ARCHIEF
NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER
. .l,,
ibliotheek van d epsbouwkunde Qnderafdetiri n!sche Hogeschoo, D3CUMEN[ATIEI:
t<41-3
DATUM:L
This document ib
transmittal to forei
made only with pri
Department.
I ocuiiEtaIIEI
Washington, D.C. 20034
PROGRESS IN FRICTIONAL DRAG REDUCTION
SUMMER
1969TO SUMMER
1970by
Paul S. Granville
Drag-Reduction Monitor for ORDHAC
(Ordnance
Systems Command Hydroballistic s Advisory
Committee)
en
apprOVesol s and each
nal s may be
ai o the Head, Ship Performance
This doc'ret has
approved
or pu1' re'e
e and sale;, 1t
d1tributio Is unlimited.L970
Department of Ship Performance
Technical Note 184
Lab.
v. Scheepsbouwkunde
Tecknische
Hogeschool%
iq
The Naval Ship Research and Development Center is a U.S. Navy center for laboratory effort directed at achieving improved sea and air vehicles. It was formed in March 1967 by merging the
David Taylor Model Basin at Carderock. Maryland and the Marine Engineering Laboratory (now
Naval Ship R & D 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 and Development Center Washington, D.C. 20034 * REPORT ORIGINATOR SHIP CONCEPT RESEARCH OFFiCE OHiO DEPARTMENT OF ELECTRICAL ENGINEERING MOO DEPARTMENT OF MACHINERY TECHNOLOGY A700 IDEPARTMENT OF I MATERIALS L_.. A800 DEPARTMENT OF APPLIED SCIENCE SYSTEMS DEVELONT OFFiCE 01405
I
NSRDL ANNAPOLIS COIANDING OFFICER TECHNICAL DIRECTORF-H
H
MAJOR NSRDC ORGANIZATIONAL COMPONENTS
DEVELOPMENT PROJECT OFFICES 01430. 50, 80, 90 NSRDC CAROEROCK COHUMNOER TECHNICAL DIRECTOR DEPARTMENT OT HYDRONECHANICS 500 DEPARTMENT OF AERODYNAMICS 600 DEPARTMENT OF STRUCTURAL MECHANICS 700 DEPARTMENT OF APPLIED MAThEMATICS 800 DEPARTMENT OF ACOUSTICS AND VIBRATION
900 NSRDL PANAMA CITY CI*ANDING OFFICER 'TECHNICAL DIRECTOR
H
H
-3
"This document contains information affecting the national defense of the United States within the meaning of the Espionage Laws, Title 18, U.S. C., Sections 793 and 794. The transmission or the revelation of its contents in any manner to an unauthorized person is prohibited by law."
DEPARTMENT OF OCEAN TECHNOLOGY DEPARTMENT OF MINE COUNTERMEASURES P720 DEPARTMENT OF AIRBORNE MINE cOUNTERMEASURES P730 IDEPAR1MENT OF INSHORE WARFARE AND TORPEDO
DEFENSE
I.
-ANIO I I P740
MDW-NSRDC 3960/46
PROGRESS IN DRAG REDUCTION - SUMMER 1969 to SUMMER 1970
The overwhelming effort in research and development for reducing
turbulent skin friction continues to be by means of polymer additives
Many
scientific and technical questions remain.
Fndamental Aspects
The mechanisms of turbulent drag reduction by polymer additives is still
a subject of imaginative
speculation.
Two approaches may be ascertained:
1.
the molecular viewpoint and 2.
the overall or continuum viewpoint.
P=61a
considers a molecular model depending on the stretching and partial uncoiling of
macromoecules and ther reaction with dLscrete. vortices.
On the other hand,
P-35 experimentally finds that the DNA molecule is more effective
in drag
reduction when in the less flexible helical conformation. P-60
introdUces the
idea of local intense viscosity within the molecular coils
which inhibits
turbulence production. P-52a presents a continuum model based on
the
viscoelastic effects on laminar stability. P-31 ascribes drag reduction to
the "filament formation" properties of polymer solutions which interfere
with the ejection process from the wall as observed in turbulent
flow past
solid boundaries.
As mentioned in previous surveys (NSRDC Hydro. Lab. TN 188 & TN
143)
the Torns effect seems to be dvorced from the presence of manifest viscoelasticity.
This is experimentally shown for orifice flows by P-30, for flow
through abrupt
pipe contractions by P-62, for vortex shedding
behind waves by P-.43, for heat
transfer across submerged jets by P-79 and for the terminal velocities
of
dropped balls by P-88.
The thickening of the laminar sublayer in the Toms effect is experimentally
demonstrated in P-66 where accurate measurements were made close to the
wall with a laser velocimeter. A contrary viewpoint is
held by P-76, P-77 and
P-78 which claims that it is the intermediate or buffer region
which is
thickened..
Correlation
Correlation of drag reduction by means of similarity-law concepts is
becoming more prevalent. P-71 and P-72 use an adjustable relaxation time
as a characteristic tme to provide
similarity.P-5 and P-61 develop
correla-tions in terms of parameter combinacorrela-tions.
Diffusion
The injection of concentrated polymer solutions for diffusion downstream
represents a more operational procedure. Experimental studies
of
distributed injection are detailed in P-38 and P-82. Studies of injection from
a slot are examined
experimentally in P-54, P-47a, and P-91 and analytically
in P-32 and P-55.
LABORATORY SUIVUYIkRY OF DRAG REDUCTION RESEARCH
1970
Title of Project Principal Investigator Description of Project Results Publications*ARIZONA STATE UNIVERSITY - Faculty..of Chemical Engineering,'Tempe,
Arizona 85281
Stability Studies in Pipe Flows using Water and Dilute Polymer Solutions
Prof. Neil S. Berman
A laser Doppler flowmeter (LDF) is used to measure time dependent
velocities at various points in a circular tube downstream of a disturbance. Water and several dilute polymer solutions are used in the study. The
variables include disturbance form, amplitude and frequency radial and axial position; and polymer concentration. Complete signal analyses are made of the fluid response as measured by the LDF.
Previous studies of the velocity fluctuations near a Reynolds number of 2100 show that both the waterthe dilute polymer solutions response depends upon the frequency and amplitude of the disturbance when the
disturbance is a thin sleeve oscillating at the wall. Reynolds number and pipe diameter are also important. At Reynolds numbers below transi-tion to turbulence and when disturbance amplitudes are high at frequencies
below one Hz the dilute polymer solutions recover their laminar behavior more rapidly thanjpure water. owever, low amplitude disturbances result in persistant fluctuations in the dilute polymer solutions and slower recovery than for pure water. Both 20 ppm solutions of Separan AP-30
and Polyox WSR 301 showed the same effect.
