NAVY DEPARTMENT
THE DAVID W. TAYLOR MODEL BASIN ao
Woshington 7, D.C.

THE MEASUREMENT OF TURBULENCE IN WATER

A Progress Report Prepared for Presentation at the
Seventh Underwater Ballistics Conference

by

Morris S. Macovsky

AG October 1948 Report No. 670

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THE MEASUREMENT OF TURBULENCE IN WATER
by
M. S. Macovsky

INTRODUCTION

The development of techniques for measuring the tur-
bulence of fluid media has progressed more in the study of gaseous
flow than of liquid flow. The David Taylor Modei Basin has re-
cently undertaken the study of turbulence in water both for the
purpose of advancing the basic understanding of the phenomenon in
water, and for the purpose of applying any fruitful results to the
analysis of model testing, and other hydrodynamic problems influ-
enced by turbulence. This paper describes the techniques that
have been applied to the study of turbulence in water, and the de-
gree of progress and success of each.

Although the practical importance of fully understanding
the phenomenon of turbulence in water has been recognized, progress
comparable to that made in air has not been accomplished. It has
been only within recent years that the meaning of turbulence in
model testing, for instance, has been appreciated. Producing the
proper turbulent boundary layer in ship models is essential to
accurate testing. Proper model testing is but one of the many
reasons which have made the necessity of measuring turbulence in
water essential to the Taylor Model Basin.

A number of techniques for measuring turbulence in water
have been suggested and a few of them have already been tried at
TMB. Hot-wire methods similar to those used in wind tunnels, dye
diffusion, and oil-drop injection techniques have been tried. Of
these, the most promising is the hot wire.

Bach of the techniques will be described, and the re=
sults ilJustrated. First, however, the basic definitions of the
turbulence parameters will be reviewed,

MEANING OF TURBULENCE

Turbulence, by definition, is a state of commotion and
agitation, As applied to hydro- and aerodynamics, it is a state
of fluid flow wherein random velocity fluctuations are superimposed
upon the mean flow. To describe such motion, physicists resort
to statistical methods,

In its simplest form turbulence, such as might occur in
an open channel behind uniform rectangular wire grids, may be
isotropic. Only two parameters are required to describe the

degree of such isotropic turbulence, namely "scale" and "intensity".

[2 Generally, the intensity /@ is given as a percentage
u

where (ae is the root-mean-square of the velocity fluctuations,
and U is the mean free-stream velocity. It has been found (1)*
experimentally that the ratio U/¥ u* is practically independent
of U, and that it increases behind a grid nearly linearly with the
distance from the grid for values of X/M between 15 and 40.

On the other hand, the scale, L, roughly defines the
distance over which turbulent fluctuations are related. Strictly,
it is a measure of the distance over which a correlation between
velocity fluctuations exists. The correlation coefficient, R, is
usually defined as R= U1 =3 where uj, and up are the velocity

u

u
fluctuations at cee iL and 2,, In isotropic turbulence this may
be written R = % since fu? =]u. The scale L is then defined as

Cy u

- Le fray, for measurements made in some direction y. Behind grids
of various sizes, it has been found that L/M, where M is the mesh
size is independent of U, but that it increases with the distance
from the grid.

In non-isotropic turbulence, such as the flow through a
small pipe, the "intensity" and "scale" depend upon the direction
under consideration and more independent parameters become necessary..

With these few remarks concerning parameters of turbulence
we proceed to describe the several methods we have tried to use in
measuring them.

OIL INJECTION METHOD

Several attempts have been made atthe Taylor Model
Basin to devise methods of measuring L and ju? in water. The
first was the photographic method reported in TMB Report C-13
(2). In this test the flow of water through a lucite tube was
photographed from two orthogonal planes, the flow being made
visible by the injection of neutrally buoyant oil drops. Figure
1 is an example of the record. The analysis of this non-isotropic
turbulence consists in measuring the turbulence velocities. axially
and radially, and statistically combining the results of at least
500 drops. Since the tedium involved in analyzing the data 1s ex-
cessive, the method is not recommendable. As yet, lack of time
has prevented complete analysis of the records so obtained.

* Numbers indicate references on page 8 of this report.

