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I3 Y7 3r 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 SUMMARY 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 applications. EXPERIMENTAL APPLIANCES Wind Tunnel (Refs. 2, 5, 4, 6, 12, and 15) The lowturbulence 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 lowturbulence 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. 5744. 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, respectively. A flat plate of 1,960 x 80 cm can be set in the test section for the study of the boundary layer. HotWire 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 timecorrelation 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 recordersreproducers H, one of which has a device I for adjusting the length of the tape between the recording and playback heads and, consequently, the delay T refss. 2 and 5) The two playback preamplifiers F The two playback 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 space correlation. 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 feedback amplifier has been designed in order to deter mine the spectral function directly, apart from the autocorrelation method. The bandpass 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 longperiod galvanometer (19 sec). CONTROL OF THE MEASUREMENTS REFSS. 2 to 17, AND 21) I. The response curve of the amplifiers of the hotwire 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 bandpass of the spectral analyser. II. The total response curve of the apparatus for measurements of time correlation, together with the hotwire 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 hotwire 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 a grid. 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 squarewaves method has made it possible to reduce those differences (fig. 6) refss. 10 and 15). Aerodynamic taking attempts of the hotwire anemomenter are in progress, the wire being placed in the field of a propeller refss. 17 and 20). The measurement errors seem to be mainly due to the hot wires; the comparative experiments are preferably made with practically identical wires. NACA TM 1371 VII. apparatus 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, and 21) 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, and 24). 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 flatplate 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 timecorrelation 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 negligible 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 are zero. 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 (ref. 18). 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 then, Q q It may be preferable to filter the parasite so that, for a T multiple of the period, one should have ROl,01 ~ 1/2 then, Q4 q The operation may be repeated in series, choosing the optimum delays; one may also make several additions in parallel with optimum delays. 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 abovementioned turbulent veloc ity fluctuations. For a delay T such that R01,01 ~ 0 and 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 R01,01 0.5 and 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 REFERENCES 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 soufflerie. 28/2/49. 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 acoustiques. 15/7/49. 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. 51/12/49. 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 pements). 50/6/50. 11. Favre, A., and Gaviglio, J.: Perfectionnements a 1'appareillage de measures statistiques de la correlation dans le temps et l'espace. 50/6/50. 12. Favre, A., and Gaviglio, J.: Etude de l'effet sur la turbulence des resonances acoustiques. Influence des modifications de la soufflerie. 50/6/50. 15. Favre, A., Gaviglio, J., and Dumas, R.: Correlation dans le temps et spectres de la turbulence en veine reduite. Control des measures. 51/12/50. 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. 51/12/50. 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 helice. 50/6/51. 18. Favre, A., and Gaviglio, J.: Detection de signaux periodiques perturbes par des parasites aleatoires par autocorrelation. Coll. Nat. Mecan. Marseille, 5/1/52. 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 turbulence. 12/7/52. 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. Lowturbulence wind tunnel. Figure 2. Apparatus for measurements of time correlation. NACA TM 1371 13 _  .. J   a 6 o   .  D  i  0 4 ..,a S . M o o I \> >) a) ^  S   / 5    cL  t .  U  a, + ^ ^ +  NACA TM 1571 o .4 9 OJ + 0 4 SI I II I II I I I I I I I II II I I I 1 1 0 000  * OOB 009 s ooS 00 I_ o 0L, 09 I   0"00 _ _ _  e  _ ___ os _ _ _  09    Ot or  + +    o  o   o < 1+  (   ~~ __S c  _ 9 ____.X *  9 4 . 0 "d "0 II o o 0 a r4 .4J 0 c) r20 E1' *44 r4E 111 I 4 TI 11 11 NACA TM 1371 1) C ,0 . . *o  a aV S0X >0 S 0  S. o o, a D g E 0 o *^ h ^i > ( y *t3 ~Eo ^s ^ .? :::::. ^  r 1 ri II i , U C 1 :::s ^ i i g ./ 8 ^ll ^ ( ^ "ir I~ 8 ^S3 NACA TM 1571 Velocity = 12.20 mps; M = 1 in; Distance to grid = 40 M Semiempirical compensation .......... Wire I .. Wire I  Wire II 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 R (T) 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. RIT) . ... . 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 s I A 3  I 1 I X3/M Transversel Velocity = 12.20 mps; M = 1 in; 9 Space correlation g O Time and space correlation O Space correlation g S 21 . a .00 a. 4 y, g Distance T = 0 I I I I I to grid = 40 M "I I I 1 I 5X3 /M Longitudinally, f 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 9L xi/M Figure 7. Control of time and space correlation measurements with zero delay, transversely g, longitudinally f, downstream of a grid. Transversely, g Velocity = 12.20 mps; M = 31/4 in; Distance to grid = 40 M * Space correlation g [ LMA O Time and space correlation T = 0 L O Space correlation g NBS j21,~ ____ .rjtrrul,7" 2 1 I I 1 1 19 1 8   In I :'5  _I I ~'~~'YL~Y1LT~I~RZC~ N LJ _a __w I NACA TM 1371 UF (n) La 0.x 0.01 0.001 Figure 8. 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 I9 atoclnc an; 08 tE21WCN ,.. a*( (b) IMA = 766000. Figure 9. Comparison of turbulence spectra in flatplate boundary layer. Presented as a function of distance from the wall. 20 NACA TM 1371 me 0 r* 0 r ul C' I II NACALangley 4755 1000  a4* i g yI C * i C 4 ca a i a w  0. C I cd z 0> a3  ,M v C3 g Wdc. 00, :3 0 ce "% o0 ~S Lu 0'a ci> c3 l F4 co r o,~a a "'C OW C i S 0. c! Hs ra0 c "s Z da V 1, E E En ?2 El E I c zo9 0 14 o H ~z cn Ae  o .o .4 r .4 > d cdM0 o' 4 ZZr s 6I. ES 6U3ii l4 l;i U N sC, C S~gS;S0. 0 1 S0 wn x ed;dLCI 06 _0 '0* _ u e1 5d M0 CJ 00 e . NZ 0 >2 eisL U?  ..'0 6 f mdauld 0C S .6 003 6 *E *3 5 2" O. 0 L2 te 0. 0.%f q a3 CU LU Q S4 e I etf 0f r3 0 cc = S. 4 0 4 C 00 S u 6 h o 6~ d_dS8 sZori6^ <5 C04 063 C; 0 0 H 'Au F f .l'i IJY1 1ggjp~u3; C bll cf sl I ;1 , 0 a oco u is 2z CiU 2S ce 0 L  cd Ci C'0 CD! 'enla cdmo iC 0 m 0 0 M V; 0"$s P6 E i '3t0 'C *oa 2 0is CU C 0. S 2 b _ 1 ea *" sIY 6 CU r m < i C7 m C W a c r2 C j Cc 0  U CL 3 i. o4: 6a o *a~ 0i,1 m (D 0 Ma $0 0 01 U CD az s a  eF4 ai Z b 06  OM a E a 0 lfl Ei Z w E .2 0i r 0 go 0 wz o~c5 .CgS N C7Sd DO z z Go u :V Cei r. .2I 0 m 006 o v * U 'C... E 0 er 0 00 'S d 26CLi (U 0 S. .0 v 0 1% 75 0 6 Qe > 0, 3 *( 6 il .C LU .0 "s a .2' & 4:. ii i I u ni3 1 2 0 6 5I LU27IU 