This report describes a method of determining the turbulence in wind tunnels. The effect of turbulence upon the diffusion of heat from a small electrically heated wire in an air stream was investigated. The turbulence of the stream was introduced by a series of geometrically similar screens placed one at a time across the upstream section of the tunnel. With the wire set at various distances from the screens, curves of temperature distribution were obtained by traversing the heated wake at a distance of 2 inches behind the wire with a small thermocouple

Schubauer, G B

English

NASA Technical Reports Server

REPORT No. 524
A TURBULENCE INDICATOR UTIUZING THE DIFFUSION OF HEAT
By G. B. &mJBAmm
SUMMARY
In cooperation with the iVai&mu.1Admkoqi Committti
for Aeronuutti, tb National Bureau of Standari%jir
aeved y8ar8 hu3 been studying methods of determining
theturbulencein wind tunnele,e8pecia.Uybythe “hot-wire”
method and tlw ephere method. ThiIIpaper d.ewibe8 a
third method.
Tlw e$ect of turlndeneeupon the dtim”on of heatfrom
a emall electrically heated wire in an air 8tream w
invedigaied. The iurbu.kneeof the streumw introduced
by a 8e%8 Of@?0?7Ld?%Xd.!ykmb 8creen8phed one d
a time acro88theupetreamseetion of thetunnel. With the
wire 8et at variou-sdtitan.ca from the 8creerhs,ourves of
temperaturedietrilnhon were obtained by traversing the
heatedwake at a dtitame of fi incha behindthe wire with
a ema.11thermomupk. A single relation m fownd to
tit betweentlw &h of the wake ai hulf muximum and
dtitarwein screenwire diumeter8from the seued seree?w.
The correlationof widthat hulf muximumwithpercentage
turlnd.emx,as meu8uredby the “hot-wire” nuzthod,could
be reprtwnted approximately by a tingle eume.
INTRODUCTION
The evaluation of wind-tunnel turbulence is by no
means common practice in aerodynamic laboratcriw,
even though tnrbulenm is recognized as an important
aerodynamic factor in wind-tunnel tests.. This situa-
tion is due largely to the fact that a turbulence deter-
mination is attended with more diiliculty and uncer-
tainty than is the average aerodynamic measurement.
It is possible ta determine quantitatively the ratio of
‘the root-mean-square of the speed fluctuation at a
point tQ the nverage speed. This quotient times
100 is usually called the percentage turbulence.
The percentage turbulenw maybe measured by a mod-
ified hot-wire anemometer and acceasory equipment,
including an ampli.iier and an electrical network to
compensate for the lag of the wire (references 1 and 2).
The apparatus ia expensive and cumbersome and its
opemtion requires considerable skill and care on the
pmt of the operator.
%npler turbulence indicatms,which,ti desired, might
be calibrated in terms of percentage turbulence by
comparison with a ‘(ho&wire” instrument, have been
sought. A device of this sort, which has found wide
use in comparing the turbulence of d.iilerent wind tun-
nels, is the sphere (references 3, 4, and 5). The corre-
lation of its critioal Reynolds Number (defied as the’
Reynolds Number for which the drag coefficient is 0.3)
with percentage turbulence has been made in several
laboratories, but the universality of this correlation is
still ,under investigation.
The prwent article describm a scheme of turbulence
measurement based on the diffusion of heat from a
D
T
3’
t
\
8&”
2
r
.U
Fmurm 1.—D@axn of ap~tns awl to tmvem theheated wake.
heated wire. It has been found by experiment “that
the width of the heated wake increases as the turbu-
lence increases, indicating a relation between the rate”
of diffusion and the degree of turbulence present in the
air stream.
