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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL MEMORANDUM 1571
APPARATUS FOR MEASUREMENTS OF TIME AND SPACE CORRELATION*l
By A. Favre, J. Gaviglio, and R. Dumas
These researches are made at the Laboratoire de Mecanique de
l'Atmosphere de l'I.M.F.M., for the Office National d'Etudes et de
Recherches Aeronautiques (O.N.E.R.A.), with the aid of the Ministere de
l'Air, and of the Centre National de la Recherche Scientifique (C.N.R.S.).
We have already explained in previous communications refss. 1 to 22)
the principle and have given description of the apparatus for statisti-
cal measurements of time and space correlation between two random vari-
ables considered with a relative delay T in time, which we have designed
with a special view to the study of turbulence.
We shall briefly review now the improvements brought to the experi-
mental apparatus, the control of the measurements, and a few particular
Wind Tunnel (Refs. 2, 5, 4, 6, 12, and 15)
The low-turbulence wind tunnel, installed indoors, has been trans-
formed (fig. 1). The test section A is 80 x 80 x 270 cm; the cone B
with low gradients has a contraction ratio of 15. It is preceded by a
settling chamber C, in which are set five removable damping screens,
and by a rapid expansion diffuser D with a screen analogous to those of
the low-turbulence wind tunnel of the R.A.E. (ref. 25). The intensity
of turbulence is of the order of 0.00210 with the diffuser screen and
*"Appareil de Mesures de la Correlation Dans le Temps et L'Espace."
La Recherche Aeronautique No. 51, Jan.-Feb. 1955, PP. 57-44.
1A Communication to the 8th International Congress on Theoretical
and Applied Mechanics, Istanbul, Aug. 1952.
NACA TM 1371
of 0.00150, 0.00090, 0.00055, 0.00045, and 0.00058 with 1, 2, 5, 4,
and 5 damping screens, respectively.
At the entrance of the test section may be placed one of the two
turbulence grids similar to those of the NBS with elements of 0.626 inch
and 0.196 inch in diameter and with meshes M of 5 1/4 inches and 1 inch,
A flat plate of 1,960 x 80 cm can be set in the test section for
the study of the boundary layer.
Hot-Wire Anemometers (Refs. 2, 5, 5, 7, 8, 11, 17, and 20)
Two hot wires can be moved along the axis X1 of the test section
and along the orthogonal axis X5.
The amplifiers reproduce the oscillations with an approximation of
6 percent in energy and for the band pass 1 to 6,000 cps, more recently,
for 1 to 3,500 cps with 4 percent. The compensation is made by the
square waves method.
Figure 2 shows the two amplifiers A, the power supplies B, the
square waves generator C, and a generator of sine waves from 0.6 to
50,000 cps D.
Apparatus for Statistical Measurements of Time and
Space Correlation (Refs. 1, 2, 5, 5, 8, 9, 10, 11, and 15)
The apparatus records simultaneously and reproduces with a relative
delay T the two voltages coming, for instance, from the two anemometers
and measures the time-correlation coefficient refss. 1, 2, and 5).
It must be borne in mind that, for this measurement, it is necessary
and sufficient that the phase shifts of the component waves due to the
inevitable transformations should be identical in the two channels for
each frequency; the difference T of the delays systematically intro-
duced being the same for all the frequencies.
The voltages are recorded on magnetic tape:
(a) directly for the waves of frequencies comprised between 200
and 2,500 cps
NACA TM 1371
(b) on an amplitude modulated wave of 3,500 cps frequency, demodula-
ted after reproduction, for the waves of frequencies comprised
between 1 to 25 cps
(c) by overlapping of the two devices from 25 to 200 cps.
The band pass is therefore unbroken from 1 to 2,500 cps refss. 8,
9, 10, and 11).