Die

HOT WIRE METHOD

In view of the tediousness of the oil-drop injection
method, other, more direct techniques were required. The hot-
wire anemometer has provided such a technique in wind tunnel tur-
bulence measurements, Direct application of a wind-tunnel typ
hot wire to water has been tried, and with a fair amount of success.

Briefly, the theory of the hot wire is as follows. From
the fundamentals of electricity it is a well-known fact that the
resistance of a metallic wire is approximately a linear function
of its temperature. With this in mind, L. V. King in 1914 (3)
discovered the relationship between the resistance of a heated
fine platinum wire, and the velocity of the cooling air stream in
pure it was placed. He found that for the wire placed normal to
the stream

He 12R,2(a + b{¥)(e.-6,)

where H is the rate of heat lost per unit length of the wire,
i is the heating current,
Re is the instantaneous wire resistance,
? is the velocity of the stream,
6 is the temperature of the wire, and
@, is the temperature of the stream.

This relationship has since been successfully applied to measuring
steady and fluctuating air velocities.

There are two-principal methods of operating the hot
wire, In the first, the temperature, i.e., the resistance, of
the wire is maintained at a constant value. The heating current
required to do this is then a function of the velocity. In the
second method, the heating current is maintained constant, and
the resistance allowed.to fluctuate with the velocity changes.
This second technique has been employed in the turbulence experi-
ments in water.

For a repialy fluctuating velocity field, the voltage
variations of the ideal hot wire-.should be in phase with the
velocity, Failure of a hot wire to do this arises from the
existence of its time constant, M, which depends upon the size

of the wire, and the operating conditions. A value of M differ-
ent from zero results in a voltage output lagging in phase behind
the velocity fluctuations, and a voltage output whose amplitude
is diminshed with increasing velocity frequency, f, in the ratio

. Both of these effects, reduction in amplitude, and

phase lag, can be corrected by proper compensation eircuits in
the amplifiers used with the instrument.

aae

The sensitive elements used in these tests are tungsten
wires 0.0003L inch in diameter. and 0.20 inch in length. Similar
wires used by Schubauer at the Bureau of Standards (4) had measured
time constants of approximately 0.002 second, Freliminary measure-
ments of the same wire in water exhibit time constants in the order
of 50 to 100 microseconds, The difference is probably accounted for
by the fact that the thermal conductivity of water is about 25 times
greater than that for air. The present tests have been conducted
without compensation for thermal lag.

The hot-wire circuit shown in Figure 2 is identical with
those described in Reference (1). From the theory of this circuit
it is possible to measure the correlation coefficients of a turbu-
lent stream by proper combination of the outputs of the two wires.
Assuming that the velocity fluctuations are small, then the voltage
fluctuations across each wire are proportional to’ changing velocities.
By means of the reversing switch S, the voltages of the two wires
can be added or subtracted before amplification. This combined
output, amplified, can then be measured by a vacuum-type thermo-
couple and microammeter. The reading of the meter is proportional
to the mean square of the voltage input. If M, is the microammeter
reading for the voltages added; and M,, that for the voltages sub-
tracted, then

M, = K(e,+e,)? K'(u, +u,)? and
M, = K(e)-e,)* = K' (a) a5)”

where @, and ep are the instantaneous voltages of the respective
wires, and u, and uo the respective turbulent velocities at
each. It cat be shoe by algebra that the correlation coefficient

= ease. LP for isotropic turbulence.
u

M atMp
For measurement of turbulent intensity, only one wire is
required. It can be shown that the per cent of intensity is

Vue = __2 Bw gt

ir (hon

where R, is the resistance of the wire at water temperature,
ais the root-mean-square voltage fluctuation as measured
by the calibrated microammeter,
R is the mean operating resistance of the wire,
i is the heating current,
F is the slope of the static calibration of the wire,

Sethe Pig

R/(R-R..) vs VV (a linear funetion), which is determined by
compar! son with a calibrated pitot in different laminar
velocities.

