NASA Technical Reports Server (NTRS) 20000059225: Review of Skin Friction Measurements Including Recent High-Reynolds Number Results from NASA Langley NTF

24 Pages·1.2 MB·English

by  NASA Technical Reports Server (NTRS)

|_
AIAA-2000-2392
Review of Skin Friction Measurements
Including Recent High-Reynolds Number
Results from NASA Langley NTF
R. D. Watson, R. M. Hall, and J. B. Anders
NASA, Langley Research Center
Hampton, VA 23681
Fluids 2000
19-22 June 2000 / Denver, CO
For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191

AIAA PAPER 2000-2392
REVIEW OF SKIN FRICTION MEASUREMENTS INCLUDING RECENT HIGH-
REYNOLDS NUMBER RESULTS FROM NASA LANGLEY NTF
Ralph D Watson"
Flow Physics and Control Branch
Robert M. Hall*
Configuration Aerodynamics Branch
John B. Anders"
Flow Physics and Control Branch
NASA, Langley Research Center
Hampton, Virginia 23681
ABSTRACT Re to 619,800 using the van Driest transformation.
This paper reviews flat plate skin friction data Previous data, test techniques, and error sources
from early correlations of drag on plates in water are discussed, and the NTF data will be discussed
to measurements in the cryogenic environment of in detail. The NTF Preston tube and Clauser
The NASA Langley National Transonic Facility inferred data accuracy is estimated to be within
(NTF) in late 1996. The flat plate (zero pressure - 2 percent of a power-law curve fit, and falls
gradient with negligible surface curvature) above the Spalding theory by 1 percent at Re of
incompressible skin friction at high Reynolds about 600,000.
numbers is emphasized in this paper, due to its
importance in assessing the accuracy of
measurements, and as being important to the 1. INTRODUCTION
aerodynamics of large scale vehicles. A The design of transport aircraft requires that
correlation of zero pressure gradient skin friction accurate estimates of skin friction be made at
data minimizing extraneous effects between tests length Reynolds numbers around 109 and Mach
is often used as the first step in the calculation of numbers of approximately 0.8, corresponding to
skin friction in complex flows. Early data compiled cruise conditions 1. This estimate is often made by
by Schoenherr for a range of momentum thickness first calculating the flat plate incompressible skin
Reynolds numbers, Re, from 860 to 370,000 friction and then correcting for various effects such
contained large scatter, but has proved as pressure gradient, three-dimensionality of the
surprisingly accurate in its correlated form. flow, compressibility, etc. Several baseline
Subsequent measurements in wind tunnels under theories/correlations are available, most of which
more carefully controlled conditions have provided differ in the skin friction level predicted at high
inputs to this database, usually to a maximum Re Reynolds numbers where there has been a dearth
of about 40,000. Data on a large axisymmetric of data.
