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AIAA 80-1373R
Skin FrictionMeasurementsby a
Dual-Laser-BeamInterferometerTechnique
D. J. Monson and H. Higuchi
Reprintedfrom
AIAAJournal
Volume 19, Number6, June 1981, Page739
This paper is declared a work of the U.S. Governmentand thereforeis in the public
domain
AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS • 1290 AVENUE OF THE AMERICAS • NEW YORK, NEW YORK, 10104
VOL. 19, NO. 6, JUNE 1981
AIAA 80-1373R
AIAA JOURNAL
Skin Friction Measurements by a Dual-Laser-Beam
Interferometer Technique
739
D. J. Monson*
NASA Ames Research Center, Moffett Field, Calif.
and
H. Higuchit
Dynamics Technology, Inc., Torrance, Calif.
A portable dual-laser-beam interferometer thai nonintrusively measures skin friction by monitoring the
thickness change of an oil film subject to shear stress is described. The method is an advance over past versions
in that the troublesome and error-introducing need to measure the distance to the oil leading edge and the
starting time for the oil flow has been eliminated. The validity of the method was verified by measuring oil
viscosity in the laboratory, and then using those results to measure skin friction beneath the turbulent boundary
layer in a low speed wind tunnel. The dual-laser-beam skin friction measurements are compared with Preston
tube measurements, with mean velocity profile data in a "law-of-the-wall" coordinate system, and with com-
putations based on turbulent boundary-layer theory. Excellent agreement is found in all cases. (This validation
and the aforementioned improvements appear to make the present form of the instrument usable to measure
skin friction reliably and nonintrusively in a wide range of flow situations in which previous methods are not
practical.)
Ci
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I
i
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ng
_o
q ,
R
r
T
t
X
x_
x*,y*
Y
Ol
AN
At
Ax
Nomenclature
= coefficient in Eqs. (22) and (25)
= local skin friction coefficient, r/q
= external flow pressure gradient
= oil viscosity function, see Eq, (A17)
= gravitational acceleration
=skin friction function, see Eq. (AS)
= incidence angle for interferometer fiat
= incidence angle for oil
= fringe number, see Eq. (A3)
= interferometer flat index of refraction
= oil index of refraction
= free-stream dynamic pressure
= refraction angle for interferometer flat
= refraction angle for oil
= interferometer flat thickness, or temperature
=time
= distance from oil film leading edge
= distance correction for surface tension
= Preston tube coordinates, see Ref. 6
= oil thickness
= initial oil film leading-edge slope
= incremental change in fringe number
= incremental change in time
= beam spacing
= fixed oil sublayer thickness on a surface
=pressure gradient and gravity correction
parameter, see Eq. (A13)
= surface inclination from horizontal
= laser wavelength
= oil kinematic viscosity
= oil density
= local skin friction
Presented as Paper 80-1373 at the AIAA 13th Fluid and Plasma
Dynamics Conference, Snowmass, Colo., July 1,1-16, 1980; submitted
Aug. 19, 1980; revision received Feb. 13, 1981. This paper is declared
a work of the U.S. Government and therefore is in the public domain.
zResearch Scientist, Physical Sciences Branch. Member AIAA.
1Research Scientist. Member AIAA.
Superscripts
( ) ' =corrected or "effective" value
(-) = average value
Introduction
ECAUSE of the importance of determining skin friction
in turbulent boundary layers, there has been a continuing
effort to develop reliable and practical methods for its
measurement. Winter _ has reviewed the major methods
developed to date. These include the floating-element balance;
mean-velocity profile data, together with the Clauser chart;
the Preston tube; and surface thin-film heat-transfer gages.
Except for the floating-element balance technique, all of the
methods are indirect because they are based on the wall
similarity in turbulent boundary layers. Thus, each one
generally has a limited range of application. The floating-
element balance method has critical gap and alignment
problems, especially when subjected to a pressure gradient,
and it is often too delicate and expensive for general use. The
versatility of all of the methods is limited in that they either
require permanent installation in a surface or they are in-
trusive in the flow.