Autocorrelations of the velocity fluctuations at two downstream points were made using time delays on a tape recorder and an analog computer
for multiplication and integration. Details will be given in reference 3
below. The autocorrelations show the decay of the low frequency sleeve
oscillation into random higher, frequency fluctuations further downstream. More complete studies are currently underway.
1. Hanson, W., Jankowski, D., Berman, N. S., "Measurements of Large Disturbances in Laminar Pipe Flow using a Laser Doppler Flowmeter,"
Phys. Fluids l2 Decembei.,
1969.
*Numbers refer to bibliography
Berman, N. S. and Cooper, E. E., "Laser Doppler Measurements of the Decay of Velocity Fluctuations in Dilute Polymer Solutions,"
Symposium on Turbulence Measurements in Liquids, Rolla, Missouri, Sept.,
1969.
Berman, N. S. and Cooper, E. E., "Stability Studies in Pipe Flows
using Water and Dilute Polymer Solutions: Time Dependent Velocity Measurements using a Laser Doppler Velocimeter," to be presented
at AIChE Meeting, Chicago, Ill., November,
1970.
UNIVERSITY OF ALBERTA, Department of Chemical and Petroleum Engineering, Edmonion, Alberta.
Drag Reduction Mechanisms
Fred A. Seyer
1. Optical measurement of the average velocity and turbulence intensity
within the boundary layer of drag reducing systems. Experimental
verification of available similarity laws.
2. Development of a molecular model which portrays the response, in-cluding orientation effects, of large molecules when subjected to
shearing and elongational flow fields.
1. The velocity measurements confirm previous observations of a
thickened sublayer. In the region of the wall where a sharp peak
is observed in the turbulence intensities of Newtonian flows, the intensities in drag reducing systems are observed to be
markedly lowered. This in part substantiates an earlier hypothesis
relating the mechanism of drag reduction to the stretching
deform-ations which occur in thea large.wall eddies.
2. A new molecular model, which for shear flow assumes movement of Rouse type subchains occurs along an ellipsoidal surface of fixed orientation, is capable of quantitative predictions of viscoelastic
properties. Of importance is that the model accounts in detail for
the stretching of the macromolecules. Large elongational viscos-ities are predicted when the molecules are elongated about 200%.
This work which is continuing suggests some important similarities between the flow behavior of polymer solutions and fibre suspensions as well as appearing potentially useful in designing more effective
drag reducers.
P-72, Ilkvacek, B. and Seyer, F. A., "An Analysis of Flow Behavior of polymer Mornelcules - I", submitted for publication, Kolloid
Zeitschrift, April
(1970).
BROWN UNIVERSITY, Division of Engineering, Providence, Rhode Island 02912
Mechanics of Polymer Miecules
R. I. Tanner
A theoietia1 and experitneritál investigation into constitutive equations for drag-reducing solutions.
) By using a thölecilar thodél consisting of beads with no hdrodynarni
interaction (Rouse-type theory) but with nOn-linear springs of. finite 1ength stresses in dilute solutions have been completed
for various 8tmple flows In particular the extensional (elonga-tional) flow was studied and computed results wei'e g1en.
e) W. Stehrenberger, Sc.M. thesis, Division of Engineerin, Brown University Providence, Rhode Island 02912
GNERAL ELECTRIC CO.,
eserch &Dee1onit Center, Schenectady
New York 12301
-a) Meähanization ofDrag Control
b) W. B. Giles
c) Work consists of laboratory investig.tion of mixers, ablative. coatings
and injection testat high speeds.
) The injection test results have been reduced to a simple empirical formula to estimate drag ±edpction as a 'unction of peed, Reynolds number, and slurry consumptioit
-e) Internal GE report in preparation.
UNIVERSITY OF GIASGOW, periment Tank, Glasgo, Scotland
The Vaiiation of Fricti Drag with Surface Drag with .urface Rdughness
in Dilute Polymer Solutions.
W. B.-Amfilokhiev and A.M. Ferguson.
.c) 1. The Mechanical Degradation of Polymer Solution by Surface Roughness. 2 The Variation of Friction Drag with Surface Roughness in Polymer
Solutions.
d) 1. Mechahical Destruction of Polymer. Polyox solutions were found
to be most sensitive to the destructive effect of roughness. Polyacrilamide solution is slightly less sensitive arid, within
the limits of these tests, Guar Gum solution is practically unaffected
by the destructive effect of roughness.
2. Influence of Roughness. (a) Friction drag can be reduced in
dilute polymer solutions even for surfaces which are very rough. (b) For surfaces with slight roughness, large concentrations of polymer solution can reduce friction drag to less than that for
a smooth surface in pure water. (c) For very rough surfaces
the friction drag cannot be reduced below that of a smooth surface, the faster the polymer structure is destroyed.
3. Influence of Concentration. (a) Polyox: for smooth and rough
surfaces there is a large reduction in moment coefficient Cm
for a very small concentration of Polyox. For very rough
surfaces small concentrations of Polyox have little influence on Cm. (b) Guar Gum: for smooth, rough and very rough surfaces
there is no reduction in Cm for small concentrations of Guar Gum. (c) Polyacrilamide: for smooth and rough surfaces there is a
reduction in Cm for small concentrations of Polyacrilamide, For
very rough surfaces small concentrations of Polyacrilamide have
little influence on Cm. The reductions for Polyacrilamide are
slightly less than those for Polyox solutions at corresponding
concentrations of polymers. P-i, P-2.
PART II.
"Some Problems of Non-Newtonian Fluid Hydrodynamics."
Dr. L. S. Artjushkøv
1. Theoretical Aspects of Turbulent Non-Newtonian Flows in Pipes.
2. Boundary Layer for a Smooth Flat Plate in Non-Newtonian Turbulent
Flow.
1. At present all tirie-independent.non-Newtonian fluids are divided
into two different groups. - pure viscous and viscoelastic fluids.
The most complete investigations both theoretical and experimental for turbulent flows of the fluids were carried out using
dimension-less analysis.
In the meantime, to remain within the limits of the semi-empirical theory of turbulence it is possible to set a general solution for a "generalized liquid" by introducing the assumption of variable
mixing length. This approach is based on the hypothesis that the non-dimensional mixing length for liquids of different classes is
not the same but varies as the property of the liquid alters.