model in the NASA Langley National Transonic As will be shown, the most commonly used
Facility extends the upper limit in incompressible correlations of skin friction do not agree to the
*SeniorMemberAIAA
"Associate FellowAIAA
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desireadccuracaythigh
Reynolds numbers, and it s distance along surface of model
is not clear which method is the most accurate. T temperature
Over the years, compilations and critical reviews
u velocity, fps
of the available data have been made, but only
shear velocity, (._,/p)1/2
recently has skin friction data at very high u_
Reynolds numbers become available. The most u* U/U_
recent data is usually tunnel wall data, with the x axial distance along model
exception of the present data which was taken on y coordinate normal to surface
a large axisymmetric model, y" y u_/v
An experiment to measure fiat plate skin friction cc angle of attack of model
at flight Reynolds numbers was conducted in the Clauser pressure gradient parameter,
Langley National Transonic Facility, NTF. The
(6"/_) (dp/dx)
purpose of the test was to provide skin friction
data at very high Reynolds numbers to compare G boundary layer thickness
with existing theories. The difficulties in Gu thickness at u/ue =0.99
measuring skin friction free of extraneous effects G" displacement thickness
and to the desired accuracy was recognized early. 6+ value of y* at edge of boundary layer
In addition to the usual problems associated with 0 momentum thickness, inches
testing at high Reynolds numbers, the cryogenic
environment of the tunnel affected both the model P dynamic viscosity
and instrumentation and complicated the test. A u kinematic viscosity
description of the test, the results obtained, and P density
comparison with other available skin friction data shear stress
will be discussed. 0 roll angle on model, see Figure 4
A factor to be considered in testing at high unit
Reynolds numbers is the difference in scales subscripts
between the wall and the outer region. At the wall,
aw adiabatic wall condition
the turbulent scales are so small that wall
roughness may be an important factor --i.e., the e at edge of boundary layer
wall must be very carefully machined to avoid i incompressible
roughness-induced effects. What for most t stagnation condition
engineering purposes would be considered w at wall
adequate wall smoothness may not be the case at x based on x coordinate
high Reynolds numbers 2. Another of the many 0 based on 0
problems is the difficulty of manufacturing
freestream condition
boundary layer rakes with tubes spaced closely oo
enough to capture the law-of-the-wall region.
superscript
reduced to incompressible form by Van
2. NOMENCLATURE Driest method (equation 6) for velocities and
Cf friction coefficient integral quantities, or by Sommer and Short T
method (equation 5) for temperature-dependent
Cp pressure coefficient
quantities
C constant in equation 7
d outside diameter of Preston tube 3. NTF EXPERIMENT
D model diameter, 12.75 inches The NTF test was designed to accurately
E constant in equation 2 measure adiabatic flat plate skin friction values at
H shape factor, _*/0 Reynolds numbers as high as possible and Mach
k van Driest constant, equation 7 numbers corresponding to flight conditions in order
to extend the existing skin friction-Reynolds
M Mach number
number database. The highest Reynolds numbers
r radial coordinate
obtainable in Langley Research Center tunnels
R unit Reynolds number, pulp_ are produced in the cryogenic transonic tunnels,
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NTFand0.3MTransonTicunnel.Forthistest,
present data and to infer cf from velocity profile
unit
Reynolds numbers as high as 94 x 106/ft were measurements. The surveys were also necessary
run, and length Reynolds numbers of 940 x 106 at to determine the boundary layer integral quantities
the downstream measurement station on the such as the momentum and displacement
model were measured. The difficult task of thicknesses.
measuring skin friction in the cryogenic tunnels is A photograph of the model in NTF is shown in
made even more difficult by model and Figure 1.
instrumentation problems related to the extreme
low temperature of the flow. 4. FLAT PLATE SKIN FRICTION DATA AND
The idea of a test for obtaining high Reynolds THEORY
number c4data in NTF is not new, and in fact, a 4.1 Theories and Correlations
program to do so was outlined by Saric 3. The Schoenherr s correlation of his own data and
ideas presented in this report were used in the data of others dating to 18725 was published
planning the NTF test, the major difference being
almost 70 years ago, but is still used in its
the model on which cfwas to be measured. It was correlated form, except at low Reynolds numbers.
determined in the early planning stage that a two- Skin friction was obtained from the drag of plates
dimensional flat plate posed too many problems in of various sizes towed in water and, not
mounting and maintaining the accuracy of the surprisingly, the data exhibits large scatter when
surface in the high dynamic pressure environment.
plotted as a function of Reynolds number. When
For this reason an axisymmetric model was correlated with an equation of von Karman, the
designed for which transverse curvature effects results agree with most carefully-controlled
were small, based on the thickness of the
experiments. Twenty years later, in 1953, the
predicted boundary layer. In addition, it was paper by Landweber was published 6, describing
necessary to account for compressibility effects at the characteristics of turbulent boundary layers
Mach numbers as high as 0.8 in order to and deriving a shear law that agreed closely with
transform the data to an equivalent incompressible the method of Schoenherr. Nine years after this,
state.
