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NASA Technical Memorandum 107734
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CHARACTERISTICS OF VERTICAL ANDLATERAL TUNNEL TURBULENCEMEASURED IN AIR IN THE LANGLEYTRANSONIC DYNAMICS TUNNEL
Robert K. Sleeper, Donald F. Keller,Boyd Perry III, and Maynard C. Sandford
March 1993
(NASA-TM-I07734) CHARACTERISTICS
OF VERTICAL AND LATERAL TUNNEL
TURBULENCE MEASURED IN AIR IN THE
LANGLEY TRANSONIC DYNAMICS TUNNEL
(NASA) 58 p
G]/09
N93-22675
Unclas
0156310
National Aeronautics andSpace Administration
Langley Research CenterHampton, Virginia 23681-0001
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CHARACTERISTICS OF VERTICAL AND LATERALTUNNEL TURBULENCE MEASURED IN AIR IN THE
LANGLEY TRANSONIC DYNAMICS TUNNEL
By
Robert K. Sleeper, Donald F. Keller, Boyd Perry III,and Maynard C. Sandford
NASA Langley Research Center
ABSTRACT
Preliminary measurements of the vertical and lateral velocity components of tunnelturbulence were obtained in the Langley Transonic Dynamics Tunnel test section using a constant-temperature anemometer equipped with a hot-film X-probe. For these tests air was the testmedium. Test conditions included tunnel velocities ranging from 100 to 500 fps at atmosphericpressure. Standard deviations of turbulence velocities were determined and power spectra werecomputed. Unconstrained optimization was employed to determine parameter values of ageneral spectral model of a form similar to that used to describe atmospheric turbulence.These parameters, and others (notably break frequency and integral scale length) were determinedat each test condition and compared with those of Dryden and Von KLrrntin atmospheric turbulencespectra. When data were discovered to be aliased, the spectral model was modified to account forand "eliminate" the aliasing.
INTRODUCTION
The Langley Transonic Dynamics Tunnel (TDT) is a closed-circuit, continuous-flow,
slotted-throat wind tunnel capable of testing in air or heavy gas at total or stagnation pressuresranging from one atmosphere to near vacuum and over a Mach number range from near zero to1.2. The test section of the TDT is 16 feet square and has cropped comers. This facility wasdesigned to fill the need for a transonic wind tunnel capable of testing dynamic models of a sizelarge enough to allow simulation of important structural properties of aircraft or spacecraft.Aeroelastic research conducted in the TDT includes the study of flutter, aerodynamic loads, forcedresponse, and active controls (unpublished information contained in Langley Working Paper 799,"The Langley Transonic Dynamics Tunnel," dated September 23, 1969 with an updated reprintdated April 1992). An important consideration in the study of forced response and active controlsis knowledge of the turbulence in the test sectionl Seven examples of wind-tunnel test programsinvolving aeroelastic models with active controls are shown in figure 1. Six of the seven areshown in the TDT and represent a cross-section of the variety and complexity of wind-tunnelmodels which could have benefited from knowledge Of the turbulence in the test section.
This paper describes the first phase of a program to define the turbulence in the TDT.In this phase, vertical and lateral components of turbulence were measured in air at one totalpressure only (atmospheric) and for a limited number of Mach numbers. Later the same turbulencecomponents will be measured in air and in heavy gas at many combinations of total pressure andMach number. Power spectral density functions of the two components of turbulence, and relatedstatistical quantities, are computed from the measured data and "define the turbulence." It is hoped
that the information contained herein will be useful to control-law design engineers as they designcontrol laws to be tested on active-controls models in the TDT.
A unique aspect of this program is the application of unconstrained optimization todetermine the values of parameters that mathematically define the power spectral density functionsof the velocity components at each test condition. One of the sections of this paper addresses theuse of an unconstrained optimization procedure and the appendix to this paper describes certainaspects of a modified power spectral density function definition introduced after aliasing wasdiscovered in the digitized data.
f
fbfb
fNkLMSRn
Objqr
V
77'
¢CA_meas
P
SYMBOLS
frequency,Hz
break frequency,Hz
normalized break frequency
Nyquist frequency,Hzsummation index
integralscalelength,ft
rncan squareratiospectralmodel denominator exponcnt
objectivefunction
dynamic prcssure,pV2/2, psfcorrelationcoefficient
tunnelvelocity,fps
spectralmodel amplitude,(fps)2/Hz
spectralmodel numerator cocfficient,scc2
nondimensional spectralmodel numeratorcoefficient
spectralmodel dcnorninatorcoefficient,scc2
nondimcnsional spectralmodel dcnorninatorcocfficicnt
unaliasedturbulcncespectrum,(fps)2/Hz
aliascdturbulencespectrum,(fps)2/Hz
measured turbulencespectrum,(f-ps)2/Hz
fluiddensity,slugsfft3
standarddcviation,fps
APPARATUS
The apparatus consisted of the following components:
Transonic Dynamics Tunnel (TDT)
The features and characteristics of the TDT are described in detail in LWP-799. Figure 2shows an aerial view of the TDT facility; figure 3 shows a plan view drawing. A sting, identified
in figure 12 of LWP-799 as "Sting 6," was used to support an X-probe on the centerline of theTDT test section at longitudinal station 72, the position where the center-of-gravity of wind-tunnelmodels is located for most tests. The sting could be inclined in pitch about its forward tip asshown in the multiple-exposure photograph in figure 4. This feature was used in calibrating theX-probe.
2
Tunnel Instrumentation
The following information was available from tunnel instrumentation: flow velocity,Mach number, total temperature, sting pitch angle, and static, dynamic and total pressures.