Such an approach gave the possiblity of obtaining the characteristics of turbulent flow for time independent liquids of different classes,
The flow characteristics of the Newtonian fluid and the dilute
polymer solution can be derive from that generalized solution
as a partial case.
A special function was introduced to take ihto account non-Newtonian and viscoelastic properties of a fluid The value of the function
for pure-viscous non-Newtonian liquids is derived by theoietical
means. For viscoelastic fluids and dilute polymer solutions the value of the function can be evaluated from empirical data.
2. This deals with the boundary layer problem of a mooth flat plate.
in the tubu1ent flow of non-Newtonian fluids and dilute polymer
solutions. Solution of the problem Is based on the method developed
by L. Prandtl.
Calculation of the friction coefficients for a flat plate with turbulent bouary layer has been made by L.. Prndtl using the
analogy between a pipe velocity profile and a boundary layer one.
Using the integration of a turbulent pipe velocity profile
L Prandtl obtained the parametric system of equations representing
the friction coefficientS as a function of Reynolds Number. .At the same time determinatiOn of the characteristics of the
turbulent boundary layer suchas displacetnént thickness, momentum thickness and others uses power law velocity profile,
Evolving the L. Prandtl method unified approach haS been developed to solve the turbulent boundary layer problem for non-Newtonian fluids and dilute polymer solution. The apprbach is based on the assumption of dependence of one mixing length in the properties of a fluid. . This approach gave the possibiity to generalize
the boundary layer problem and .to obtain full characteristics of the turbulent boundary layer for a smooth flat plate In.
non-Newtonian fluids, dilute pblymer solutioOs and Newtonian
fluids using the lagarithmic velocity profile. pL.
UNIVERSI OF ILLINOIS, Department of Chemistry and Chemical Ehgineering,
Urbana, Illinois 61801 - .
Influence of Drag Reducing Polymers on Changes of the Structure of Turbulence Close to a Wall
Thomas J. Hanratt-y and Gilread Fortuna
Electrochèmica- techniques have been developed in this-là.boratory to study the structure of turbulence in the viscous sub-layer. (See
Physics of Fluids Supplement,
l97, p.
120)! These techniques arebeing used to study the effects of drag reducing polymers in the sublayer. 7
a) Drag reducing polymers have been found to affect strongly all of the
turbulence properties of the viscous sub-layer. No evidence of
intermittancy has been obtained.
UNIVERSITY OF IOWA, Institute of Hydraulic Research, Iowa City, Iowa 522)-i.0
1. a) Effect of surface roughness on drag reduction. Prof. Mchael Poreh.
Theoretical study.
A simplified model describing the effect of surface roughness on the logarithmic velocity profile and drag reduction for flows
of dilute polymer solutions was proposed. The theoretical model is found to be in good agreement with the available experimental
data.
M. Poreh, "Flow of dilute polymer solutions in rough pipes," Institute of Hydraulic Research Report No0 l26 1970.
2. a) Diffusion of polymers in a turbulent boundary layer.
Prof. Michael Poreh. Theoretical study.
A method for predicting th diffusion rate of inert scalars and
drag reducing polymers within a turbulent boundary layer was derived. The analysis indicates that the drag reducing properties of the
polymer decrease the diffusion rate in a turbulent boundary layer.. M. Poreh, K. S. Hsu, Diffusion from a line source in a
turbulent boundary layer," submitted for publication.
M Poreh
K.S. Hsu, "Diffusion of drag reducing polymers ina turbulent oundary layer," submitted for publication0
LTV RESEARCH CENTER, P. 0. Box 6l-i--i-, Dallas, Texas 75222 Study of Drag-Reducing Additives
C. S. Wells, Jr.
Investigations of effects on polymer drag reduction of turbulent diffusion and shear degradation; development of correlations to predict skin friction for various types of turbulent shear flows; effects polymers on wall pressure fluctuations; development of
coating.
a) 1. Turbulent shear flow diffusion is significantly altered by
uniform injection of polymer solutions through a porous wall.
Diffusion from the wall is reduced, which is in qualitative agreement with changes in momentum aiId heat transport.
2 The'critical hear stress for nsetOf drag' reduction is in'creaed by degradation at high wall shear stresses, while the parameter
describing the .ate of change of friction reduction with shear
tress is riot changed g±eatLy..
3. The unive±'sal corrélätion for turbulit shear.'laye flow of
drag-reducing polymer solutions developed form pipe data has shown
to apply to flow on a rotating disk. This gives' a quantitative
laboratory toolfor friction experiments at high'wali shear stresses
which. are generalizable to external boundary layer flow
p_8Lt., p_81:, p-82.
UNrTERSITY OF MThI'ESOTA;St.AthOny Falls Hydraulic Laboratory
Minneapo'lis Minnesota '554l
) Influence of Drag Reducing Polymer on Surface Pressure Fluctuation
"J. M. Killen and J. 'Almo
Measeiet hävé beëñ made of drag and ü±'face pressure
'flctution spectrurn on the boundary of'a cylinder rotating'
axially in a large tank as influenced by the addition of'
various polymers to the test water. Both smooth ad rough surfaces
are used
The addition'ofroughnëss to a smooth,surface appeared to'rincrease surface pressure fluctuation intensity in proportion to increased friction factor. The addition of a drag reducing polymer to, a smooth surface appéred ,to decrease p±essure fluctuation intensity. in proportion to friction factor intensity at low frequencies and less than proportional, to friction factor reduction at high frequencies The addition of a drag reducing polymer
to a
rough sui'face gave less reduction'iri surface pressure fluctuation intensity than proportional friction factor reduction at low frequenciesand greater than proportional to friction factor reduction at
high frequencies. ' '
..: '
2. a) Injection of'PolymerAdditives into Relatively Large Scale'
Boundary Layers
J. M. Wetzel and J. F. Ri:pken '
Concentrated solutions, Of Polyox WSR-30l pave been iijected tangentially into the developing turbulènt bcundary'layer of.
a 'large flow steam! Cdrcentration and velocity profiles have
been measured for various injection rates and distances downstream
'from the. injection slot, in'boundary.layers up.to about 'one foot
thick. ' . '
For low quant:ities of injected polymer, the concentration profiles
have been dimensionally correlated using parameters derived for
injection of a passive scalar. For high quantities of injected polymer, the polymer did not diffuse as well, with relatively high
concentrations being observed at the wall even at large distances from the injection slot. Plottings of the dimensionless velocity
profiles indicated that polyther injection influenced only the inner layer, the outer layer remaining essentially the same as for water
flow. The zero-crossing rate of the turbulent heat-transfer
fluc-tuations as measured with a flush-mounted hot film sensor was related to the wall shear stress forboth water and polymer flows.