Recently, Tanner and Blows 2 and Tanner _.4 described a
new viscosity balance method that overcomes many of the
limitations of the other techniques. Their method uses laser
interferometric thickness measurements of oil films flowing
on surfaces subject to shear stress and relates those
measurements to the surface shear stress through a simple
theory. Higher order effects--from surface tension, gravity,
pressure or shear gradients, and three-dimensionality of the
flow--are easily accounted for. The method has several
important advantages. First, it is a direct method like the
floating-element balance technique and does not require
calibration in a known flow. In addition, the instrument is
simple and inexpensive, is potentially very accurate, can be
used in any type of steady flow, is easy to locate at various
points on a surface, and is nonintrusive because the oil film is
usually too thin to significantly affect the air flow. 2
Despite these advantages, the method has not been widely
adopted because of several practical difficulties in Tanner's
original procedure. His method required accurate
740 D.J.MONSONANDH.HIGUCHI AIAAJOURNAL
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® @® ®® ®
FLOW_ /?/ OIL
(_) HE-NE LASER
(_) TELESCOPE
(_) NEUTRAL DENSITY FILTER
(_) IRIS DIAPHRAGM
(_ INTERFEROMETER FLAT
(_ STOP
(_) HALF-WAVE RETARDATION PLATE
Fig. 1
(_ POLARIZATION BEAM SPLITTER
FOCUSING LENS
POLARIZER
_) 6328 ,_, FILTER
SILICON PHOTODIODE
MODEL SURFACE
Schematic of dual-laser-beam skin friction interferometer.
measurements of both the distance from the beam focal point
to the oil film leading edge and of the time at which the oil
flow started. Tanner 3 measured the leading-edge distance
before a run by visually setting the focal point of a reference
beam with known spacing from the measurement beam at the
oil leading edge. This can be subject to error in some ap-
plications because of the difficulty in exactly locating the oil
edge and in accounting for oil spreading after the
measurement. In addition, to measure the distance, Tanner
found it necessary to rigidly mount his equipment to the wind-
tunnel top wall; at that location, tunnel vibration and wall
displacements can disturb the measurement, making beam
repositioning difficult. Furthermore, Tanner assumed that the
oil-flow time was equal to the tunnel running time. This also
was subject to error because of prerun oil flow, tunnel starting
transients, and early-run oil surface waves.
In this paper, a dual-laser-beam instrument with fixed beam
spacing, and the procedures for its use are described. This
method of measuring skin friction eliminates most of the
limitations of Tanner's technique. The need to measure the
distance to the oil leading edge has been eliminated. Further,
the theory has been extended to determine the "effective" oil-
flow time from the interference fringe count as a function of
time, rather than by direct measurement. This automatically
eliminates all of the inherent timing errors in the original
method. Finally, all of the instrument components are located
remotely from the wind tunnel. This eliminates nearly all
effects of tunnel vibrations, makes relocating the
measurement point on the surface easy, and leads to an in-
strument that is easily transportable from one tunnel to
another.
Description of Instrument and Theory
A typical wind tunnel installation of the dual-laser-beam
instrument is shown in Fig. 1. The instrument measures the
rate of change in thickness of a flowing oil film at two points
just behind the leading edge of the film. The linearly polarized
output from a He-Ne laser is expanded by a telescope and
passed through a neutral density filter to reduce the beam
power level to a value that avoids excessive oil heating (see
discussion by Tanner 3). The single beam is then divided into
two parallel beams, using an interferometer flat. One beam
passes through a half-wave retardation plate to rotate its
polarization by 90 deg, and both beams are focused on the oil.
The beams reflect off the model surface, are then separated
with a polarization beam splitter, and each is focused on a
photodiode.
AN 3 = -10 --
UPSTREAM "" v v v v
BEAM l.l ,:IN2 " -20
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STARTED
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x Ax
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Fig. 2 Typical dual-laser-beam interferometer fringe record from a
wind-tunnel test; beam spacing is 5 ram.
Polarizers and narrow-band interference filters are used at
the detectors for additional noise reduction. The detector
signals are recorded on a two-channel chart recorder. As the
oil thickness changes, the recorded light intensity is
modulated by alternating constructive and destructive in-
terference between beams reflected from the oil and model
surfaces. 2 The transmitting and receiving optics are mounted
on tripods separate from the wind tunnel for versatility in
locating the measurement points.