the method of Spalding 7 was published. This
It was decided that no new skin friction method was derived from his sublayer-buffer-log
measuring techniques would be developed for this profile, but did not account for the outer portion of
test, since development was considered too time- the boundary layer. If the usual law of the wall
consuming for an experiment in NTF. It was also constants are used in Spalding s cf equation the
required to measure the skin friction as accurately answer is incorrect, since the wake is not
as possible, a notoriously difficult measurement to accounted for correctly. The constants were
make, even at ambient temperature. Three adjusted for use as the incompressible theory in
different standard techniques were used with the the Spalding-Chi compressible skin friction
rationale that they would either provide method ° to produce a more reasonable c,f level.
consistency among themselves or point out By adjusting the constants of course, the level
inadequacies in the experiment. A skin friction can be changed, but, more important, the slope of
balance was used since it is the only way to cf vs R, does not match that of the Karman-
measure skin friction directly. Also used were Schoenherr correlation over the complete
Preston tubes and boundary layer surveys, from Reynolds number range. Other methods which
which skin friction was inferred by a modified have been used are Ludwieg-Tillmann 9, and
Clauser method. There has been a renewed recently, Fernholz and Finley 10,which is based on
interest in the validity of the law of the wall lately4, both inner and outer similari_ and is compared
as evidenced in the report of George and Castilto. with data to Reof 200-300 x 10_.
The law of the wall is used extensively here to
The Karman-Schoenherr equations are:
.og,0(2.0)
(I)
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whereCFistheaveragsekin
friction coefficient.
The local skin friction coefficient, cf,was obtained by differentiating the first of the two equations.
The Spalding equations are
4
R/°eIl 1ek Uu I/06k_U,u+e/, uI1,;u/'2;/'/1,u;(/_°1u';
_ + 1
X 12 e 12 20 60 252
(2)
Re
ku+ 6
e
2
where c. =--
t iu:/_
The Ludwieg-Tillmann equation is
cf = 0.246 x 10-°678Hx Re°268
(3)
The Fernholz and Finley equations are
c{, +cN+/;
--_-- _-In
where In (-_--_-) = In(Rx) = 0.3 +In(Re)
l-Y (u_ u) (4)
z_ = I_ dy
Ju U_
and In/Y] _=-2.7 for Re > 2000
\L-l}
P
_---0.404 tn(Re)+O.37 for4252<R e <2000
k=0.4, C=5.1, M=4.70, andN=6.74
high Reynolds numbers, the crossover point
The methods of Karman-Schoenherr, occurring at Re between 6000 and 7000. The
Spalding, Ludwieg-Tillmann, and Fernholz and Karman-Schoenherr correlation includes Kempf s
Finley are shown in Figure 2. From the figure, it is data to Re of about 370,000 (Rx of 450 x 106.)
obvious that the theories do not agree with each The Spalding method relies on the constants of
other over the complete range of Reynolds the law-of-the-wall, and thus might be in question
numbers. The methods of Karman-Schoenherr at high Reynolds numbers unless these constants
and Spalding show opposite trends at low and are shown to be the same as for lower Reynolds
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numbers. Ludwieg-Tillmandneviatesfrom
KarmanSchoenhebrrelowReabout3000and 5. NTF EXPERIMENT - RESULTS AND
aboveReabout20000.FernholazndFinleyis DISCUSSION
lowetrhantheothetrheories.
