K. and Lumley, J.L., "Limitations on the Measurement of Turbulence Using a Laser-Doppler Velocimeter," Electro-Optical
Conference, New York, N.Y. (Sep 1970).
George, W.K. and Lumley, J.L., "The Measurement of Turbulence with a
Laser-Doppler Velocimeter," ASCE Conference on Water Resources. Phoenix, Ariz. (Jan 1971). Preprint 1345.
George, W.K. and Lumley, J.L., "The Measurement of Turbulence Using a Laser-Doppler Velocimeter," American Society of Mechanical
Engineers/International Standard Association Symposium on Flow, Pittsburgh, Pa. (May 1971). Preprint 5-2-28.
UNIVERSITY OF SOUTHAMPTON
Department of Aeronautics and Astronautics,
Southampton, England
Turbulent Pressure Fluctuation in Water with Additives
A. Millward and G.M. Lilley
and Cd) The pressure fluctuations at the wall beneath a turbulent boundary layer were measured for various concentrations of dilute polymer solutions to determine the effect of the polymer on the structure of the flow and to provide an insight into the mechanism causing the drag reduction which has been observed in such flows Measurements of the pressure fluctuatuations wre made in a 2-inch diameter pipe at Reynolds numbers of approximately 3.5 X i05 with
solution concentrations from 1 to 20 ppm of a polyethylene oxide
(Polyox WSR 301) and from 5 to 50 ppm of a polyacrylamide. (Separan AP 30). It was inferred from the results that the presence of the polymer molecules reduced the formation of the small eddies
occurring-in the region of the wall sublayer This result is in agreement with
the thickening of the wall sublayer reported in other investigations. It follows from the reduction of drag in dilute polymer solutions that there is also a reduction in the dissipation of energy from the flow.
In water the dissipation process can be expressed in terths of a
characteristic frequency involving the parameters u/v, whereas in
the presence of the polymer additives, the rneasuremenZ show a change in the characteristic frequency of dissipation. This change is shown
to involve parameters expressing the length of the polymer molecule and also, by implication, the so1uton concentration. The mechanics of drag reduction is explained in terms of a branching process in-volving energy transfer to the polymer molecules at an energy level which is lower than that of viscous dissipation As a consequence of this mechanism there is also a reduction in the production of
turbu-lent energy in order to maintain an equilibrium energy structure.
Department of Mathenatics, Southampton, England
Basic Studies of Grid and.Shear Turbulence in Polymer Flow
C.A. Geated
Cc) and (d)
Laboratory studies have ben conducted using laser velocimeter measuring systems on both grid turbulence and turbulence in a square
duct, both on a small scale The water channel facilities are now being improved, and the results will soon be repeated on larger
scale One-dimensional power spectra have been measured at different distances from a grid and for the shear-flow case, lateral and
longitudinal components of the velocity fluctuation as well as cross correlations have been measured at different distances from the
boundary. The measured values of u'2 seem to be generally lower than those given elsewhere in the literature.
Theoretical investigations on the limitations and appliçabilityof
laser measuring techniques have been carried out. Also theoretical models of the Burgers type are being studied for. grid turbulence.
(e) Greated, C. and Dürrani, T.S., "Signal Analysis for Laser Velocimeter Measurements," Journal of Physics E, Vol. 3, pp. 7536.
TEXAS MM UNIVERSITY
Department of Chemical Engineering,
College Station'Tex. 77843
1. (a) Rheological Characterization of Dilute Drag-Reducing POlymer
SolUtions (b) R. Darby
Cc) Measurement of shear stress, first and. second normal stress
differences, oscillatory shear, and transient rebound rheological
functions for fresh and aged polyacrilami.de solutions from 100 to 500 parts per million concentratiOn range.
All solutions exhibit marked elastic as well as nonlinear shear
be-havior. Aging effects are much more pronounced for the more dilute
solUtions.
(14)
2.
(a)
Energy Dissipation in. Superimposed Oscillatory Steady Flow ofDrag-Reducing Solutions R. Darby
Experimental and theoretical study of energy dissipation in dilute drag reducing polymer solutions in steady tube flow with super-imposed small amplitude oscillatory components of various
fre-quencies and amplitudes.
Cd) Project. in initial stages.. No results to date.
UNIVERSITY OF TOKYO
Department of Marine Engineering,
Tokyo, Japan
Study of Friction Reduction of Polymer Solutions T. Tagori
Studies about characteristics of friction reduction of polymer
so-lutions, the hydrofoil in dilute polymer soso-lutions, and the measuring methods of flow velocity in dilute polymer solutions.
(ci) The shearing stress on a flat plate was measured by means of a flat
surface-type hot film and a local skin-friction dynainometer in fresh
water and solutions of polyacrylamide The measurements of lift,
drag, and pressure distribution of hydrofoil were carried out in
so-lution of polyethylene oxide. As a result, it was shown that the performance of foil in polymer solutions became worse than in fresh water Various current meters were calibrated in fresh water and in
solutiOns of polyethylene oxide.
(e) Tagori, T.., "Friction Reduction in Dilute Solutions of Polymer," Science of Machine, Vol. 23, No. 1 (Jun 1971).
UNIVERSITY COLLEGE OF WALES Department of Physics, Aberystwyth, Wales
Rheological.Research -.
W.M. Jones, O.H. Davies, and M.C. Thomas of the Department-of:Physics and K. Walters and A. Dodson are doing experiments in the Department
of Applied Mathematics.
The work is concerned with the experimental and theorçtical investi-gation of the flow of dilute polymer solutions in various flow geometries The main concern is with the stability of the flow and with the
evalu-ation of material constants. Molecular interpretation of the results
is being undertaken. Drag reduction is alsO being investigated.. The materials being studied are polyacrylarnide, Polyox, and Keizan (a polysaccharide) in aqueous solutions 0.05 percent w/w).. The controls are water and glycerine solutions in water. The geometries being
studied are straight pipes (circular and elliptical cross section), bent pipes (into arcs of circles), corrugated pipes, granularbeds, and
the Couette geometry (coaxial cylinders, inner rotating).
Cd) Drag reduction is observed in the turbulent flow in straight, bent, and
corrtigated pIpë. Drag reduction is observed when secondaiyflowis measurable in bent pipes, and there is sometimes drag reduction when
Taylor vOrtices ocàur
in
the .oaxial cylinder apparatus. At certain critical rates of flow, drag reduction occurs in laminar flOw throughthe corrugated pipes. No drag reduction has beenobserved in granular beds.
Drag reduction occurs in pulsatile flow through straight pipes
under
certain critical conditions although the energy supply to the pumpproducing the flow is not reduced. . .
Drag reduction occurs in turbulent flow in straight pipes, both when
the flow is destabilized and when the flow is stabilized.
C ).Jones, W.M. and Marshall, D.E.,
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