The probe shown in Figure 3 has been used for both corre-
lation and intensity measurements. The upper hot wire is fixed
to the faired brass strut; the lower, is adjustable in the vertical
plane by the micrometer screw as illustrated. Wire separation can
be adjusted to a maximum of 3 inches *® 0.001 inch. The hot-wire
tungsten elements are soft-soldered across two steel sewing needles
which in turn are soldered to fine brass tubes connected to the lead
wires, Since it is not possible to solder tungsten directly, the
wire was first copper plated electrolytically except for the 0.20
inch measuring section.

TURBULENCE MEASUREMENTS IN THE MODEL CIRCULATING WATER CHANNEL

Measurement of turbulence behind two geometrically :
similar grids were conducted in the 1/22-scale model of the circu-
lating water channel at the TMB. The experimental arrangement is
illustrated in Figure 4. The hot wire probe was mounted in the
channel at distances of 15, 20, and 25 mesh lengths downstream from
erids of 4- and 3/4-inch mesh size. At each position, both corre-
lation and intensity measurements of the created turbulence were
obtained. The speed of the channel for all tests was approximately
1.8 feet per‘second.

The results of the experiment are illustrated in Figures
5 through 8. In each instance it has been assumed that the turbu-
lence was isotropic, and that the channel without the grid was
nearly laminar. Actually, it is believed from preliminary measure-
ments that a turbulence intensity of about 1% characterized the
grid-free channel. ,

In Figure 6, correlations are compared with similar mea-
surements made by Hall in a wind tunnel (5). Lack of close agree-
ment between the two may be accounted for by the differences of the
two media, differences in the initial turbulence of the stream, and
insufficient correction of TMB results. Since these experiments

are preliminary neither time constant compensation nor wire-length
(1) corrections have been applied to the data.

In spite of their preliminary nature, the TMB data con-
firm qualitatively the law previously mentioned regarding the
variation of scale with distance from the grid. Figures 6 and 7
illustrate this in the increasing area under the correlation curves
for the greater distances from the grid.

The decay law of intensity, and its independence of
Reynolds number are illustrated in Figure 8. Comparison of the

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TMB results with those obtained by Hall (5) and Schubauer (1)
shows that the data for water are not only in agreement with
the slope of the decay curve, but also in order of magnitude,
Differences between Hall's curve and Schubauer's curve have been
attributed (5) to differences in initial wind-tunnel turbulence.

PRINCIPAL DIFFICULTY OF THE HOT WIRE IN WATER

It has been found in wind tunnel applications of the
hot-wire anemometer that frequent brushing of the wire is com-
pulsory for maintainance of a constant calibration. The rate of
dirt accumulation in water, even drinking water, is many times that
for air and the calibration of the wire changes within a matter of
minutes in water. Constancy of calibration is accomplished only
by very frequent brushing. Consistency of results where a constant
calibration is required, such as in the measurement of intensity,
ean only be obtained by observing data immediately after the wire
has been cleaned. In measurement of correlation, however, it was
assumed that both wires were accumulating dirt at approximately the
same rate, and hence, changing calibration at the same rate. Al-
though their sensitivities were gradually diminishing, the wires
could still measure correlation provided their response character=
istics remain nearly alike. Even in the correlation measurements,
however, the two wires were frequently cleaned.

APPLICATION OF HOT WIRES TO TURBULENT
BOUNDARY-LAYER INVESTIGATIONS

Turbulence in boundary layers has been a subject for in-
vestigation for some time in wind tunnel work. Only recently,
however, has research been undertaken at TMB to investigate the
nature of the boundary layer on ship models. Not only is it of
importance to know the characteristics of the laminar and turbu-
lent regions, but locating the region of transition from laminar
to turbulent boundary layer is essential in estimating frictional
resistance.

Locating the region of transition under variable opera-
ting conditions, therefore, was the first phase of the investiga-
tion undertaken with the hot wire. Preliminary tests have been
conducted on a wood friction plane 6 feet long, 12 inches wide,
and 0.50 ineh thick with ends tapering to a thickness of 0.04
inch, The plane,fitted with 6 fixed hot wires, was towed in the
deep water basin at Carderock. The hot wires were platinum;
0.0015 inch in diameter and 0.25 inch in length. The normal dis-
tance of the wires from the surface was measured, and the average
distance was 0.016 inch which was well within the laminar boundary
layer at the wire locations.