5.1 Tunnel, Model, Instrumentation, and Test
4.2Data Conditions
Overthepast30yearsexcellenrteviewsof 5.1.1 Tunnel The range of operating
availableincompressibleand compressible conditions for the National Transonic Facility
boundarlayyerdatahavebeencompiledT.hese (NTF) at Langley Research Center 23is as follows:
includtehecompilatiofonrincompressifblolewsby Mach numbers from 0.2 to 1.2, total pressure from
ColesandHirstfromtheStanforCdonferencine one to 9 atmospheres, total temperature from
19681,t1hecompilatioonfscompressibflolewdata --320 to 150deg. F, and Re/ft from 3.7 to 146 x
byFernhoalzndFinleyin19771a2n,d19811a3n,d 106 at Mach 1. For cryogenic operation, liquid
theexaminatioonfIncompressidbaletato1996by nitrogen is injected into the flow downstream of the
FernhoalzndFinle1y°.Sincethattime,otherdata test section, and vaporized to maintain low tunnel
hasbeenpublishedm,osthighReynoldnsumber temperatures. Intermediate temperatures can be
datahavingbeentakenonthewallof wind attained by regulating the amount of liquid nitrogen
tunnels.Thesedataappeatrobedifferenftrom injected. The tunnel can also be run using air if no
flatplateboundarlayyerdataTM, i.e., the boundary cooling is required. For the present tests, both
layer has developed in regions of wall curvature ambient temperatures and cryogenic temperatures
and strong adverse and favorable pressure were used to obtain the desired Reynolds number
gradients, and is usually not characteristic of range.
equilibrium flat plate boundary layers until a The test section is 25 feet long, and 8.2 ft
sufficiently long run has been made. Relaxation square 24, making it possible to mount very long
has apparently not been completed before models in the tunnel to produce large length
entering the test section. Reynolds numbers. The model described here
Reference 15 from 1996, listed data in was 17.28 feet long. The test section is slotted to
addition to that of reference 10, but did not present minimize blockage effects, which were 3.3%
skin friction measurements at high Reynolds based on an inviscid geometric area ratio.
numbers. In 1984, Gaudet 16, published data at Measured model pressures demonstrated that the
Mach 0.8 on the sidewall of the RAE 8 ft by 8 ft flow over the model was uniform, validating that
wind tunnel and reexamined the data of reference the slotted design worked as expected.
17. Other data was published in 1994 by Standard tunnel data reduction and tunnel
Motallebi TMon the wall of a wind tunnel for Re from instrumentation 25 were used; however, local
26,000 to 106,000 in compressible flow; however, values of flow parameters on the model were
skin friction was not measured in all cases and the recalculated from measured model conditions
data are not used for comparison here. The using the Fortran routines of NTF. The Beattie-
tabulated data of Fernholz, Krause, Nockemann, Bridgemann equation of state was used to
and Schober 19is compared in Figure 3 with high calculate the properties of both nitrogen and air26.
Reynolds number data of Gaudet, low Reynolds 5.1.2 Model The design of the model was a
number data of Coles 2° and Purtel121, and the compromise among several factors. It was
methods of Karman-Schoenherr (K-S) and desirable to have a long model in order to produce
Spalding. For this figure the compressible profiles large length Reynolds numbers. The diameter
of Gaudet, were re-reduced and transformed by was required to be large enough so that the model
the van Driest transformation 22, which was also would not deflect significantly under its own weight
used for the NTF data transformation. Noted in and to allow room for the balance and other
the figure is the Rerange of the data taken in NTF instrumentation to be mounted internally. In
on an axisymmetric model, and reported in a addition, it needed to be large enough that
following section. transverse curvature effects would not significantly
The methods of Karman-Schoenherr and affect skin friction. It could not be too large, or
Spalding will be used to compare with the present model loads and blockage effects would be
data, since they agree reasonably well with the excessive.
best experimental data available at this time over A sketch of the axisymmetric 347 stainless
a large range of F_. steel model is shown in Figure 4. It was an
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axisymmetrcicylinder12.75inchesindiameter at all test conditions. It has been shown 29that the
havinganosedescribebdyasuperellipsaen,d7
tube can extend well into the wake portion of the
cylindricsaelctiondsownstreaomfthenose.Ports
boundary layer with no adverse effects; however,
wereinstalleidnthemodealtStation1sand2,at
the tubes were 0.058 inches in diameter, and did
x=73.95and121.95inchesr,espectivelyS.kin
not extend into the outer portion. The nose was
frictionwasmeasuredby a balanceandby
unchamfered and polished, and the ratio of
Prestontubesat Station2, andby rakesat
internal to external diameter was 0.6. Care was
Station1sand2. Thewholemodeli,ncludintghe
taken in mounting the probes so that the tubes
nosew, aspolishetdoasurfacefinishof4
I_ in. would be firmly attached to the surface and to
No transition trips were used on the nose. The ensure that no mounting apparatus would protrude
model was sting-mounted in order to minimize into the flowfield (see Figure 5 b).