A typical dual-beam interferometer output record is shown
in Fig. 2. Each crest on a trace represents an oil thickness
corresponding to constructive interference between the
reflections. Thus, by simply counting the number of fringes
over a given time span, the resulting change in oil thickness
can be precisely computed in terms of the known laser
wavelength. The erratic behavior of the signals just after the
tunnel is started is due to transient waves observed in the oil.
Usable traces begin after the waves disappear and after the oil
thins to the point where only a single fringe occurs over the
diameter of the laser focal spot diameter.
The procedure for computing skin friction from in-
terferometer records such as those shown in Fig. 2 is given in
the Appendix. The oil density, index of refraction, spacing
between the two laser measurement beams, and the laser
wavelength are constants that are required as input for the
calculation. Also, the oil kinematic viscosity must be ac-
curately known over the test temperature range. If needed,
this can be easily measured using the dual-beam in-
terferometer from a gravity flow experiment and the
reduction procedure (also given in the Appendix). An ad-
vantage of measuring the oil viscosity in this way is that the
laser beam spacing does not have to be known--as can be seen
from Eqs. (A5) and (A21) of the Appendix, it cancels out of
the final expression for skin friction. Finally, the laser in-
cidence angle with respect to the test surface must be
measured, although if it is close to 90 deg, high accuracy is not
required.
Description of Experiment
Oil Viscosity Measurement
The present dual-beam instrument was first used in a
gravitational flow setup to measure the viscosity of several
Dow Corning 200 silicon oils. As pointed out by Tanner 4
silicon oil is desirable for skin friction measurements because
it is available in a wide range of viscosities that are relatively
insensitive to temperature; moreover, it has low surface
tension and a very low vapor pressure. The viscosity
measurements were made on a polished aluminum disk, on
the back of which a thermocouple was mounted to measure
oil temperature. A timing mark was recorded when the disk
JUNE1981 DUAL-LASER-BEAMINTERFEROMETERTECHNIQUES 741 ....
MODEL 9:1
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SECTION SECTION TEST SECTION 0.3 X 0.3
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Fig. 3 The 1 ft x l ft low-speed - _-
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/
18 19 20 21 22 23 24 25 26
TEMPERATURE, T °C
Fig. 4 Silicon oil viscosities measured with the dual-laser-beam
interferometer.
was tipped from a horizontal to a vertical position to initiate
the flow. Results of the viscosity measurements are given in
the next section.
Skin Friction Measurement
Skin friction measurements with the dual-beam in-
terferometer were made in the test facility shown in Fig. 3.
The facility is an open-cycle, low-speed wind tunnel with a 14-
cm-diam aluminum cylinder extending along the tunnel axis
from the tunnel entrance to the diffuser. The maximum
freestream speed is 50 m/s. A fully developed turbulent
boundary layer exists on the cylinder. The skin friction
measurements were made at three axial stations on the
cylinder at a speed of 37 m/s, and at the central station over a
speed range of 21 to 48 m/s. Large plexiglass side windows
allowed laser beam access in and out of the tunnel. The oil
temperature was measured by inserting a thermocouple in a
metal plug in the tunnel wall. After the laser beams were
located and aligned, oil was placed along a line just upstream
of the forward beam reflection point. When the tunnel was
started and the oil flow initiated, a timing mark was recorded
and the measurements were initiated, as shown in Fig. 2.
For purposes of validation, a simultaneous measurement of
skin friction was obtained with a 1.07-mm-diam Preston tube;
a measurement was also derived from mean velocity profiles.