APPARATUS
The apparatus for producing the heated wake and
traversing it to determine its width is shown in iigure
1. A platinum-iridium wire 2.8 inches long and 0.002
337
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338 REPORT NATIONAL ADVISORY
inch in diameter is located at A. At B two no. 36
wires, one of copper and the other of constam%m, me
soldered together forming one junction of a thermo-
couple. The other junction of the same size at C is
placed just far enough from B to be completely outside
the heated wake. The prongs carrying the heating
wire and the thermocouple are attached rigidly to the
arm D, which can be rotated about a vertical axis
passing through the heating wire to carry the thermo-
couple B acrw the wake. The platinum-iridium
wire was heated by an electric current ranging from
0.2 to 0.8 ampere, depending on the heating desired.
The current could be maintained sufficiently constant
by means of a rheostat and a O to 1 ampere range
mmneter. The thermocouple w-as connected to a
Angle in degrees
Ftauw+ l—Dktrfbntfon cn..es obtafnd by tiverahg the b@ed wake at a &
tame of 2 fncheafrom heatd wfro. Curve (a): L1 ~t tnrbukmca Curve
(b): 3.5fwmnt turbnkca.
sensitive wall galvanometers (sensitkity 0.06 micro-
volt per mm per m scale distance).
Figure 2 shows two typical distribution cm-ma
obtained with the apparatus for a spacing of 2 inches
between the heating wire and the thermocouple.
Curve “a” corresponds to a turbulence of 1.1 percent
and ‘tb”, ta n turbulence of 3.5 percent. For both
curves the heat input was 5.7 mitts and the air speed
36 feet per second. Since the maximum ordinate of
curve “a” corresponds tQ a temperature rise of only
3° C., and the copper+mstantan thermocouple has a
thermoelectric power of 41 microvolt per degree
Centigrade, the necessity for a rather sensitive gal-
vanometers is obvious.
THEORY
It is desirable that the heating wire have a small
diameter so as to create little disturbance of the flow.
The transve~e flow of heat will be due to ordinary
COMMTIT’EE FOR ADRONAU’IICS “
molecular conduction plus the eddy conduction arising
from the turbulence initially present in the air stream.
Let us consider first the case where the stream is com-
pletely free from turbukm”ce and the wire produces a
negligible disturbance. Regarding the wire as a line
source of heat and the air speed as uniform, the tem-
perature distribution is given at points not too close to
the wire by the equational
-ptfl
AT= ATm&x (1)
ivhere y is distance across the wake measured from the
center; z is distance downstream from the wire; AT
is the temperature rise at any point (x, y); AT.= is
the maximum temperature rise at the point (z, o); u is
air speed and p, c, and k are density, speciiic hmt at
constant preswrq and thermal conductivity of the rLir,
respectively.
It will be observed that equation (1) is ana-
logous to the expression for the linear flow of heat
from an instantaneous plane source. The rtpproxi-
mations involved when applied to the present prob-
lem may be illustrated by visualizing the process
described by equation (l). A line of air particles, ~fter
behg heated by contnct with the wire, is cmried on
in the z direction with the speed o. While the line
movw through the distance z, during the time intorvrd
~) the heat flows outward from the line of particles in
the +y direction, and rttz has Mained the distribution
given by equation (l). Clearly, the finite size of the
wire, the conduction of heat in the z direction, the
retardation of the flow by the wire and the stirring
action due to whatever eddies me formed in the wrtko
of the wire have been neglec6ed.
If the air incident upon the wire is turbulent, there
is an apparent conductivity expressed by (k+~),
where B is the eddy conductivity due to the turbulence.
Equation (1) then becomes
=@?
AT= ATmt+~k~z (2)
The width of the wake at half mrminmm tempera-
ture is selected to reprc.sent the width chmacteristio
of the wake. From curves such as shown in figure 2
the angle subtended at the wire by the wake width ot
half maximum mrry be obtained. For convenience,
the results will be expressed in terms of this angle
rather than in actual width, the term rtnguhm width
and the symbol a being used to designate the angle.
I TfM @ ram of the tmmwatnra distribution beblnd a Mm mum [n lnmlnnr
ah flow asgfven by Draw (’1’mm Am. II& Ohm Er@Imr& VO1. 25 M31,P. 30)b
Y
AT-25 8 ‘ Ko(z)
whzra g h the heat output PW tudt length of tbo wlraj z standsfa+tbe combination
(~_)anrlKo(z)fs a B* functhxr of zero ordar. At large vrdum of z,
Ko (z) maybe mt eqnaf to
-J
& After axpamifng~ for ~<<r and neihat-
fng 9naff - equatfon (1) foflovm.