The apparatus consists of (fig. 2):
The two recording preamplifiers E, with a common oscillator of
5,500 cps, and on either channel the networks effecting the division of
the respective spectra into waves of 200 to 2,500 cps for direct recording,
of 1 to 25 cps for modulation of the 3,500 cps carrier, and of 25 to
200 cps for the aforementioned overlapping
The two recording amplifiers F (with appended oscillators of
80,000 cps and of 40,000 cps) and their power supplies G
The two magnetic recorders-reproducers H, one of which has a
device I for adjusting the length of the tape between the recording
and play-back heads and, consequently, the delay T refss. 2 and 5)
The two play-back preamplifiers F
The two play-back amplifiers J, with their networks effecting,
after the detection of the carrier, the reconstitution of the initial
spectrum on each channel
The two power amplifiers K which, after adding on one hand and
subtracting on the other, supply the thermocouples; the output voltages
of these thermocouples represent the mean squares Ma of the sum and
Mb of the difference, respectively (Dryden method); two extra amplifiers
for the oscilloscope
The apparatus L, which gives the sum and the difference of Ma
and Mb (and will soon reckon their quotient), together with an oscil-
lator for 20, 200, 1,000 cps, by means of which may be effected a sup-
plementary control of the phase and energy response of the two channels
during the process of measurements; this oscillator is also used for
the measurement of the delay T
The power supplies N; the oscillograph 0; the galvanometer M
with adjustable period (3 sec).
The equality of phases on the two channels is checked for each
frequency refss. 2 and 5).
NACA TM 1371
When the two voltages correspond to two variables measured at two
different points of space, one obtains the coefficient R of time and
In the particular case when it represents the same variable measured
at the same point of space, one gets the autocorrelation coefficient
from which the spectral function can be deduced.
Spectral Analyser (Refs. 9, 10, 15, 14, 15, and 16)
A selective feed-back amplifier has been designed in order to deter-
mine the spectral function directly, apart from the autocorrelation
The band-pass is in width 4.5 percent of the median frequency
chosen for frequencies comprised between 1.5 and 2,500 cps.
The energy is measured by means of a thermocouple and a long-period
galvanometer (19 sec).
CONTROL OF THE MEASUREMENTS REFSS. 2 to 17, AND 21)
I. The response curve of the amplifiers of the hot-wire anemometers
(ref. 7) has been determined as regards energy and phase by means of
sine waves and square waves of variable frequencies, and so has the
band-pass of the spectral analyser.
II. The total response curve of the apparatus for measurements of
time correlation, together with the hot-wire anemometers, has been estab-
lished with sine waves of variable frequencies, as regards the energy
(fig. 5), the equality of phases on the two circuits for each elementary
oscillation refss. 2 and 5) (the delay T being a multiple of the period),
and the autocorrelation function refss. 2 to 15).
The energy is constant, variations not exceeding 1l6 or 19 percent
of the standard deviation 0.03 for 1 to 2,500 cps refss. 2 to 16).
Frequent checking are made in the course of measurements especially
in the case of 20, 200, and 1,000 cps oscillations frequencies.
III. The spectra are obtained on one hand by Fourier transform of
the autocorrelation curves and on the other hand directly by means of
the spectral analyser and are then systematically compared. These
measurements are made in the case of turbulence downstream of a grid
NACA TM 1571
refss. 9, 10, 13, 14, and 24) and also in the case of a boundary layer
of a flat plate (examples: figs. 4, 5, and 8) refss. 15 and 24).
These spectra are satisfactorily concordant from 5 to 2,000 cps
now (fig. 4).
IV. The vibrations of the hot-wire holders (ref. 2) and of the
tunnel walls (ref. 4) have been examined and reduced; their effects are
watched with the oscilloscope during the experiments.
The effect on the measurements of the acoustic resonances has been
found to be negligible refss. 6 and 12).
V. Comparative measurements have been made refss. 4, 6, 9, 10, 12,
and 13) at each stage of the transformations of the wind tunnel:
(a) Length of the test section reduced from 400 to 270 cm,
contraction ratio of the cone increased from 6.4 to 15,
the new settling chamber placed behind the diffuser with
its screen, and five damping screens inserted successively
in the bulge
(b) Installation of the first part of the return circuit with
two corners with vanes
(c) Size of the test section reduced from 80 x 80 cm to
80 x 40 cm (ref. 15).
These comparisons have not shown any appreciable changes in the
results from one stage to the other, as regards the turbulence behind
One must except, however, the influence of the initial turbulence
and, consequently, of the damping screens, which is very important in
the case of the boundary layer and the shape of the grid.
