Some measurements of time and space correlation in wind tunnel

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Title:
Some measurements of time and space correlation in wind tunnel
Series Title:
NACA TM
Physical Description:
21 p. : ill. ; 28 cm.
Language:
English
Creator:
Favre, Alexandre
Gaviglio, J
Dumas, R
United States -- National Advisory Committee for Aeronautics
Publisher:
NACA
Place of Publication:
Washington, D.C
Publication Date:

Subjects

Subjects / Keywords:
Turbulence -- Research   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Abstract: Results are presented of research obtained by means of an apparatus for measurement of time and space correlation and of a spectral analyser in the study of the longitudinal component of turbulence velocities in a wind tunnel downstream of a grid of meshes. Application to the case of a flat-plate boundary layer is illustrated. These researches were made at the Laboratoire de Mécanique de l'Atmosphère de l'I. M. F. M. for the O.N.E.R.A.
Bibliography:
Includes bibliographic references (p. 7-8).
Statement of Responsibility:
by A. Favre, J. Gaviglio, and R. Dumas.
General Note:
"Translation of "Quelques mesures de corrélation dans le temps et L'Espace en Soufflerie." From La Recherche Aéronautique No. 32, Mar.-Apr. 1953."
General Note:
"Report date February 1955."

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University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003807829
oclc - 128137101
sobekcm - AA00006143_00001
System ID:
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Full Text
NfrM-1310







I2I- t 1 3 -7 1) 3 8 v' 7 -? 29

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

TECHNICAL MEMORANDUM 1570


SOME MEASUREMENTS OF TIME AND SPACE

CORRELATION IN WIND TUNNEL*1

By A. Favre, J. Gaviglio, and R. Dumas


SUMMARY


These researches are made at the Laboratoire de Mecanique de
1'Atmosphlre de 1'I.M.F.M., for the Office National d'Etudes et de
Recherches AMronautiques (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 shall sum up the results which we have obtained by means of the
apparatus for measurements of time and space correlation and of the
spectral analyser in the study of the longitudinal components ul of the
turbulent velocities in a wind tunnel, downstream of a grid of meshes M
refss. 1 to 15); and we shall give the first results in the case of a
flat-plate boundary layer (ref. 10).

The correlation R(VT/M, X1/M, X/M) is measured between two
velocities ul considered with a relatiTe time delay T, at two points
of space at a distance X1 from each other parallel to the general
velocity V of the flow, and at a distance X5 orthogonally.


I. TIME CORRELATION, TURBULENCE SPECTRA DOWNSTREAM OF A GRID


For X1 = X5 = O, only one hot-wire anemometer is used. Numerous
time correlation, or autocorrelation curves, R(VT/M) have been drawn,
the spectral curves being obtained on one hand by transforming them, and
on the other hand by direct measurements with the analyser, for
velocity ul, behind two grids of meshes M = 5 1/4 and M = 1 inch ,
successively, at distances of 40 M downstream of the grids, and at
various speeds and Reynolds mesh numbers BM refss. 2 to 9, 11, and 12).

"Quelques Mesures de Correlation Dans le Temps et L'Espace en
Soufflerie." La Recherche Aeronautique No. 52, Mar.-Apr. 1955, pp. 21-28.
1A communication to the 8th International Congress on Theoretical and
Applied Mechanics, Istanbul, Aug. 1952.
2Analogous to those of the NBS (ref. 15), with elements being respec-
tively of 1.6 and 0.5 centimeters diameter.






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As an example, figure 1 (ref. 12) represents an autocorrelation
curve of the velocities ul at 40 M downstream of that grid of mesh
M = 1 inch, the mean velocity being V = 12.27 meters per second,
S= 21500.

As an example also, figures 2 and 5 (ref. 12) show the values of
the spectral function F(n) obtained by Fourier transform of the pre-
ceding autocorrelation curve or by direct measurements by means of the
analyser (n frequencies).

The autocorrelation curves have a limited radius of curvature at
the origin refss. 2 and 5). The equivalent frequency N of the only
sine wave, the autocorrelation curve of which would have the same curva-
ture at the origin, can thus be measured and can show the decay rate of
energy (ref. 16)5.

On figure 2 we have drawn the spectral curve given by H. L. Dryden
as a first approximation by transformation of the correlation curve f
represented in an approximate way by an exponential curve (ref. 15).

In the spectra, from 40 to 2000 cps, the experimental points are
neighboring this empirical curve. For the lower frequencies, from 1
to 40 cps, the measured energy is smaller.4 The same seems to hold true
for the spectra of NBS and of NPL (ref. 15).