A TURBULENCE INDICATOR UTILTZIN(3 THE Dll?FUSION OF HEAT 339
When ~~~a
1
—=2 in equation (l), y is the half width
at half maximum. Making the substitution 2y=~
nnd solving for q, we obtain
4–
w=190.8 & (3)
where a. is the angular width in degrees at half maxi-
mum for lrtminar flow. Mddng a similar substitution
in equation (2), we obtain
J@qq7ja=190.8 —pm (4)
RESULTS
Measurements were made in the 4&foot wind tunnel
of the National Bureau of Standards, in an air stream
made turbulent by rLseries of geometrically similar
square-mesh screens placed one at a time rtcross the
upstream section of the tumel. The amount of tur-
bulence obtained from any one screen was varied by
working at several distance9 from the screen. The
first, second, and third columns of table I give, respec-
tively, the mesh and wire diameter of the screens and
tho distance in wire diameters from the screens for the
several working positions. The distance wws measured
J
7 t
O$d x M= 5-
6 0 * = 374-.
\
“k - -:%
5 >
3 +
04
?
2 !
&
%3
ii
Y
2 o~ \ +
o0 + +
I b -..
0 m m w m /m fm Iwo H@ lam 2m
D/d = L7isfcrnce from screen in wire dbmetens
Fmwm 3.-vmiatImof a,.} withWstmcafrmnEueemWn-ff$a inwwnwlrediamet@m
where CC[isthe angular width for turbulent flow. By
squaring equation (4)
where at”,b is the angular width due to the turbtience
fdone.
From the foregoing expressions, it is clear that the
heat output does not have to be known.a It is nec-
essary only that the heating be constant, during a
traverse of the wake, and of .w@ient magnitude to
allow the temperature distribution to be measured.
2Tho temperature rise h w small ttat th mwiaffon cf k with wake tempatnra
may L@m@ctcd.
from the screen to a point midway between the heating
wire and thermocouple. Since the screen pattern in
the speed distribution persisted to nbout 65 wire dinm-
eters downstream from the screen, the measurements
were made at distances greater thnn 65 diameters.
The fourth column of table I gives the observed
nnguhw widths for n 2-inch spming between the heat-
ing wire and thermocouple. The vahms of a,~,b crd-
culated by equation (5) are given in the fifth column
of table I. A comparison of these two columns shows
that the effect of q becomes less as a increas~. From
runs made nt wind speeds ranging from 8 to 55 feet
per second, it was found that a varied with the speed,
but that Chrb was constant to within the limits of
ewetientfd uncertnintit%. Since a~u,b=
r
36400@,
pcl?x
340 REPORT NATIONAL ADVISORY COMMI?ITQE FOR AERONAUTICS
the eddy conductivity B must therefore be proportional Icantthatthe points fall about a single curve intc the air-stream velocity o. figure 3, -whereas they follow a family of curves in
~GuaE 4.-Varfatimoffwmmtaga buimlmcawkhdbtanfmfrom W#3ns erpress3 in screenwhw diameten.
Figure 3 shows the variation of a,W~ with distance,
expressed in screen diametem, from the several
7 /
x M= 5- x /0
- ~ “ = 3y4=.
~.=f.