Wetzel, J. M., Alma, J. A., and Killen, J. M., ttTurbulence Measure-ments n Dilute Polymer Fls," Symposium on Turbtilence Measurements
in Liquids, University of Missouri, Rolla, September
8-9, 1969
(in Press)
Wetzel, J. M. and Ripken, J. F., Shear and Diffusion in a Large Boundary Layer Injected with Polymer Concentrate, University of
Minnesota, St. Anthony Falls Hydraulic Laboratory Project Report 11L., Feb. 1970 (In Press).
Sehgal, C. K. Effect of Polyier and Velocity Profiles in a
Commercially Rough Pipe, University of Minnesota, M. S. Thesis, March
1970.
Tsai, F. Y. The Turbulent Boundary Layer in the Flow of Dilute
Solutions o Linear Molecules, Ph D. Thesis, University of
Minnesota, December 1968 (also to be published as St. Anthony Falls Hydraulic Laboratory Project Report No. 113).
UNIVERSITY OF MISSOURI-ROLLA, Department of Chemical Engineering, Rolla,
Missouri 65401
1. a) Turbulence Measurements in Polymer Solutions
J. L. Zakin & G. K. Patterson
Hot-film anemometer measurements were made on a number of organic
drag reducing solutions of varying drag reducing ability. Turbu-lence in.,tensities, energy spectra, and probability density dis-distribuations were measured. The frequency response of the wedge probes used had been previously validated.
a) Turbulence intensities similar to those normally observed in Newtonian fluids as well as higher than normal were obtained.
The turbulence levels were correlated with a Deborah number with
four spearate regions. The Deborah number depends on the fluid relaxation time which is determined by polymer molecular weight, intrinsic viscosity, concentration, and molecular flexibility. It
is sensitive to polymer degradation. 10
2,
Energy spectrawe±e normal for most solutions.. However,shifts to
higher levels at high. wave number were observed for,a.few solutions in iqhibh the microscale. Reynlds number.was high.
Probability density functionswere normal formost solutions except
for the region Of highest Deborah number. Here high center peaks and wide tails were observed giving flatness factors much la'ger than the
Gaussian distribution.
) Rodriguez,J.M.,. Ph.D. Thesis, University of Missouri - Rolla,
1969
"Frequency Response of Wedge Hot-Film Probes in Viscoelastic Fluids," in Proceedings of the International Symposium on Turbulence Measure-ments in Liquids, G.K. Patterson afid J.L. Zakin, editors, Goi'don and
Breach, ir.
"Turbulence. Measurements in D±agReducing Flow," J.M. Rodriguez, G.K.
Patterson &J.L. Zakin, to be presented at Fluid Damics Symposium,
McMaster.Univ. Hamilon, Ontario, Canäda,Augut.
(1970).
) Friction ReductiOn in S1urrr Flow
J.L. Zakin and M. Poreh (work done at Tebnion, Haifa, Israel)
Concentrated suspensions of sandandof plastic particles continin drag reducing additives were pumped through a transparent round tube
Pressure drops and critical velocities were measured.
Polymer solutions degraded faster than without solid .A complex soap solution showed nO permanent mechanical egrdation and gave significant reductions in pressure drop at low velocities compared with the slurry
without additives The critical velocity was also lower with the com-plex sOap. Energy losses were reduced by up to 70 pei'cent.
e) "Friction Reduction.ith Polymer Additives in Hydraulic Transport and Shear Degradation of Dilute Polymer Solutions," by A Brosh, M S Thesis, Technion,
1969
(n Hebrew).P-92.
"Drag Reduction in Hydraulic Transport of Splids,' by M. Poreb, J.L.
Zakin, A Brosh, and M Warshavsky, Proc ASCE, Hydraulics Div , HY L1.,
903 (l97O)
Drag eduction in Hydrocarbon Soap Solutions
JL.Zakin (part of this work. was performed at thëTehion, Haifa,
Israel)
The effects of concentration,aging, shear stress and te presence of peptizrs on drag reduction of hydrocarbon o1uions of aluminum soaps
were studied. .
At low soap concentrations, these systems showed an upper critical shear stress above which drag reduction was gradually lost Degradation of the soap micelle.struetare occurred relativ1y rapidly above this point aid recovery was very slow The effect of peptizers is complex In some
situations it enhanced and in other cases reduced the drag reducing
ability 'of the sbap solution.
"E'ect: of, Third Comonents on Drag Reduction in Aluminum Soap-
Hydro-carbon Systems,'t K C Lee, M S Thesis, University of Missouri - Rolla,
1970.
NATIONAL PHYSIC4L LABORATORY, Ship Division, Feitham, Middlesex, England
Basic studies of d.rag reduction
G.E. Gadd
An instrurnent has been developed in which fluid from areservior emerges
from a small hoIe and the jet- is struck by the teeth of a rotating wheel. Viscoelasticity causes variations of the flow rate associated with a spurting of the emerging flow from the wheel.
) Viscoelasticity can be detected in very low concentrations, less than
20 ppm in Polyox solutions. At higher concentrations the onset of visco-elasticity occurs atlower wheelspeeds. It-is suggested that this-
cor-relates with he observations of some iivestigators that the threshold shear s-tress for dragreduction diminishes with increased concentration. It is also suggested that drag reduction occurs when turbulent frequencies close to the wall become hih enough for vicoe1asticity to affect the turbulence.
e)
P-29
NAVAL POSTGRADUATE SCHOOL,- Departmeit of Mechanical Engineering, Monterey,
California 939)4-0 -
-Resistance to the. Flow of Dilute Aqueous Polymer SOlutions T.Sarpkaya
Pressure arid. direct drag measu±ements have been made on circilar cylinders
of .5-nch to 1.5--inch diameter in dilute sOlutions of "Polyox". The
maximum Renoids number was about 500,000 so that the flow regimes of
laminar, transition and post-transition were covered. The experiments
- .were carried out in a water tunnel designed specifically for this pi'oject.