VI. The comparison of the time correlation curves, obtained with
different hot wires, disclosed appreciable differences for wires of the
same diameter and especially for wires of different diameters. The
improvement of the compensation by the square-waves method has made it
possible to reduce those differences (fig. 6) refss. 10 and 15).
Aerodynamic taking attempts of the hot-wire anemomenter are in
progress, the wire being placed in the field of a propeller refss. 17
The measurement errors seem to be mainly due to the hot wires; the
comparative experiments are preferably made with practically identical
NACA TM 1371
The results obtained for the turbulence behind a grid with the
for time and space correlation measurements:
transversely, i.e. at several distances X3 refss. 9, 10, 16,
21, and 24)
longitudinally, i.e. at several distances X1 refss. 14, 16,
the delay T being zero and agreeing with the results con-
cerning the transverse and longitudinal space correlations
and f, respectively, (example: fig. 7) refss. 9, 10, 21,
VIII. The comparison of the spectra (fig. 8) refss. 13 and 24) with
those of H. L. Dryden (NBS) and of F. G. Simmons (NPL) established for
the turbulence behind a grid in quite similar conditions is satisfactory.
The measurements have been especially developed up to 1.5 cps. The
comparison with A. A. Townsend's spectra (ref. 22) is also satisfactory
although the experimental conditions are slightly different.
IX. The qualitative comparison of the spectra established for the
turbulence of a flat-plate boundary layer (fig. 9) (ref. 15) with those
of A. A. Townsend is fairly satisfactory, although the experimental
conditions present some differences (ref. 25).
A FEW APPLICATIONS OF TIME CORRELATION MEASUREMENTS
Among the applications which can be made of time-correlation measure-
ments between two variables or of autocorrelation for one variable, and,
in addition, to those concerning the turbulence studied elsewhere (ref. 22),
we shall mention some other experiments refss. 18 and 19).
Application of Time Correlation to the Relative Increase of a
Periodic Signal Disturbed by a Random Parasite refss. 3, 18, and 19)
1. In a previous paper (ref. 5) we have considered the coefficient
of time correlation R11,22 between two signals ul and u2 disturbed
by two parasites El and E2, respectively, and the coefficient of time
correlation R10,20 between the nondisturbed signals2 and noticed that,
if one can choose a delay T, such as the time correlation coefficient
between the parasites and between the signals and the parasites, to be
With ul = u2 = EI = E2 = 0,
ql = ul2 E 12
q2 = U222 .
NACA TM 1571
uC2 = EU = UI = u2E2 = EE2 = 0 (1)
one finds that
H11,22 = R10,20l VAlY/ 1 + cq) (1 + q2)
The coefficient of time correlation between the disturbed signals
is proportional to the coefficient of time correlation between the non-
disturbed signals, when the delay is such that the coefficients of time
correlation between the parasites and between the signals and the parasites
With periodic signals and random parasites, condition (1) is easily
fulfilled; thus, these signals can be detected. With sine waves of the
same frequency, the coefficient of time correlation R11,22 or of auto-
correlation R11,11 will be for appropriate delays a sine wave of the
same frequency, which will constitute a time detection of these signals
In the case of a single signal, it may be preferable to replace the
autocorrelation R11,11 by the time correlation R11,12 with an iden-
tical signal disturbed by a less intense parasite.
2. We have made trials of the detection of a sine wave by autocor-
relation refss. 18 and 19). For example, figure 10 (ref. 19) shows the
autocorrelation curves of the parasite alone the spectrum of which
stretches mainly from 400 to 1,100 cps and of the signal of i 600 cps
disturbed by the parasite.
It may be seen that, for a delay T superior to 8 ms, the latter
is close to the sine wave of 600 cps of amplitude 0.4.
Other tests have enabled us to verify the above formula and to
detect the presence of the signal for very small values of q with a
great sensitivity (ref. 19).