6 — - +.=yz-
A . m y4-
/
5 /
0
,1
~ +
Q4 x
k
/
~
33-
B
/
2 /
++
4
I >
/
0 I 2 3 4 5
Percent turbulence
FIQuaE&-CorreMlon of q.> with p?rcsnhge tnrbulmm. M denotesthe scrmn
mti (% iflustrathn fn 5s%8 and 4.)
screens. Figure 4 is the corresponding diagram of
percentage turbuleneq measured by the “ho&tie”
method, for the same series of screens.3 It is signiii-
~Thesadatawereobtained by W. O. M@c, Jr. and theauthorfn cmnnedionwfth
~Otber ~ projact of tba awodm.mrnb*an.
figure 4. A possible interpretation of this resuh is
that the “ho&wire” method differentiates between the
scale of the turbulence produced by screens of different
size, but that the diffusion method does not. It is
reasonable tc assume that the eddy size may bear a
direct relation to the screen size. If so, it seems pos-
sible that the wire of about one centimeter length
employed in the “hohvi.re” method may rwer~oe out
the speed fluctuations to a progressively greater degree,
and give a smaller response, ns the eddies get progres-
sively smaller. This subject is now under invediga-
tion at the Natiomd Bureau of Standards.
.Figure 5 shows the correlation of a,tir, with percent-
age turbulence. Obviously, from figures 3 and 4 th~
correlation cannot be represented exactly by a single
curve. However, the majority of points fall near a
straight line passing through the origin, the marked
deviations entering only for the %inch rmd jf-inch
mesh screens.
When the effect of spacing between the heating wire
and thermocouple was investigated, it was found that a
was essentially the same regardless of the spacing in the
range horn ~ inch to 6 inches. This means that
the wake is wedge-shaped, the Width at half maximum
varying %early with z. From these results @ was
calculated and found to be proportional tc x.
‘It is possible to summarize all the results to date in
an empirical equation for /3 of the following form:
~==vz @ a[1u-
A TURBULENCE INDICATOR UTILIZING TEUil DD?FUSION OF -T 341
where K is a constant of proportionality and @ ti
the root-mean-square of the speed fluctuation. The
constrmt K is equrd to 0.63 p c.
A study of difhsion such as outlined here offers n
promising field for future research both in theory and
experiment.
NATIONAL BUREAU OF STANDARDS,
WASHINGTON, D. C., March 8, 1935.
REFERENCES
1. Ziegler, M.: The Application of the Hot-Wire Anemometer
for the Investigation of the Turbulence of an Air Stream.
Ver61.Ken. Akad. v. Wetemch, Amsterdam, vol. 33, 1930,
p. 723.
2. Mook, W. C., Jr., and Dryden, H, L.: Improved Apparatus
for the Measurement of Fluctuations of Air Speed in Tur-
bulent F1ow. T. R. No. 448, N. A. C. A., 1932.
3. Dryden, H. L,, and Kuethe, A. M.: Effect of Turbulence in
Wind Tunnel Meaaurementa. T. R. No. 342, N. A. C. A.
1930.
4. Millikan, C. B., and Klein, A. L.: The Effect of Turbulence.
Airoraft Engineering, August 1933, p. 169.
6. Sauerwein, R T.: Sphere Drag Determined by Coastiig
through Still Air. Jour. Aero. Sci.. vol. I, no. 3, July
1934, p. 147.
TABLE I
Sclwn Wfr
,Iesbofsucan (fnohes) dlamlame
t
5 by 6-------------- LO
3X by 3!.4i. . . . ..-._- .625
1by l----------- .192
~ by ~-.. -...___ .Q32
~ by ~________ . c-47
Mstanee
,m r.ueau
fawlre
fame- ,
141
114
97
!2%
IE3
%
T%
510
349
216
1,SW
K!?
m
::
~g
‘$
Av~e Mnd 6Pe&.iE28,2ft. (8.)-1-1,104an (S)-I
Average ah tarnxtore=l&& C.
beti-~;”’”~ Hg:%%XW grams (cm
@o.240 @L (gram)+ (“ +
k-&eWlfH d. (s)+ (cm + [“ o. (CIn)-q+
1-5JY3 cm
aQ-LU40
,d-
3.w
&g
&w
a10
:E
4.83
7.m
L 70
;:
Z92
L 75
L 49
L 76
L99
::
L53
1.63
L so
272
a Iwb
dw!rees
3.83
i%
582
2.s3
*35
3.64
4.72
IL92
H
i%
L36
.W9
LS4
1.61
;~
L m
L 41
Z46


A turbulence indicator utilizing the diffusion of heat

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