Sun GH ee

A simple series heating circuit similar to that of Fig-
ure 2 was used to heat the wires. A current of 1.0 ampere was
maintained, and the fluctuating voltage output of the wires was
amplified and recorded by a string oscillograph. No compensation
for thermal lag was used. :

Definite evidence of transition was detected on one of
the two wires located at the midlength of the plane. A sample of
the record is given in Figure 9. The record which may be expected
from mixed or transitional flow is typified by Figure 9(c). At
higher speeds it is seen that the flow was turbulent, being char-
acterized by higher frequency and the expected smaller amplitude
fluctuations resulting from lack of compensation.

Similar experiments have been conducted on a ship model
with equal success. The hot wire, therefore, can be used in this
manner to distinguish qualitatively between laminar and turbulent
flow. Measurement of scale and intensity of the turbulence in
boundary layers in being considered, and such results should pro-
vide significant information regarding the accuracy of present
methods of artificially creating turbulent boundary layers by
various size rods placed ahead of the model being towed.

DYE DIFFUSION METHOD OF MEASURING TURBULENCE

A third method of measuring turbulence intensity, which
depends upon the diffusion by turbulence of a dye injected into
the stream, has been tried in the model channel, A fine brass rod
replacing one of the strands of a }-inch mesh, and bent in the
form of an L extending 15 mesh lengths downstream was used as an
injector of a water solution of red dye.. A similar rod attached
to a pipette served as a sampler probe. With the channel operating
at a speed of about 1 knot, cross-stream surveys by sampling the
water were made at distances of 4, 3/4, and 1 inch from the nozzle
of the injector. The concentration of the samples of each survey
was compared with the original concentration of dye by means of an
electrophotometer. The boundary of the diffusing dye wake, defined
as the standard deviation of the cross-stream distribution of dye
concentration was determined at the three stations. The slope of
the boundary so determined was applied to determine the value of
the turbulence intensity in the region of the dye injector nozzle.
In Figure 8 the result of the experiment is seen to agree, in order
of magnitude, with the hot wire results. Since the experiment was
carried out in a rather crude fashion, better agreement was not
expected.

CONCLUSION
Since the measurement of turbulence in water is still
in its preliminary stages, it is impossible to discuss any real

=~ 7 =

deviations from the laws describing the phenomenon in air. First
appearances would indicate that the same laws hold in both media,
With further development of the hot-wire technique, and possibly
the dye-diffusion technique, it may be possible in the near future
to confirm or amend the laws of turbulence as they apply to air

to describe the situation in water. Aside from its use in investi-
gation of fundamental properties of turbulence, the hot-wire has
already shown that it will be a valuable tool for the investigation
of boundary layers of ship models, a study which, as is becoming
increasingly apparent, is necessary for improving prediction of full-
scale performance.

REFERENCES

1, "Measurements of Intensity and Scale of Wind-Tunnel Turbulence
and their Relation to the Critical Reynolds Number of Spheres,"
by H. L. Dryden, G. B. Schubauer, W. C. Mock, and H. K. Skramstad,
NACA Tech Report 581, 1937.

2, "The Development of Facilities and Photographic Methods of the
Study of Turbulence in Water," by P. Hisenberg, M. S. Macovsky, and
C. HE, Lemich, TMB CONF Report C-13, Sept. 1947.

3. “On the Convection of Heat from Small Cylinders in a Stream

of Fluid: Determination of the Convection Constants of Small
Platinum Wires with Applications to Hot-Wire Anemometry," by L. V.
Kine, Roy. soc). Lond... Phit Trans), Ve. cla. 1OlAs

4. "Theory and Application of Hot-Wire Instruments in the Investi-
gation of Turbulent Boundary Layers," by G. B. Schubauer, and P. S,.
Klebanoff, NACA, ACR No. 5K27, March 1946.

5. "Measurements of the Intensity and Scale of Turbulence," bv
A. A. Hall, Aero. Res. Com., Rep, and Memo. No. 1842, August 1938.

PRNC-8000-11-19-48-?

Time Trace

FIGURE | COPY OF PHOTOGRAPH OF OIL—-DROP

METHOD FOR MEASURING TURBULENT
FLOW THROUGH A LUGCITE TUBE AT
A MEAN VELOCITY OF 10 FT/SEG.