boundary layer interference effects, which would The only set of Preston tube data know to the
be caused by model struts. The NTF sting mount authors covering the range of Reynolds numbers
had roll and angle of attack capability that could be for which measurements were to be made was
used to set the model at nominally zero angle of that from Laval University 3°. Rather than rely on a
attack. Initially, Preston tubes were mounted single set of data, a high Reynolds number
circumferentially around the model to measure the calibration was made at Princeton University in the
nonuniformity of the flow and adjust the angle of Superpipe Facility 2. The data from the Princeton
attack.
test was cast in the parameters of four different
The design of the nose and flow over the calibration methods 3134 to see if any one method
model were predicted using CFD methods. It was gave superior results in determining skin friction
determined from these calculations and boundary from known inputs. It was found that all methods
layer calculations 27 that the pressure gradient gave the same results. Patel s high Reynolds
would not be a factor in measuring flat plate skin number calibration was found to predict the
friction. Similarly, the ratio of the boundary layer Princeton data at high Reynolds numbers, and
to the model radius was estimated 27to be 0.25 at was used to reduce the NTF data.
the second measurement station, and transverse
Inference of skin friction from velocity surveys
curvature effects on cf were estimated to be less is most accurate if tubes on the boundary layer
than 1.5 %, at R0of about 600,000. rake are positioned within the logarithmic portion
5.1.3 Instrumentation Three methods of of the turbulent boundary layer. In addition, the
determining skin friction on the model were used: edge of the boundary layer should be defined so
a skin friction balance, Preston tubes, and velocity that the integral quantities (_and (_ are accurately
profiles from which skin friction was inferred by the calculated from the profiles. The boundary layer
Clauser method. Photographs of the three calculations discussed previously provided the
instruments used on the model are shown in guidelines for tube placement. The tips of the pitot
Figure 5. Preston tubes and the skin friction tubes were not chamfered, and were polished, as
balance were tested at Station 2 at both hot and was done for the Preston tubes
cold flow conditions. The boundary layer rake was
Model pressures were measured by an
used at Station 1 at the hot flow condition and at
electronically scanned system, and model
Station 2 at hot and cold flow conditions.
temperatures by copper-constantan (Type T)
The problems associated with the direct thermocouples accurate to 1 degree K. One port
measurement of skin friction by balance are well on each ESP module was dedicated to measuring
known 28. Additional problems resulting from a known reference pressure that was also
operating a mechanical device in a cryogenic measured by a secondary standard. Whenever
environment required that a risk reduction the reference pressure difference deviated by
experiment be done in a smaller tunnel -- the - 0.19% of full scale the modules were re-zeroed
Langley 0.3 Meter Transonic Cryogenic Tunnel. online.
The problems encountered in the risk reduction 5.1.4 Test Conditions The model was tested at
experiment were larger than anticipated and Mach numbers from 0.2 to 0.85 and unit Reynolds
greatly influenced the design of the final balance. numbers from 6 x 106 to 94 x 106 per foot. A
Preston tubes were sized from boundary layer matrix of the test conditions is shown in Figure 6.