Significant alteration of thedrag coefficient was found in the three regimes of the flow for the cylinders. While the fresh polymer solution provideda smooth transition with drag coefficients below those corres-ponding to tap waters aged solutions caused a shaptransition at a
critical Reynolds number and yielded drag Ooefficients i,n the order of
O.1-f. At the critical Reynolds nurnber,lãrge scale pressure osôillations
were noted at an angular position of approximately 700 from the front
stagnation point. It appears that the presence of the degraded polymer
particles precipitates a. sudden inst&bijity.and transition to turbulence.
Visual observations of the flow around the cylinders and of the dye issuing from small holes convince one.that the presence of polymers
causes sti'ong secondary flows, not encountered in tap water flow, and that the drag reduction is achieved as. a result of the combined effects of the reductlon of the wake size and of the chaiige of the dynamic
characteristics of the vortices in the wake and the resulting
altera-tion of the pressure distribualtera-tion. Experiments are at present being
continued with varipis, types of hydrofoils.
) "Stagnation Point Flow of a Second-Order Visco-Elastic Fluid," T.
Sarpkaya aid P.G. Rainey to appear in Acta Mechanica.
NAVAL RESEARCH LABORATORY, Surface Chemistry Branch, Washington, D.C. 20390
Drag reduction
tpdes
R.C. Little, R,J. Hansen and P. Peyser
Experimental iivestigations are being made of the drag-'educing ability
of polymers and association colloids in aq.ueous and nonaqueous environ-ments.
The onsetof drag reduct.ipn has .been shown to be a function of molecular
weight, concentration and pipe diameter or flowing solutions, of Polyox.
The view is taken that aggregate formation under flow conditions is the appropriate mechanism which accounts for the observed concentration
dependence of the onset wall shear stress. The 'experthental dataare bonsistent with Joly's theoretical work which states that aggregate size in polymer solutions i,s, a function of molecular weight, concentration and
shear rate.'
The ability of association colloids to resist mechanical degradation
in high shear fields has recently been dernonstrated in a hydraulic fluid recii"bulating system involving a hydraulic gear pump. .A constant drag
reduction level of 2Q% uner practical brking conditions of continuous
shear has been maintained fbr25O hours of operation. The experiments
tend to confirm the view previously taken that monomeric units of these materials form long chain polymers by association (as opposed to chemical
bonds). When the drag reducing species 'is fragmented upon passing through a reg-io, of intense shear the original species will 'be regenerated by re-assOciation of the fragments unde.,r less ifltense conditions
Drag reduction experiments using a rotating disk, apparatus showed that Polyox solutions may or way ilot exhibit a temperabure dependence in the amount of drag reduction observed. Low concentrations (below that needed to produce the maximum drag reduction curve) show decreased drag reduction asthe temperature is increased over the range of 10 to 90 C.
Concentration in excess of that needed to produce the maximum drag
reduc-tion curve 'show little or no dependence on temperature in the experimental
range studied.. The results are .explained.both in tems of changes in. polymer end-to-end distance and the compensating effect of an: exess of
polymer molecules needed. to maintain the drag reducing flow.
e) P6, P-5l, P-50,P-52
.NAVAI SIP ESERCItA1D DEVELOPNT LABORATORY, Annapolis, Maryland 21-i-O2
.) 1) Heat transfer and drag red'uct,on in polymer solutions.
Drag reduction mechanism investigation
Pump behavior' . . .
b) ,L.F. Marcous, E.G. Howard, G.F. Wi]iielmi
c)' 1) Measurement of convective heat transfer and. frictioi factor in pipe flow
Correlate turbulence damping to viscous boundary layer thickening etermine centrifugal rump behaVior while pumping polymer solutio.s
d) 1) ConvectiVe heat transfer in tu'biilent ripe flow is
rduced. by.
aboutthe same percentage. as friction, factor under given coditions.
2) Qualitative correlation has been found.
) Howard, R.G.and Marcous, L.F.,, "Analogy between Heat and Moeitu Transport in Viscoelastic Solutions," Proc Fluid Dynamics Symposium at McMasterUniv., Qntar:i, Canadä,.Aug'l970 '
NAVAL SHIP RESEARCH'AND DEVEJOPNT CENTER, Hydromechan.ics Laboratory, Washington, D.C. 2003-i- . '.
Measurement of the local frictional ±esistance on a fiat lte with
ejection of polymer solution..
W.G..Souders, J.L. Powe,.J.J. Nelka ' .
Measurements of the local fri'ctiota'l resistance on a flt plate with the ejection of polymer solutions were performed during"March 1970 in 'the
NSRDC 36-inch Variable Pressure Water Tunnel. 'The shear rnéurements
were made in the lamina.i sublayei".usin both aStanton ttibe and a' sub-layer fence. These'shear probes were calibrated just prior to polrmer ejetion against a restOn tube of known calibration. The mean wall polymer concentratioi was measured sinultaneously in close vicin,ty of
the shear probes nd.at other selected locatiois on the plate by
with-drawing fluid samples from the plate surface.
e) .P-73 . . ' '
NAVAL UNDERSEA RESEARCH AND DEVELOPIVIENT CENTER, "Pasadena' Laboratory, Pasadena.
California 91107 . . ' '
1. a) Polymer supply rates for friction reduction in high-shear flows
A.G. Fabula
This is an experimental and: analytidal study of polymer supply rates required in. high-speed flows In recent work, the mechanical degradation of polymer solutions in pipe fiowand its significance for
bounday-layer flow has been studied. Degradation of captured polymer solution samples has aio been intfetigated.
That mechanical degradatioh doe occur in pipe.flow is clear from the observations in earlierwork with the 2-inch pipeline. However,
corn-parison of the levels of "specific energy dissipated" (average enerr dissipated perunit of discharged volume fo one pass) in typical pie experiments with the orrespoiding uantity for typical boundary layers
indicates that mechanical degradation wil1.be of minor importance in external boundary layers with typical polymer concentrations This
con-clusion is based on the observed degrees of degradation in pipe flows where the specific energy dissipated is about 50 times that in boundary
layer flow..
A brief study has been made possible extraneous mechanical degra-dation of polymer solution samples catured through gall taps and pitot
tubes in high-speed flOws. Theoretical and experimental evidence for sul .egradation has been foud, but theproblem has.been foimd.tobe quite minor for cases of typica interest.
e) P-26
2. a) Elongational flows of friction-reducing fluids
A.G.Fabula
Greater. understanding of the basic mechanism of the Toms effect is the aim of this work. The approach taken is to stud the rheology of
fric-tion-reducing fluids in elongational flows, because such
fiows
areimportant in turbulent motions.
Currently, emphasis is on cavity bubble growth and collapse in visco-elastic fluids.. An experinintal study using Berthélot tubes to look for effects of polymers upon cavity nucleation and growth has been
started.