The Preston tube measurements were made at the same three
axial stations as the oil-flow measurements, as well as at
several azimuthal locations for each station to verify sym-
metry of the tunnel flow. The mean velocity profiles were
taken only on the top of the cylinder at the central station and
only at freestream speeds of 22 and 36 m/s. Skin friction was
computed from the Preston tube data, using the procedures of
Patel. _ The Patel calibration consists of a set of three
calibration curves expressed in terms of the Preston tube
coordinates, x ° and y* [see Eqs. (2-4) of Ref. 5]. These,
however, do not" match at the crossover points that were
suggested by Patel and thus give unnatural discontinuities in
the computed skin friction. Therefore, in this paper, the
intersections of the three calibration curves were numerically
7
z B
s
,-r
X 10-3
O 200-c_ntistoke OIL FLOW,
CALCULATED TIME
• 200-centistoke OIL FLOW,
MEASURED TIME
• VELOCITY SURVEY -
LAW-OF-THE-WALL FIT
PRESTON TUBE
u. +-5% TURBULENT BOUNDARY-
,.,_'_ '_
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¢ 1.07
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DOWNSTREAM DISTANCE FROM TUNNEL
TEST'SECTION ENTRANCE, m
Fig. 5 Comparison of skin friction measurements at 37 m/s. Note:
The data from each station are spread horizontally for visibility; all
correspond to the same location.
obtained and applied in the data reduction to eliminate the
discontinuities.
Skin friction from the mean velocity profiles was obtained
by plotting the data on a Clauser chart to fit the law-of-the-
wall, as suggested by Coles. 6 Although the boundary layers
were axisymmetric, no transverse curvature effect was ob-
served on these plots.
Results and Discussions
Results of the measurements of Dow silicon oil viscosity
using the dual-beam interferometer are shown in Fig. 4 for
oils of nominally 50- and 200-cS viscosity. The data are
compared with nominal curves from Dow's product
literature. The data were reduced using computed oil-flow
times by the method described in the Appendix. The 50-cS oil
data lie within ±2070 of the Dow curve, and the 200-cS oil
data lie within ± 2076 of a curve that is 97°70 of the Dow curve.
These variations are within the supplier's tolerances and those
by Tanner. 7 Both curves on Fig. 4 were used to obtain the oil
viscosity at a given temperature for the skin friction
calculations.
Measurements of skin friction using 200-cS oil, a boundary-
layer velocity survey, and Preston tube measurements are
compared in Fig. 5. The data were measured at three axial
locations on the cylinder at a freestream speed of 37 m/s.
They are also compared with an axisymmetric turbulent
boundary-layer code that incorporated the Wilcox-Rubesin
Reynolds stress equation turbulence model, s As an initial
condition for computation, the momentum thickness in the
code was matched with the measured momentum thickness at
the tunnel test section entrance. Higuchi and Rubesin 9 found
that this turbulence model and matching condition gave good
742 D.J.MONSONANDH.HIGUCHI AIAAJOURNAL
8 × 10 .3
o-7
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u.
L. 4
8
z
03
z z
centistoke OIL FLOW TIME
0 200 CALCULATED
a 200 MEASURED
D 50 CALCULATED
• 50 MEASURED
110 20 40 60 70 80 100
FREE-STREAM FLOW SPEED , m/see
Fig. 6 Oil-flow skin friction measurements 1.07 m from the tunnel
test-section entrance.
O 50 AND 200 centistoke OIL FLOW
u_6
zs
u. 4
u.
¢J
z 3
o
u. 2
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• VELOCITY SURVEY-
LAW-OF-THE-WALL FIT
PRESTON TUBE
TURBULENT BOUNDARY-
LAYER CODE
I A i i L J , i J
110 20 30 40 50 60 70 80 100
FREE-STREAM FLOW SPEED, m/see
Fig. 7 Comparison of skin friction measurements 1.0"/ m from the
tunnel test-section entrance.
agreement with measured skin friction on an axisymmetric
model similar to that in the present tests. The dual-beam
interferometer data were reduced, using both measured and
calculated flow times for comparison. The error bars shown
represent the maximum scatter measured for several repeated
runs. The Preston tube data include various azimuthal
positions on the axisymmetric cylinder to check for flow
symmetry.
The dual-beam interferometer skin friction results shown in
Fig. 5 are in excellent agreement with both the Preston tube
results at all three locations and with the result from the
velocity profile at the central station. The fairly large scatter
in the Preston tube data at the forward station arises from
flow asymmetry caused by the tunnel entrance screen. All
measurements agree well with the turbulent boundary-layer
calculation at the two downstream stations. The dual-beam
interferometer data at the forward station are a few per-
centage points lower than predicted, possibly because of the
aforementioned flow asymmetry. Finally, notice that the
dual-beam interferometer results are identical, using either
measured or calculated flow times.