calculations. They were designed so that the tube The highest unit Reynolds number was attained at
was in the logarithmic region of the boundary layer Mach 0.6. The highest unit Reynolds number at
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which data could be obtained at Mach 0.85 was 65 this method temperature-dependent quantities
x 106, a consequence of the load constraints for such as p and IJ are replaced in parameters and
the model. Noted in the figure are the conditions equations by their values at a temperature
at which data was obtained on Preston tubes, the intermediate between the wall and freestream
balance, and the boundary layer rake. At most values -- the T-prime condition. Allen used the
tunnel conditions, all three devices were tested, Sommer and Short method, which is the Rubesin
but at Mach 0.7 only Preston tubes were run. and Johnson equation with constants determined
for Mach 3.82 in air35. The Sommer and Short T-
Due to the finite blockage of the model in the
tunnel, it was necessary to calculate the local prime method was used in this report for all
Mach number, which could be slightly different Preston tube reductions. The equation defining
from the freestream Mach number. This was done the T condition is
by averaging pressures at three orifices just ahead
of Station 1 and using this pressure as the local T"r-e- = 1.+ 0.035 M_e+0.45(-_-- 1./ (5)
static pressure to calculate the nominal local Mach
number. To define the model pressure in the In order to present velocity profiles and
vicinity of the measurement stations, 11 orifices integral quantities in an equivalent incompressible
around Station 1 and 11 around Station 2 were form, velocity profiles were transformed using the
averaged. These averaged pressures were used Van Driest method 21, which was shown to
as the local static pressure in calculating cp at their transform velocity profiles in the outer region of
respective stations. Similarily, three temperatures adiabatic wall boundary layers at Mach 11 in
near the two primary data positions were averaged helium 36. Velocities are transformed in proportion
in calculating Twl and Tw2. to the density variation from the wall to the edge of
the boundary layer by this method; i.e., the vertical
Representative pressures and temperatures
coordinate, y, is not transformed.
over the model are shown in Figure 7. It is
evident that the pressure gradient is sufficiently Called generalized velocities by Maise and
close to zero and that its effect on the local shear McDonald 37, the van Driest transformation is
stress can be considered negligible. This is more defined as
accurately quantified in later discussion. It is also
evident that there is little change in the pressure u': i0 du
gradient with Mach number. While not as uniform
as the pressure distribution, the model With the transformed velocity profile and the
temperature variation is small, being more uniform density evaluated at the wall, new values of e, (5"
at ambient temperature, as would be expected. and ue result. These transformed properties are
5.2 Factors affectinq NTF Skin Friction used to calculate Re and c f. The transformation
Measurements was coupled with the Clauser method to infer the
There are at least seven factors associated shear stress from velocity profiles by an interactive
with the conditions of the NTF test that can have graphical method. The incompressible profile was
an effect on measured surface shear. These plotted along with the incompressible law of the
factors are compressibility, pressure gradient, heat wall, and the data was fit to the law of the wall by
transfer, surface curvature, surface roughness, iteration. It is estimated that the data could be fit
lateral divergence (three-dimensionality) of the to the law of the wall with a resolution of about
flow, and the freestream disturbance level and 0.5 % in cf by this method. The accuracy of the
scale. All effects, except the freestream results are a function of the constants in the law of
disturbance level, were examined before the NTF the wall, defined as
test was begun to insure that they could be
--=-In yu_ +C (7)
controlled/minimized to the extent that a flat plate
u_ k _w
skin friction could be measured.
where k=0.41 and C=5.5
5.2.1 Compressibility Effects Tests were
conducted at Mach numbers from 0.2 to 0.85. The profile data were originally reduced with
Above approximately Mach 0.3, compressibility C=5.0, however it was found that C=5.5 gave a
effects must be considered in the flow. One better fit to the Preston tube data and skin friction
approach, and the one used by Allen in Preston theory.
tube reductions 2931, is the use of the T method. In
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5.2.2 Pressure Gradient-Relaxation Effects chamber behind the wall, and then to outside the
Preliminary tests were run in the Langley 0.3 tunnel.