3.
a) Effects of thermal and turbulent flow exposure on friction reduction effectiveness, and polysaccharides and synthetic polyers:P.R. KensJ.W. Hort
.High niolecular weight polr(ethylene oxide) is presently the most
effec-tive friction-reducing polymer at low concentrations.. Our tests shbw, however, that after prolonged exposure to turbulent flow, polyacrylamide
is considerably more effective. -A 14.0 ppm solution of.poiy(ethylene oxide)
was nO more effective than a 20 ppm solution of Olyacirlamide, and
equa.11y effective s a 140 ppm solution of polysaccharide from the bacterium
'I
Xanthomonas campestris. Guar gum showed the greatest stability to tur-büIent flow exposure, but was less effective in reducing friction than the.other three polymers at low concentrations after exposure.
-Them4l expbsure studies revealed greater stability for the synthetic
polymers than the polysaccharid.es After 2-i- hour exposure to
75 C,
5 and 50 ppm solutions of the synthetic polymers retained considerable
frict±on reduction effeätiveness, while the olysaccharides showed very
little. Under super1-eated conditions at 120 C, poiy(ethylene oxide) and the polysaccharid.es were degraded rapidly with negligible
friction-reducing ability after 2 hours. .A 50 pm solution0of polyacrylamide, - .however, reduce.friçtion 50% after 2 hours 120 C.
e) .p_15 . . .
Lj. a) Flow noise pipe flow studies
b) J.M. Caraher. .. . . .. . ..
.
...
.c) A Linch pipe flow facility has. been installed. This blowdown facility
is being used with both tap water and. solutions of polymers in tap water
to study the effect of dissolved polymers on wall pressure fluctuations.
Spectral. and correlatioii ana1yis will be used to show the effect of
poymer additive on the power spectral density of pressure fluctuations,
on convection velocities,.and.on disturbance. decay rates.
A agnetic flow meter has been obtained to re1ace the venturi
meter which was givitig erroneous values of niéan flow speed. The
Robertshaw flow controller has .been relocated for better operation and
testing has been ätartëdagain. - .
OHIO STA UNIVERSITY, Department of Chemical EngineeringCOlumbts, Ohio
432lO..
Visual studies of the flow in the ublayer of drag reducing polymer and
soap solutions .. . . . .
.
Prof. H.C. Hershey
Visual studies of the wall area during turbulent flowtising .high-eêd
photography and traCer particles. Also the flow around a probe will
be photographed. using both a solvent nd a drag rduci.rg solution.
a) A series of aiuminum..disoapshas been studied.in toluene. It was found
that a minimum concentration for stability exists below which the
asso-ciation colloid mayThe broken down eitherby high shear or by ageingor
by a combination. Above this concentration the association colloid may be broken down by high shear, but it reforms upon standing.
r
UNIVERSITY OF OKLAHOMA, School of Aerospace and. Mechanical Engineering,
Norman, Oklahoma 73069
Aerodynamic skin friction reduction
Edward F. Buck
Turbulent skin friction reduction on airfoils coated with polyurethane
foam - PCV compliant surfaces
Drag reduction of between 10-30 percent below that of smooth hard surface airfoils were measured on NACA 009 airfoils teted in a wind tunnel at Reynolds numbers between 1.9 x 10 and 3.2 x 10°.
0-1
Blick, E,F. and Boyce, M., "Fluid Flow Phenomenon in Dusty Air," ASME
Paper No. 69_WA/FE_2Li. to be published in Journal of Basic Engineering.
Buck, E.F., Leakey, S.P. and Jacobson, E.D., "Evaluation of Loss of
Intimal Compliance on Resistance to Flow in the Common Carotid Artery,"
Vascular Surgery, Vol. 4, No. 1, pp. 39-).i.3, Mar 1970,
PEN1SYLVAIIA STATE UNIVERSITY, Ordnance Research Laboratory, University Park, Pennsylvania 16802
1. a) (1) Water tunnel testing of olynier vehicles
(2) Suction slot studies
J. F, McMahon
(1) Developing techniques for in-line degrading of polymer additives and removal of reaction products. (2) Analytical study of slot flow
by numerical analysis; experimental study of slot flow magnified by
using glycerine as the working fluid. 2. a) Theory of the action of polymer additives
Fitzhugh W. Boggs
This work is planned to develop an understanding of the mechanisms by which noise and drag reduction are achieved using a combination of the
theories of continuum mechanics and the theory of dilute polymer
solu-tions.
It has been shown that the constitutive equation in the form established from continuum mechanics can be derived from the theory of dilute polymer
solutions developed by Kirkwood and his students. It has also been shown
that for the general constitutve equation for low rates of shear, vortices having axes in the direction of flow are damped and that the dimensions and the rate of damping of these vortices depend on the concentration and the
intrinsic viscosity.
).. ttRelationship Between Flow Pattern, Constitutve Equation and Mo1ecu1a
Structures," by F. W. Boggs, Viscous Drag Reduction (Plenum Press),
1969.
P-1.4
TE
N1TSThVANIA STATE U1'IVERSITY, Department of Aerospace Engineering,University Park, .pennsyvania 16802
Turbulence measurement in pb1ymer solutions by Doppler scattering
W George and. J Lumley
The Doppler shift is measured in coherent (laser) radiation scattered from traQer particles in homogeneous turbulent flow, by homodyning scattered and unscattered radiation on a photocell Flows of both polymer solutions and solvent alone are investigated The intent is
to measure the instantaneous fluctuating velocity, and consequently
such quantities as spectra and probability densities.
System is ope±ativè and. spectral measurements in water have been taken.
Optical system currehtly undergoing redesign to perit measurement of
dissipation spectra.
Lumley, J.L., George,W,K. and Kobashi, Y., Influence of Doppler Ambiguity and Noise on lent Spectra by Dopper Scattering,"
(1970)
Liquids, Rolla, Missouri.
George,W.K. and Lumley, J.L., "Limitations bulence using a Laser-Doppler Velocimete,"
18
"A Brief Analysis . of the
the Measurement of
Turbu-Proc. Symp. Turb. Meas. in
on the Measurement of
Tur-prepared for. publication.
.Stanic,S,, "Axiythretric Extension of High MOlecular Weight Linear Polymers," Master of Science Thesis, September 1970, The Department
of Aerospace Engineering, The Pbnnsylvania. State University at
University Park.
