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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 flatplate 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 hotwire 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. 2128. 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. NACA TM 1570 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. NACA TM 1370 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 abovementioned 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. NACA TM 1570 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 abovementioned 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 hotwire 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 bandpass of the apparatus for meas urements of time correlation, reduction of the intensity of the windtunnel turbulence from 0.00045 to 0.00058. NACA TM 1570 Figure 8 (ref. 12) relates to the new measurements, made after the abovementioned 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 diameterratios 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. NACA TM 1570 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 abovementioned 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 * NACA TM 1570 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. NACA TM 1370 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. MartinotLagarde, 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 wavenumbers. 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. NACA TM 1370 9 2 Sc CCD c.J o R i Yit F, O II 81 **5 1 o JJ I '. ta) C . NACA TM 1570 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. NACA TM 1370 .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 * Gu + 80 X I00 E 30 B 40 B 60 2625 5250 10500 NACA TM 1370 o c U 1. 0 00 Mo I m o 3 s 3 " , 0 El .0 o Cr' I 5: .4 M Oi j a O @ C l) Sci 0 rl 0 41 0 * O) 4  0 r o 0 r CD CQ * S 44) 0a) * 0 aj 0 ? h 1 o NACA TM 1570 (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 I a .. 1 1N 1s \ i Uo 4 a0) NACA TM 1570 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. I R T I./ X3 1) 0.4 07, 06 04 ~ rT 1  01 S 6 7 19 0 0  O7 0. \        0 x. M,0'03)#" O' 'l        0'    i *N1 > * 05   0 A . '. L II 0o4 \  I I I I    o. I I 02 % .I I 6I 1 1 2 . a 2 S0.. 01 0 z zztz 7   i 4' 1 U 4 2 I I I , u  ^ = = .  ^ Q3 _ 10 2 S f. M 0 s' M O  LM b630  I 5I 16 I 17 I la I I i~~~ i 11T a1 m *'~ . 5 b .  I I I' I I1 PI 6 I 17 VT/M VT/M VT/M VTiM 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. NACA TM 1570 'L1 I I I I I 1 I I NACA TM 1570 17 _____ & 0 II O C1 I .q a 00 'a) 1 .. Cd L lul b i / /^ ?'i __ _ CLI NACA TM 1370 R (VT/M * X,/M, X/M )  SX,/M. zX,/ /MQ 473 l I l /M 0.946 I ~/M 1.892 II _^/M 7.__ __l l1 F I I 111l lx7 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. NACA TM 1370 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 NACA TM 1570 Figure 12. Autocorrelation in turbulent boundary layer of a flat plate. V = 12.20 mps; M = 1 inch; distance = 40 M; Rx = 766000. NACA TM 1370 S(n) 30si 1 T I fLSu ^4I4*44V' *_I K  Zn 15mm 3 mm 6 mm 12 mm 18 mm 24 mm 135mm A 6 006 012 025 050 075 100 562 20 1 1 13 [^ ^ : X ^ V   ^ i r ~ 10 * 5   I I L II I I o <= = =::= = ==:J= =:==:  _ _ l ^ i _ Figure 13. T J NO w W ) I oaoo UO VC00Io Q 0 0 0 8000000 00 0 a Ce', N" N1 N"P) O 0a v!ouq6ou. O 3Voo 0a e .4 C4 c m vm"I' o Kea C l 0 Turbulence spectra in flatplate boundary layer as a function of the distance from the wall. R_ = 766000. NACALangley 22855 1000 T IS1 Jill I I I I I I 1 1 1 1 1 I I I 1 7 1 1 7`L Xt I rssa^ L .5, C 3 wcdJ C, ~i E a' a <.2a a M C.  c R i aa, Se., .I >.4 C 0X 10 C "3 Sc a ti. <" ai M" E 0 E.. Cd SQ cd u a H a 5 'wj3c2! ,Eu, U CL C Sgn > 4"1 CD 2 m rn s gs o s 0 ~ 0 C do= L. ,E OV d taa S c, 0 2 0d Cc r 3' 0 2 aU V mg gs 3"^'a CLi^ m l co d C a a, ~ ~ ~ C w :'**'~tS CL 0 a' , a, a'3 o _ ) i UB C. Cu C c LS e Q e ' a, C. a B  ~ ao u , o. u E CU. U~ a  a' ~C C '~0 CU . U UO a, ux .c aj m B 01 AIi UNIVERSITY OF FLORIDA 31262 8106 5426 