Meter Transonic Cryogenic Tunnel, where the 5.2.4 Transverse Curvature Effects The
effects of both favorable and adverse pressure transverse curvature effect is a geometric effect
gradients on measured skin friction were characterized by the ratio of $ to model radius.
examined. This was accomplished by moving the Boundary layer calculations were made using 2-
upper wall of the test section to produce pressure foot long elliptical noses, model pressure
gradients of different magnitude. Figure 8 (a) distributions from Newtonian impact theory,
shows the effects on Preston tube measured cf in estimated transition locations, and model radii of 3
terms of I], the pressure gradient parameter used and 6 inches to estimate the magnitude of this
by Clauser to generate self-similar equilibrium effect. The measured ratios of (_r were found to
profiles 38. Data are shown at Mach numbers of be 0.25 at the second data acquisition station,
0.6 and 0.8 at two different unit Reynolds resulting in an increase in cf less than or equal to
numbers, and l]_is a transformed value obtained 1.5%, based on the calculations.
by using the van Driest transformed value of (5".
5.2.5 Surface Rouqhness Effects In order to
Compressibility and Reynolds number effects are
insure that the model was hydraulically smooth,
not completely removed using I_ however, the
boundary layer calculations were used to
correlation should be adequate for estimating local
determine the y* = 5 height normal to the surface.
pressure gradient effects. For these test
Figure 9 shows y in inches plotted against y* for
conditions
the most severe case, that at highest unit
Reynolds number. Based on this figure, the rms
Cf = 1. - 0.7 I_, (8)
wall roughness should be smaller than 30 pin.
(Cf)_=0 When constructed, the complete model and skin
friction balance element had a measured
As shown in Figure 7(a), the pressure gradient
on the nose is strongly favorable switching to roughness of 4 p inches and a value of y* of about
one. Based on the y'=5 criterion, surface
strongly adverse about x=13 inches, and relaxing
roughness should not have significantly affected
to very small adverse pressure gradient about
the skin friction measurements of this test.
x=30 inches. The pressure gradient is zero at
x=50 inches. The question arises as to whether 5.2.6 Lateral Diverqence Effects Three
the outer part of the boundary layer had relaxed to dimensionality of the flow is evident even in flat
the equilibrium zero pressure gradient state by.the plate experiments where great care has been
first measurement station. Station 1 was located taken to insure the two-dimensionality of the outer
at x=73.95 inches, 44 inches from the beginning of flow. From velocity profiles measured across the
small adverse gradient. Measured values of (5and flow, plots of e are always somewhat ragged, in
e were 1.3-1.5 and .065-.075 inches here, or 31 (5 keeping with skin friction measurements at the
and 630 e from the beginning of small adverse same locations and variations in the wake
pressure gradient and 17 (5and 340 e from zero component. This may be due to the raggedness
pressure gradient. The distance required for in the transition process, and/or the presence of
relaxation for flows with adverse pressure gradient near-wall structures in the boundary layer,
followed by zero pressure gradient is about 5-10 inducing a standing pattern in the flow. When
(339" there is finite three dimensionality in the flow,
5.2.3 Heat Transfer Effects The effect of effects are added to the usual two dimensional
nonadiabatic wall temperature effects on skin raggedness. In order to minimize the three
friction were also measured in the 0.3 Meter dimensionality of the flow on a longitudinal
Tunnel. The total temperature of this tunnel can cylinder, the expected droop due to the model
be rapidly varied from above ambient temperature weight was calculated and found to be
down to 100 K, making it possible to measure c_ approximately 0.25 degree. Since the model
over a range of T,fraw. The results are shown in could be adjusted within 0.1 degree, it was felt
Figure 8 (b) for Mach 0.6 and Mach 0.8. that the effect could be minimized by careful
Repeatability is shown by the agreement between alignment of the model. Initial runs were devoted
two different runs. For most runs in this tunnel, to model alignment. In addition, rake, balance,
the wall was slightly nonadiabatic due to heat and Preston tube measurements were always
transfer through the tunnel wall to a plenum made in the same azimuthal plane, which will be
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