As an alternative test of the dual-beam interferometer skin
friction technique, additional measurements were made at the
central axial station over a wide range of freestream flow
speed. The results for both 50- and 200-cS viscosity oil are
shown in Fig. 6. The less viscous 50-cS oil was used only at
lower speeds. The scatter in the data represents the maximum
variation for repeated runs at each flow speed. Within this
scatter, the 50-cS dual-beam interferometer data are in ex-
cellent agreement with the 200-cS results. This agreement for
a factor of 4 change in oil viscosity provides increased con-
fidence in the method and demonstrates that the agreement of
the 200-cS oil data with other methods shown in Fig. 5 is not
fortuitous. Finally, notice that the results are again identical,
using either measured or calculated flow times.
Some of the dual-beam interferometer results shown in Fig.
6 are compared in Fig. 7 with Preston tube and boundary-
layer velocity survey measurements, and with the turbulent
boundary-layer prediction. The dual-beam interferometer
data are for both oil viscosities, but using only calculated flow
times. The error bars represent the maximum scatter
measured for repeated runs. For the Preston tube at 21 m/s,
measurements were made at various azimuthal locations.
Within this scatter and the accuracy of the measurements, the
dual-beam interferometer data are again in excellent
agreement with the Preston tube data over the entire speed
range, and also with the two velocity survey results at 22 and
36 m/s. All methods disagree only slightly with the turbulent
boundary-layer prediction, although the measured data
appear slightly higher than the prediction at the lowest speeds.
Part of this discrepancy could be caused by the previously
discussed flow asymmetry. Overall, the measurements for all
three methods and the prediction are within 5% of each other.
A major goal of this study was to verify the present method
in which the oil film leading-edge distance and the flow
duration are computed rather than measured. To test the
method, the leading-edge distances were directly measured in
the gravity flow tests using the method discussed by Tanner, _
and the oil-flow durations were measured in all of the tests.
The flow durations in this study were deliberately chosen to be
fairly long; this was done to minimize the influence on the
described measurements of any transient events, at the start of
the oil flows, that might introduce errors. (The oil viscosity
tests were recorded for 20-60 min, and the skin friction tests
for 2-10 rain, depending on oil viscosity and air speed.)
Although not required for the dual-beam oil viscosity
measurements, the oil-film leading-edge distances can be
computed from Eq. (A20) in the Appendix.
The computed leading-edge distances for the oil viscosity
tests in this study ranged between 93 and 100% of the
measured values. The slightly lower computed values are
consistent with the effect of surface tension on this type of
flow, as discussed in the Appendix. The computed flow-times
ranged between 97 and 103% of the measured values for the
gravity flow tests, and between 98 and 106% for the skin
friction tests. For the latter, the slightly higher computed flow
durations are consistent with the initial presence of surface
waves in the flow, which add to the rate of oil removal. This
close agreement explains why the skin friction results are the
same in Figs. 5 and 6, using either measured or computed flow
times. The above comparisons, plus the previously discussed
good agreement between the dual-beam interferometer skin
friction results and other methods, provide solid confirmation
of the method presented in the Appendix.
The only problem encountered in the operation of the new
dual-beam interferometer arose from occasional dust particles
in the oil. The wind tunnel had no inlet filter and was located
in a fairly dusty area with high daytime activity. Many dust
particles could be observed on the oil surface after most runs.
They could cause two problems: 1) a dust particle exactly at a
beam focal point surely could cause erratic interferometer
behavior; and 2) a large dust particle just ahead of a beam
focal point could locally perturb either the oil or the air flow
enough to influence the skin friction measurement, but could
not be detectable on the interferometer records. In fact, the
latter was probably the largest cause of the oil-flow data
scatter found in this study. Support for this view is found
from the data in Fig. 5. The measurements at the forward
station were taken at a time when there was less dust than
normal in the air, and the scatter there is much less than for
the other measurements.