On figure 5 are also reproduced the spectra measured by R. W. Stewart
and A. A. Townsend (ref. 18) with slightly different grids. The same
peculiarity appears for the lower frequencies in the case of low Reynolds
numbers RM; for higher Reynolds numbers it is not detected; the band-
pass of the spectral analyser used is limited to about 20 cps.


As G. K. Batchelor (ref. 17) has
very strong for most frequencies is
components of homogeneous turbulence.
components of the turbulence behind a
tropic. They are also nonhomogeneous
on the grid shape.


shown, the tendency to isotropy -
very slight for the large scale
In particular the large scale
grid in a uniform flow are aniso-
(ref. 18). They can be dependent


N2 = 4F2\P =
4g2dt f/


f
0


n2F(n) dn U
42r 2


N = 455 cps
A = 0.45 cm


H. W. Liepmann (ref. 19) performed numerous measurements of X, under
different test conditions, varying the rates of energy dissipation, the
spectral curves, and the number of passages through zero to ul per unit
time.
4In the case of that grid the rods of which are of circular section.






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II. COMPARISON OF TIME CORRELATION WITH LONGITUDINAL SPACE

CORRELATION: G. I. TAYLOR'S HYPOTHESIS


According to Taylor's hypothesis (ref. 14) the time correlation
curves R(VT/M) may be assimilated to the longitudinal space correlation
curves R(X./M) or f, if the relative intensity of turbulence is very
low, with the condition VT/M = X1/M and the general movement being
rectilinear and uniform.

We have measured, in the same experimental conditions, the time
correlation and the longitudinal space correlation.

It must be noted that the wake of the upstream wire disturbs the
measurements of R(X/M) but not of R(VT/M); in order to lessen this
effect, a small lag X is used.

The results agree with an approximation similar to that of the
measurements, as shown, for instance, in figure 4 refss. 9 and 12).

Thus Taylor's hypothesis is directly verified in the case of the
above-mentioned experiments made behind a grid in a wind tunnel by meas-
urements of time correlation and longitudinal space correlation.


III. TIME AND SPACE CORRELATION, LONGITUDINALLY


The time and space correlation, longitudinally R(VT/M, XI/M)
behind a grid of mesh M = 1 inch, has been measured in the course of
two series of experiments refss. 9 and 12).

The first series of curves in figure 5 (ref. 9) relates to longi-
tudinal distances X1/M of

0.000 0.241 0.485 0.720 1.20 1.95 5.14 4.56 6.64 8.72

the mean velocity being V = 12.25 mps, the Reynolds number RM = 21500.

The second series of curves in figure 5 (ref. 12) deals with longi-
tudinal distances X1 / of

0.000 0.256 0.475 0.946 1.892 5.78 7.57


the mean velocity being V = 12.27 mps, RM = 21500.






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The latter measurements have been made after several improvements
of the experimental apparatus5 (ref. 15).

Figure 6 gives the isocorrelation curves corresponding to the second
series of the above-mentioned measurements, which are in first approxi-
mation ellipses whose axes have an inclination of about 450 and whose
diameter ratios comprised between 0.027 and 0.055 are, on the average,
of the order of 0.04, namely,


R 0.90 0.80 0.70 0.60 0.50 0.40

a/b 0.048 0.054 0.055 0.055 0.028 0.027


One finds that the time and space correlation longitudinally reaches
a maximum for each distance X/M when the delay is close to the time
necessary to cover this distance at the general velocity:

VT/M X M

The time and space correlation longitudinally downstream of a grid
in a wind tunnel, with a delay compensative of the general movement
R(VT/M = X1/M, XI/M), retains high values even for distances which are
great in comparison with those that would practically suffice to make
null the longitudinal space correlation R(X1/M).


IV. TIME AND SPACE CORRELATION, TRANSVERSELY


The time and space correlation transversely R(VT/M, X5/M) behind
a grid of mesh M = 1 inch has been measured in the course of two series
of experiments refss. 4 to 7, 11, and 12).

Figure 7 (ref. 11) shows the first results obtained for transversal
distances X,/M of

0.000 0.0394 0.0788 0.157 0.515 0.650 1.26

the mean velocity being V = 12.20 mps, RM = 21500.

5New amplifiers of hot-wire anemometers, improvement of the compensa-
tion by means of the square waves method, use of wire of 5p in diameter,
extension from 2.5 to 1 cps of the band-pass of the apparatus for meas-
urements of time correlation, reduction of the intensity of the wind-tunnel
turbulence from 0.00045 to 0.00058.