JNIVERSITY OF RHODE ISLPJ'ID, Department of Ocean Engineering, Kingston,
hode Island 02881
1. .) Effect of polymer additires on propeller performance
b T. Kowaiski . ... ..
c) Measurements of thrust and torque of a model proeller -i-.67 inch diameter
in water with and without polymer additives
) Injetion of polymer ahead of the propelle±' disc reduced propeller thrust
and increased the torque. Overall effect decreased the propeller effi-ciently by about fivepercnt for .0 ppm average (Polyox FRA)
concentra-tion at the pi'opeller disc. Paper submitted for. publication.
2. a) Effect of polymer injection on the drag of a flat plate
T. Kowaiski and. K. Depooter (work done at University of Waterloo, Canada)
Various concentrations of Polyox FRA solutions were injected at different rates through four in number 5 degree slots in the surface of a 6 by 1 foot flat plate. Drag measurements were made to find the optimum com-bination of polymer concentrations and injection rates.
Results of combination of the injection rate, polymer concentration and distribution of injection between the four slots is presented in the form
of graphs. Optimum combination for maximum drag reduction can be obtained
from these curves. e), Paper in preparation.
3.
a) Measurements of turbulence characteristics in water and dilute polymersolutions
.b) T. Kowaiski
Measurements of turbulence characteristics were made inside a boundary
layer in water with and without polymer (Polyox FRA) additives. Flush
mounted, wedge, parabolic and x-type hot film sensors were used to
measure turbulent velocities.
The results indicate that the presently available hot film sensors
per-mit great many useful measurements to be made in conducting liquids.
The general application has to be, however, carefully considered since the calibration in liquids with impurities or with additives, especially drag reducing polymers, is still a very difficult and uncertain
pro-cedure.. The most reliable results are the ones obtained from the data arranged as a ratio of two measurements thus cancelling out the
cali-bration factor.
Paper read at the Symposium on Turbulence Measurements in Liquids, University of Missouri - Rolla, September
1969.
UNIVERSITY OF SOUTHAITON, Mathematics Department, Southampton, England
a) Measurements of turbulence statistics in polymer solutions using a
laser flowmeter
C. A. Greated
c) A laser flowmeter has been used to study turbulence frequency spectra behind a rectangular grid of bars, in water and in an 80 ppm Separan
AP 30 solution. The meter has now been further developed to enable
Reynolds stresses to be measured and. also mean velocities to within a fraction of a millimeter of boundaries. This is now being used to investigate the turbulence structure for shear flow in a rectangular
pipe using Polyox and Separan solutions.
Measurements behind a grid show that the effect of the polymer additive is to steepen the fall-off in the frequency spectrum towards the high wavenumbersin addition to reducing the overall relative turbulence
intensity. These effects are only marked at positions close to the
grid.
P-33
UNTVERSITY OF STRATHCLYDE, Department of Pure and Applied Chemistry, Glasgow,
Scotland
Investigation of drag reducing mechanisms
Professor A.M. North, E.H. Dunlop
Drag reduction by high molecular weight polystyrene in toluene is being studied using narrow molecular weight distributions and a wide range of
temperatures, -70°C to +30°C. The effect of varying the tacticity of
the polymer will also be investigated. It is hoped to gain an insight into the molecular parameters responsible for drag reduction and incor-porate them into a more suitable polymer additive.
d,e) No results or publications so far as apparatus is still in course of
construction.
UNIVERSITY OF TOKYO, Department of Marine Engineering, Tokyo, Japan
Study on friction reduction of polymer solutions
Professor Tetsuo Tagori
Study of characteristics of friction reduction of polymer solutions;
study of the mecharnism of friction reduction of polymer solutions; and
study o± engineering application of friction reduction of polymer
solu-tions.
Resistance tests on a flat plate with polymer solutions injection
"Friction Reduction in polymer solutions," Tetsuo Tagori and Isao Ashidate, Bull.
Soc1
Nay. Arch. Japan, No. )i.79 (1969) (in Japanese)."Resistance test on a flat plate with polymer solutions injection," Tatsuo Tagori and Isao Ashidate, Preprint of Ann. Meeting, Japan Soc. Mech. Eng. No. 196 (1968)(in Japanese) Written contribution 12th
I.T.T.C. (1969).
"Small pipe Friction Meter and a Study on Fish Drag by it," Tetsuo Tagori and Isao Ashidate, Preprint of Ann.Meeting, Japan Soc. Mech.,
Eng. No. 216 (l969)(in Japanese).
"Resistance Tests on a Porous Flat Plate with Polymer Solutions
Exudation' Tetsuo Tagori and Shinko Kim, Preprin.t of Ann. Meeting,
Japan Soc. Mech. "Study on Dilute Preprint of Ann. Japanese).
Eng. No. 216 (1969)(in Japanese).
Polymer Solutions," Isao Ashidate and Tetsuo Tagori, Meeting, Japan Soc. Mech. Eng. (1969, 1970)(in
UNIVERSITY COLLEGE OF. WALES, Department of Physics., Aberystwyth, Wales
Rheological research
W. M. Jones, D. M. Davies, O.H. Davies, D. E. Marshall of the depart-ment of physics and K. Walters, H. A. Barnes, and A. Dodson of the
department of applied mathematics.
The work is concerned with the experimental and theoretical investiga-tion of the flow of dilute polymer soluinvestiga-tions in various flow geometries. The main concern is with the stability of the flow and with the
evalua-tion of material constants; molecular interpretaevalua-tion of the results is
being undertaken. Drag reduction is also being investigated.
The materials being studied are solutions of polyacrylamide, of
polyox, and of "kelzan'T (a polysaccharide) in aqueous solutions
0.05%
w/w). The controls are water and glycerine solutions inwater. The geometries being studied are straight pipes (circular and
elliptical cross section), bent pipes (into arcs of circles), cor-regated pipes, granular beds, and the Couette geometry (coaxial
cylinders, inner rotating).
Drag reduction is observed in the turbulent flow in straight pipes,
in bent pipes, and in corrugated pipes. Drag reduction is observed when secondary flow is measurable in bent pipes and also there is drag reduction when Taylor vortices occur in the coaxial cylinder apparatus. At certain critical rates of flow drag reduction has been observed in
granular beds.
Drag reduction occurs in pulsatile flow through straight pipes under certain critical conditions although the energy supply to the
pump producing the flow is not reduced.
P-3.1, P-b, P_L.l, P2
BIBLIOGRAPHY - FRICTIONAL DRAG REDUCTION
SUMMER 1969 to SUMMER 1970
Polymer Additives
p-i.