8 NACA TM 1571
Reduction of Parasites Ratio With Reference to
Disturbed Phenomena by Addition With Delay (Refs. 18 and 19)
1. Let ut be the variable representing a phenomenon disturbed by
a parasite Et. Let us add the disturbed variable to itself with a
time delay T; we then have3
Q + R10,10
q 1 + R01,01
Thus, it is possible to reduce the parasite disturbing a phenomenon
by addition with delay. This reduction will be at its maximum when T
is such that the ratio of the autocorrelation coefficients of the phenom-
enon, and of the parasite, to both of which the unity has been added,
will be at its maximum.
In the case of a periodic variable ut and of a random parasite,
one may take a delay multiple of the period and such as
R0,01 << 0
It may be preferable to filter the parasite so that, for a T
multiple of the period, one should have
ROl,01 ~ -1/2
The operation may be repeated in series, choosing the optimum
delays; one may also make several additions in parallel with optimum
With Ct2 = Et+T2,
ut2 = ut+2,
Q = Ut + t+T) 2(E + Et+T2.
q = Ut2/ E 2
NACA TM 1371 9
2. We have made (ref. .18) some measurements, using a sine signal of
frequency n and, for the parasite, the above-mentioned turbulent veloc-
For a delay T such that
R01,01 ~ 0
R10,10 ~ 1
n .157 180 210 500 570 570 570
Q/q 1.90 1.97 2.04 2.41 2.04 1.91 2.22
the mean value 2.08 approximates the theoretical value 2.
For a delay T such that
R10,10 ~ 1
and n = 80, the ratio Q/q reached 4.25, 4.52, and 4.42, slightly
above the theoretical value 4.
Translated by A. Favre
MACA TM 1371
1. Favre, A.: Appareil de measures statistiques de la correlation dans
le temps. VIO Cong. Intern. Mecan. Appl. 1946, Paris.
2. Favre, A.: Mesures statistiques de la correlation dans le temps.
VIIo Cong. Intern. Mecan. Appl. 1948, Londres.
5. Favre, A.: Mesures statistiques de la correlation dans le temps.
Premieres applications a l'etude de movements turbulents en
4. Favre, A.: Perfectionnements a la soufflerie pour obtenir une tres
faible turbulence. 15/7/49.
5. Favre, A.: Mesures de la correlation dans le temps et l'espace en
aval d'une grille de turbulence pour la composante longitudinale
de la vitesse. 15/7/49.
6. Favre, A.: Etude sommaire de l'effet sur la turbulence des resonances
7. Gaviglio, J.: Etude d'anemometres a fils chauds. 15/7/49.
8. Favre, A.: Nouvelles measures de correlation dans l'espace et le
temps en aval d'une grille de turbulence avec appareillage modifie.
9. Favre, A., Gaviglio, J., and Dumas, R.: Mesures de la correlation
dans le temps et l'espace et spectres de la turbulence en soufflerie.
Coll. Intern. Mecan. 1950, Poitiers. Publ. Sc. et Techn. Minist.
Air no 251.
10. Favre, A., and Gaviglio, J.: Mesures de la correlation dans le temps
et 1'espace, et spectres de la turbulence en soufflerie (develop-
11. Favre, A., and Gaviglio, J.: Perfectionnements a 1'appareillage de
measures statistiques de la correlation dans le temps et l'espace.
12. Favre, A., and Gaviglio, J.: Etude de l'effet sur la turbulence des
resonances acoustiques. Influence des modifications de la soufflerie.
15. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps et
spectres de la turbulence en veine reduite. Control des measures.
NACA TM 1571
14. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps et
dans l'espace longitudinalement en aval d'une grille de turbulence.
15. Favre, A., Gaviglio, J., and Dumas, R.: Mesures dans la couche limited
des intensity's de turbulence, et des correlations dans le temps;
spectres. 51/5/51. Coll. Intern. MWcan. Marseille, 5/1/52.
16. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans ie temps et
dans 1'espace: transversalement, transversalement et longitudinale-
ment avec retard compensateur du movement d'ensemble, en aval
d'une grille de turbulence. 50/6/51.
17. Gaviglio, J.: Essais de tarage d'un fil chaud dans le champ d'une
18. Favre, A., and Gaviglio, J.: Detection de signaux periodiques perturbes
par des parasites aleatoires par autocorrelation. Coll. Nat. Mecan.