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Figure 8 (ref. 12) relates to the new measurements, made after the
above-mentioned improvements, for the same values of X /M, the mean
velocity being V = 12.27 mps, RM = 21500.

Figure 9 gives the isocorrelation curves corresponding to the new
measurements (ref. 12), which are in first approximation ellipses whose
diameter-ratios comprised between 0.56 and 0.49 are, on the average, of
the order of 0.44, namely,


R 0.90 0.80 0.70 0.60 0.50 0.40 0.50 0.20 0.10 0.00

a/b 0.56 0.59 0.45 0.49 0.49 0.49 0.47 0.45 0.41 0.48


V. TIME AND SPACE CORRELATION LONGITUDINALLY AND TRANSVERSELY,

WITH COMPENSATORY DELAY OF THE GENERAL MOVEMENT


Figure 10 represents time and space correlation longitudinally and
transversely R(VT/M, X/M, X/M) for zero delay VT/M = 0 and also
for a delay compensative of the general movement VT/M XJ/M behind
a grid of mesh M = 1 inch for distances X/M of

0.000 0.256 0.475 0.946 1.89 5.78 7.57

the mean velocity being V = 12.27 mps, RM = 21500.

Figure 11 gives the corresponding isocorrelation curves. They are
in first approximation ellipses whose diameter ratios decrease with R:

R 0.90 0.80 0.70 0.60 0.50

a/b 0.51 0.25 0.20 0.15 0.12

One finds that the influence on the correlation between the com-
ponents ul of the velocities at two points behind a grid of the dis-
tance between these points in the direction of the general movement is
partly compensated, even for relatively great distances, by delays equal
to the time necessary to cover this distance at the speed of the general
movement.






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VI. TIME CORRELATION, TURBULENCE SPECTRA IN THE BOUNDARY

LAYER OF A FLAT PLATE


The measurements are made at 0.91 m from the leading edge of a flat
plate; the mean velocity is V = 12.20 mps, the Reynolds number
RX = 766000 (ref. 10).

The grid being taken off, the preturbulence was of 0.00045 with four
screens, and the boundary layer was laminar; a grid of M = 1 inch being
set in, the preturbulence is of 0.01480, and the boundary layer is turbu-
lent (thickness 8 = 24 mm).

The autocorrelation has been measured for the component ul of the
turbulent velocity, at various distances X /5 from the plate (fig. 12):

0.06 0.12 0.25 0.50 0.75 1.00 5.62

An important evolution of these curves as a function of the distance
to the plate takes place in the boundary layer.

The smallest delay T for which the correlation is zero assumes the
respective values:

7.5 10 12 24 8.3 5.5 5 ms

On the contrary, the equivalent frequency N and the rate of energy
decay change only slightly.

Figure 15 gives the spectra corresponding to the above-mentioned
experiments, obtained either by transformation of the autocorrelation
curves or directly.

They differ but little from those of the turbulence behind a grid
for frequencies from 40 to 2000 cps; for frequencies lower than 40 cps,
they show a marked evolution as a function of the distance from the wall
in the boundary layer.


Translated by A. Favre
*






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REFERENCES


1. Favre, A.: Appareil de measures statistiques de la correlation dans le
temps. VIo Cong. Intern. Mcan. Appl. 1946, Paris.

2. Favre, A.: Mesures statistiques de la correlation dans le temps.
VIIo Cong. Intern. Mecan. Appl. 1948, Londres.

3. Favre, A.: Mesures statistiques de la correlation dans le temps.
Premieres applications a l'etude de movements turbulents en
soufflerie. 28/2/49. a paraltre dans la serie des Publications de
1'O.N.E.R.A.

4. Favre, A.: Mesures de correlation dans le temps et l'espace en aval
d'une grille de turbulence, pour la composante longitudinal de la
vitesse. 15/7/49.

5. Favre, A.: Nouvelles measures de correlation dans l'espace et le
temps en aval de grille de turbulence avec appareillage modified.
51/12/49.

6. Favre, A., Gaviglio, J., and Dumas, R.: Mesures de la correlation
dans le temps et l'espace, et spectres de la turbulence en souf-
flerie. Coll. Intern. Mecan. 1950, Poitiers. Publ. Sc. et Techn.
Minist. Air, No. 251.

7. Favre, A., and Gaviglio, J.: -Mesures de la correlation dans le temps
et l'espace, et spectres de la turbulence en soufflerie.
(d4veloppements). 50/6/50.

8. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps
et spectres de turbulence, en veine reduite. Control des
measures. 31/12/50.

9. Favre, A., Gaviglio, J., and Dumas, R.: Corr6lation dans le temps
et dans l'espace longitudinalement en aval d'une grille de turbulence.
51/12/50.

10. Favre, A., Gaviglio, J., and Dumas, R.: Mesures dans la couche limited
des intensities de turbulence, et des correlations dans le temps;
spectres. 51/5/51.

11. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps et
dans l'espace: transversalement, transversalement et longitudi-
nalement avec retard compensateur du movement d'ensemble, en aval
d'une grille de turbulence. 50/6/51.






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12. Favre, A., Gaviglio, J., and Dumas, R.: Nouvelles measures de
correlation dans le temps et 1'espace, longitudinalement, trans-
versalement, longitudinalement et transversalement en aval d'une
grille de turbulence. 10/7/52.

15. Favre, A., Gaviglio, J., and Dumas, R.: Appareil de measures de la
correlation dans le temps et 1'espace. VIlIO Cong. Intern. MJcan.
Theor. et Appl., Istanbul, 1952. Recherche Aeronautique No. 51,
1955. J.A.S.

14. Taylor, G. I.: The spectrum of turbulence. Proc. Roy. Soc. London,
Ser A, 164, 476, 1958.

15. Dryden, H. L.: A review of the statistical theory of turbulence.
Quarterly of Appl. Math., Vol. I, No. 5, April 1943.

16. Martinot-Lagarde, A.: Introduction au spectre de la turbulence.
N.T. G.R.A. 55, Paris 1946.

17. Batchelor, G. K., and Stewart, R. W.: Anisotropy of the spectrum of
turbulence at small wave-numbers. Quart. Journ. Mech. and Appl.
Math., Vol. III, Pt. 1, 1950.

18. Stewart, R. W., and Townsend, A. A.: Similarity and self preserva-
tion in isotropic turbulence. Phil. Trans. Roy. Sc. Ser. A,
No. 867, Vol. 245, 12/6/51, London.

19. Liepmann, H. W., Laufer, J., and Liepmann, Kate: On the spectrum of
isotropic turbulence. NACA TN 2475, 1951.








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0.001 0.01 0.1 1 10

Figure 2.- Spectrum of turbulence downstream of a grid obtained by
Fourier transform of autocorrelation, or directly measured.
V = 12.27 mps; MI = 1 inch; distance = 40 MII; Compensation square
waves method, RJ = 21500.







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.g


& 30 21000


(b) Spectra obtained by Favre, Gaviglio, and Dumas. V = 12.27 mps;
M = 1 inch; distance = 40 M; RM = 21500; N =435 cps.


Figure 3.- Spectra of turbulence downstream of a grid by transform of
autocorrelation or measured directly.


k, = ()


x
M
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B 60


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5250






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(a) First measurements (ref. 9). V = 12.25 mps; M = 1 inch; distance = 40 M;
S= 21500.


(b) New measurements (ref. 12). V = 12.27 mps; M = 1 inch; distance = 40 M;
= 21500.

Figure 5.- Time and space correlation longitudinally R(VT,'I, X'II/M)
for turbulence downstream of a grid.






14 NACA TM 1570








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Figure 7.- First series of measurements. Time and space correlation
transversely R(VT,'MI, X3; J1) for turbulence downstream of a grid.
V = 12.20 mps; IA = 1 inch; distance = 40 TA; RI = 21400.

















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Figure 8.- New measurements. Time and space correlation transversely
R(VT,'M, X3/ ,I) for turbulence downstream of a grid. V = 12.27 mps;
M = 1 inch; distance = 40 M; RM = 21500.


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Figure 10.- Time and space correlation longitudinally and transversely
R(VT,'MP -X1, M, X1/M, X3,; M) with compensatory delay of general
movement for turbulence downstream of a grid. V = 12.27 mps;
M = 1 inch; distance = 40 M; RM = 21500.






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X1 /M
R=Q4 RA


1.3 R


i


Figure 11.- Time and space isocorrelation longitudinally and transversely,
with compensatory delay of general movement R(VT'M ~ X1,'M, X1,'M,
X3/M) for turbulence downstream of a grid. V = 12.27 mps; M = 1 inch;
distance = 40 M; RM = 21500; T ~ XI,'V.


R=0.6


R=0.7


R=0.8






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Figure 12.- Autocorrelation in turbulent boundary layer of a flat plate.
V = 12.20 mps; M = 1 inch; distance = 40 M; Rx = 766000.







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