Amfilokhiev, W. B. & Ferguson, A. M., "The Variation of Friction
Drag with Surface Roughness in Dilute Polymer Solutionsu
University of Glasgow, Dept. of Naval Architecture Experiment
Tank Report 8, August 1968
Amfilokhiev, W. B. & Ferguson, A. M., "The Change of Frictional
Drag with Surface Roughness in Dilute Polymer Solutions", 12th
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Arranaga, A. B., 'Friction Reduction Characteristics of Fibrous and
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Artjushkov, L. S., "Some Problems of Non-Newtonian Fluids
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Part II - Boundary Layer for a Smooth Flat Plate in Non-Newtonian
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Interpretation and Correlation of Drag Reduction" A.I. Ch. E.
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Astarita, G. et al ,
"Velocity Profiles in Turbulent Pipe Flow of
Drag-Reducing Liquids", Chemical Engineering Science, Vol. 24,
August 1969, p. 1241
Astarita, G. & Nicodemo, L., "Behavior of Velocity Probes in
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md., & Eng. Chem.
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and Drag Reduction Characteristics of Association Colloids in
Non-aqueous Fluids", Paper No. 3e, Drag Red. Symp. A. I. Ch. E.
Meeting Feb. 1970
Bailey, B. 3., "Behavior of the Critical Taylor Number in Dilute
Polymer Solutions", Nature, Vol. 222, No. 5191, Apr. 26,. 1969,
p. 373
P-lU. Barnes, H. A., Townsend, P. & Walters, K., "Flow of Non-Newtonian
Liquids under a Varying Pressure Gradient", Nature, Vol. 224,
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P-li. Barnes, H.A. & Walters, K., "On the Flow of Viscous and
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- i S
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P-iZ. Bilgen, E., "Effect of DIlute Polymer Solution on Discharge
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P-13. Bilgen, E., "On the Stability of Dilute Visco.elastic Flow Due to a
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P-14.
Boggs, F.W., "Investigation of the Vortex Structure in Shear Flow of
Dilute Polymer Solutions", Paper No.. 14c, Drag Red. Symp.
A.I.ch.E.. Meeting Feb.1970
P-14a. .Buevich, lu. A., "A Model of the DragRediiction Associated with the
Injection of Particles in a Turbulent Flow of a Viscous Fluid,
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P-15
Canham, H J S & Long, R F
'Boundary Layer Additives to Reduce
ShipResistahce," presented to Roy. Inst. Nay. Arch., Apr 1970
-16.
Carey, W.. ..W. & Turian., R. M., "Settling of Spheres in Drag.Reducing
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-17.
Chung,, J.S. & Graebel, W. P., "Laser Anemometer Measurements o,f
Turbulence in Non-Newtonian Pipe Flows," Ph.D. Thesis, Univ.
Of Michigan, Nov. 1969 (AD-699533)
-l8.
Cole, L. D., "Measurement of the Viscoelastic Relaxation Time of
Drag-Reducing Polymer-Water Solutions," NSRDC Dept of Acoustics
and Vibration Tech. Note DAV-297-942, Apr. 1970
P-l9. Corman, J. C. "Experimental Study of Heat Transfer to Viscoelastic
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.P-Z0.
Darby, R., "Transient and Steady State Rheological Properties of
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Dove., H.L., Canham, H.J.S., Catchpole, J.P. & Long, R..F.,
"Trials on HMS Hi.ghburton-Effect.of the Ejection of Polyox into
the Boundary Layer," Combined Report: Admiralty Experiment
Works Report 11/69 and Admiralty Materials Laboratory Report
B/liZ (.W), July 1969
Ellis, A. T., Ting, R.. & Nadolink, R.H., "Some Effects of Storage
and Shear History on the Friction Reducing Properties of Dilute
Polymer Solutions, " presented to AIAA/Navy Marine Systems,
Propulsipn and ASW Meeting, May 1970, AIAA Paper No. 70-532
.Ellis, A.T., Waugh, J.G. & Ying, R.Y., "CavitationSuppression
and Stress Effects in High-Speed FlOws of Water
dth Dilute
Macro,rnolecuie Additives, " AIAA Paper 70-532, May 1970
P-.24.
Ellis, H. D., "Effects of Shear Treatment on Drag-Reducing Polymer
Solutions and Fibre Suspensions," Nature,Vol. 226, No. 5243,
Apr, 25,. l97O,p. 352
Ellis, H.D. & Jeanes, J.A., "Drag Reduction with Suspensions of
Fibres," Admiralty Underwater Weapons Estab. A. U. W. E.
Tech. Note 342/69, Nov. 196.9
Fabula, A. ..G. & Burns, T.J.
,"Dilution in a Turbulent Boundary
Layer with Polymeric Friction Reduction, " Naval Undersea R&D
Center NUC STP 171, Apr. 1970
Fortuna, G. & Hanratty, T. 3., "Effect of Drag Reducing Polymers on
Turbulence Close to a Wall", Paper No. 14g Drag Red. Symp.
A.I. Ch. E. Meeting,Feb. 1970
P-28. Fruman, D., Sulmont, P. & Loiseau, G., "Mesure des Vitesses
dans les Flu.ides Viscoelastiques au moyen de Tubes de Pitot,"
Journal de Mcanique,Vol, 8, No. 4, Dec. 1969
P.-29.
Gadd, G. E., "Pulsatile Flow Instrument for Detecting Viscoelasticity
in Dilute Polymer Solutions,
Nature, Vol. 225, No. 5234,. Feb. 21,
l970p. 724
Giles, W. B.
"Orifice Flows of Polyethylene Oxide Solutions, "
Nature, Vol. 224, No. 5219, Nov. 8, 1969, P. 584
Goldstein, R. J., Adrian, R. J. & Kreid, D. K., "Turbulent and
Transition Pipe Flow of Dilute Aqueous Polymer Solutions, '
md.
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P-31a. Gordon, R. J.
,"Mechanism for Turbulent Drag Reduction in Dilute
Polymer Solutions," Nature, Vol. 227, No. 5258, Aug. 8, 1970,
p. 589
Granville, P.S., 'Drag Reduction of Flat Plates with Slot Ejection of
Polymer Solution,
Naval Ship R & D Center Report 3158, Nov. 1969;
also Journal of Ship Research, Vol. 14, No. 2,June 1970
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Nature, Vol. 224, No. 5225, Dec. 20, 1969,
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p-34.
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P...35