19. Favre, A., and Gaviglio, J.: Applications des measures de correlation
dans le temps a la reduction des parasites aleatoires par rapport
a des signaux periodiques. 12/7/52.
20. Gaviglio, J.: Nouveaux essais de tarage d'un fil chaud dans le champ
d'une helice. L2/7/52.
21. Favre, A., Gaviglio, J., and Dumas, R.: Nouvelles measures de correlation
dans le temps et l'espace, longitudinalement, transversalement,
longitudinalement et transversalement en aval d'une grille de
22. Favre, A., Gaviglio, J., and Dumas, R.: Quelques measures de correlation
dans le temps et l'espace, pour la turbulence en soufflerie.
VIII0 Cong. Intern. Mecan. Th. et Appl., Istamboul 1952.
Recherche Aeronautique no 52, 1955. J.A.S.
25. Schuh, H., and Winter, K. G.: Investigation of the Turbulence
Characteristics of an Experimental Low Turbulence Wind Tunnel.
VIIo Cong. Intern. Mecan. Appi. 1948, Londres.
24. Dryden, H. L.: A Review of the Statistical Theory of Turbulence.
".uart. of Appl. Math., Vol. 1, no. 1, April 1945.
25. Townsend, A. A.: The Structure of the Turbulent Boundary Layer.
Proc. Cambridge Phil. Soc., Vol. 47, Pt. 2, 1950.
NACA TM 1571
Figure 1.- Low-turbulence wind tunnel.
Figure 2.- Apparatus for measurements of time correlation.
NACA TM 1371 13
-_ ---- -.. ---J --- -- a 6--
-- --- .----
-- --i -
S-------- -.---- ----------M
I \> >)
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-- -- -- cL- --- -t
------.- -- U- ---------- -a,
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NACA TM 1571
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NACA TM 1371 1)
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-----1 ri II
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NACA TM 1571
Velocity = 12.20 mps; M = 1 in; Distance to grid = 40 M
.......... Wire I
-.-.- Wire I
------- Wire II
Diameter = 7 microns
Il Ii I I I I I I I I I I
I ml I 1 I I 1401 I I
T I IT
i Velocity = 12.20 mps; M = 1 in; Distance to grid = 40 M
-- Compensation by square wave method
.. I O Wire III
SDiameter = 5 microns
0 Wire V
- T r "r ----t-, _] i , ,r ,
.I i ~l 1 I I ll I I_ I I II I I I I l i l I I I T
RPTJ Velocity = 12.27 mps; M = 1 in; Distance to grid = 40 M
Compensation by square wave method
0 Wire V Diameter = 5 microns
S Wire S A 2 Diameter = 7 microns
IN 4 i I i i i l I I 1 I I I i 1 I l 1 I I I i I I P ]- -
Figure 6.- Autocorrelation measured by different hot wires and by
two methods of compensation.
. ... . i I ~ l l l
I I I I1 r 1 1
J I Il I l I I I I J- I I
NACA TM 1371
I 1 I X3/M
Velocity = 12.20 mps; M = 1 in;
9 Space correlation g
O Time and space correlation
O Space correlation g
a- -.0-0 a.-- 4
T = 0
I -I I I I
to grid = 40 M
"I I I 1 I 5X3 /M
Velocity = 12.27 mps; M = 1 in; Distance to grid = 40 M
O Space correlation
Space and time correlation T = 0
A 4 51 6
Figure 7.- Control of time and space correlation measurements with
zero delay, transversely g, longitudinally f, downstream of a grid.
Velocity = 12.20 mps; M = 3-1/4 in; Distance to grid = 40 M
* Space correlation g
O Time and space correlation T = 0 L
O Space correlation g NBS
2 1 I I 1 1
NACA TM 1371
Comparison of turbulence spectra downstream of a grid
obtained at NBS, HPL, and LMTA.
NACA TM 1371
* = 0028
+ S 0020
o = oolls
X 1 000,73
& f ooo00
0] = 0007
a 5aaoagg8g a n
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tE21WCN ,.. a*(
(b) IMA = 766000.
Figure 9.- Comparison of turbulence spectra in flat-plate boundary layer.
Presented as a function of distance from the wall.
20 NACA TM 1371
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