DAVID TAYLOR MODEL BASIN

OCTOBER 1948

To
Amplifier

oe

Ss <i)

To
Potentiometer

ee c
To

Potentiometer

ANH tif
6V 6v

FIGURE 2. HOT WIRE CIRCUIT USED IN MEASURING
CORRELATION BETWEEN VELOCITY
FLUCTUATIONS.

DAVID TAYLOR MODEL BASIN
OCTOBER, 1948

FIGURE 3 HOT WIRE PROBE FOR TURBULENCE MEASUREMENTS
DAVID TAYLOR MODEL BASIN

TMB 30259 : I! OCTOBER 1948

all grids

HONEYCOMB

ND
P <.>4— TURNING VANES

¢__ DIRECTION OF
MOTION

FIGURE4 SCHEMATIC DIAGRAM OF THE EXPERIMENTAL ARRANGEMENT
IN THE I/22-SCALE MODEL OF THE CGIRCULATING
WATER CHANNEL

DAVID TAYLOR MODEL BASIN
7 OCTOBER 1948

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DAVID TAYLOR
MODEL BASIN

6 OCTBER 1948

---- M=1/2" (NACA)
—-— M=1/2" (HALL)

M =1/2"
HOT WIRE
3/4

M=1/2" DYE DIFFUSION

10 40
X/M ,
DISTANCE FROM GRID IN MESH LENGTHS

FIGURE 8 HOT-WIRE OBSERVATIONS OF DECAY OF ISOTROPIC
TURBULENCE IN WATER COMPARED WITH SIMILAR
WIND TUNNEL DATA

60 CYCLES (PER SECOND TIMING TRACE

WAN NMA NA ANAABA TA Wiad Se A
\ \
lit My vanstan VIVVU Vevey VWVVV iY SANG GAPUA CHARAN LS UVa MtiTAMVLVAGS4 Vaated VAAL VW WU VV VAN

(a) SMALL LAMINAR OSCILLATIONS; TOWING SPEED V=1.25 KNOTS
X-REYNOLDS NUMBER, Rx = fa X 105

AAA

(b) INCEPTION OF TRANSITION; V=1.49 KNOTS, Rx=6.15 X 10?

Pe SSSA GSVHCU EER MCCIQIIUCG SOO NGO NORTE ES

(c) TRANSITIONAL FLOW; V=1.74 KNOTS; Rx= 7.18 X -

Av enNANNA AK AAAAAAL NANHAAAA A NAA WAN SAAN AA VW WM WW WN AKAN ANA A AA SUARWAAKAAAAA COL NAAR ARAN,
| \ e |
vi NAVA h vo cer slaiinabieteseva bees duet ae, VW VV Vivien cual

(d) TURBULENT LAYER; V=1.99 KNOTS; Rx= 8.21 X 109

SALA AANA AAAS AN AMAA AAP
er Ne

(e) TURBULENT LAYER; ae 2.25 ce Ry = 929 X 105

PONT N NAN ANANNAAAA AAA AA AANA A KAVUN NAKA AA AAW AAA yaaa NAKA AAA AA AAM AAR AR AAA AMAA AY HANA MAAN A AAA AQAA AMAA AAA AA
ATA VAVIERRE Seu Grtvecaiwiet VVN FOU UCR CCG UCR III VV VW WWHVUEV EVN ENVY VEN VEKEV VU OLORIGbEb bi el

C2) HGH FREQUENCY TURBULENCE; DECREASE IN AMPLITUDE ‘Is
PARTLY CAUSED BY LAG EFFECT OF HOT WIRE Hae WAS NOT
COMPENSATED; V=3.50 KNOTS; Ry=1e44 X 1

FIGURE 9: OSCILLOGRAPH RECORDS OF HOT WIRE RESPONSE TO
VELOCITY FLUCTUATIONS IN THE BOUNDARY LAYER OF
A THIN, FLAT PLATE TOWED IN WATER. HOT WIRE
WAS LOGATED 3 FEST AFT OF FORWARD EDGE OF
PLATE.
DAVID W. TAYLOR MODEL BASIN WASHINGTON, D. C. OCTOBER 48