Time-averaged values of these quantities, based on a sample rate of 4 samples per second over aduration of 15 seconds, were available.
Anemometry System
Figure 5 shows the two major components of the anemometry system: an anemometerconsole and a cross- or X-probe. The probe is shown greatly magnified. The probe contains twofilaments arranged in an X-pattern and separated by 0.04 inches. The filaments are mutuallyperpendicular and each is aligned at 45 ° with respect to the axis of the probe. For durability, filmfilaments, which are constructed by bonding a thin film of platinum onto the surface of a fused
quartz substrate, were chosen over wire filaments. The film filaments were about 0.08 inches longand 0.002 inches in diameter. A view of the X-probe showing its actual size is presented in figure
6. In figure 7 the X-probe is shown in the TDT test section mounted at the end of Sting 6.The X-probe was mounted on the sting in such a manner that it could be rotated about its axis.
The anemometer measured voltage variations, over a broad frequency range, from eachfilament of the X-probe. A dummy probe was used to provide a measure of the cable resistance.The characteristics of the elec_c_ cables_that cpnne_cted__e probes to the anemometer metmanufacturer's specifications. Voltages from the X-probe were calibrated to provide bothcomponents of flow velocities in a plane that includes the probe axis. (The probe is insensitive toflow normal to this plane.) The pair of anemometer voltage signals and their difference were
sampled at 200 samples per second, yielding a Nyquist frequency of 100 Hz.
Other Instrumentation
In anticipation of possible sting motion due to vibrations, the sting was instrumented with
accelerometers. These possible sting motions, if large enough, could have contaminated thereadings from the anemometer since an anemometer cannot distinguish between voltages producedby the passage of moving air over a stationary X-probe and voltages produced by the passage of amoving X-probe through stationary air. Accelerations of the sting give an indication of stingmotion and were used to determine if there was _ontamination. Such contamination would be
manifested as additional power in the spectral density functions at the vibrational frequencies.The accelerations were sampled at 200 samples per second.
Overall System
The overall system, including instrumentation and data acquisition devices, is schematicallyillustrated in figure 8. A dual-trace oscilloscope was used to monitor the anemometer signals andthe spectrum analyzer was used for on-line evaluation of the data measurements. All data werepassed through a 1000 Hz low-pass filter before being saved digitally (at the respective samplerates noted above) on the MODCOMP data acquisition computer.
TEST PROCEDURE
A test procedure that minimized test time was employed. The procedure involved
systematically altemating between acqu_ng data that would later be used to calibrate theanemometer (calibration data) and acqumng data that would later be reduced using the results fromcalibration (test data). Data for the vertical component of tunnel turbulence which included
3
calibrationdata were acquired before those of the lateral component. There were eleven calibrationconditions and nine test conditions.
Figure 9 is a semilog plot of dynamic pressure as a function of Mach number and showsthe TDT operating boundary for air. The various arching curves are contours of constant total
pressure. The TDT operates along these contours as motor speed varies. All calibration and testconditions were on the atmospheric total pressure curve (2200 psi). The calibration conditionscovered the range of tunnel velocities from 50 fps to 550 fps in increments of 50 fps. The testconditions, shown in the figure by open circles, covered the range of tunnel velocities from 100fps to 500 fps, also in 50 fps increments. Corresponding ranges for Mach number and dynamicpressure for the test conditions are from 0.09 to 0.44 and from 11 psf to 250 psf, respectively.
Acquiring Data
Calibration data were recorded in tests of 15-second duration and test data in tests of
3-minute duration. Time-averaged tunnel instrumentation values were provided at the initiation andthe termination of data tests to monitor the extent of value changes during tests. Calibration dataand test data consisted of voltage outputs from the two filaments of the X-probe. Calibration datawere acquired at known values of tunnel velocity and sting pitch angles over the angle range from-5 ° to +5 ° in increments of 1°. This range of sting pitch angles is depicted in figure 4. When thesting pitch angle was set to 0°, test data for the vertical component of tunnel turbulence wereacquired. Tunnel velocity was then changed and this process was repeated.
After all calibration data and test data were acquired for the vertical component of tunnelturbulence, the X-probe was rotated 90 ° about its axis, the sting pitch angle was set to 0 °, and,without further calibration, test data for the lateral component of tunnel turbulence were acquired atall tunnel velocities.
CALIBRATION
The mean tunnel flow at the location of the X-probe was assumed to be along thecenterline of the test section.
After data acquisition, the next task was to apply the calibration in the conversion of thefilament voltages to flow velocities. First, a grid of filament voltages for the calibration tunnelvelocities and sting pitch angles was constructed. Next, linear regression was applied to providesmooth voltage variations with angle change at each velocity. Then, a table look-up proceduresimilar to that of reference 1 was employed to interpolate or extrapolate the turbulence velocitycomponents from the measured voltage time histories (test data).
Figure 10 shows the linearized X-probe calibration results expressed in terms of a grid offilament voltages. The filament-voltage scales are identified by their attitude angles with respect tothe probe axis. The figure shows a general increase in voltage for both f'daments with velocity andsmall regular, negatively-sloped changes in voltages due to pitch angle. At the higher velocities,the slopes of the changes due to pitch angle become more negative.
The process of calibration was conducted in the vertical plane while the plane of responseof the X-probe was aligned vertically. The vertical calibration was also applied to the lateral
measurements since the probe was merely rotated for the lateral measurements. Thus, both thevelocity components were converted from voltages using the calibration relationships derived fromthe vertical measurements.
4
DATA REDUCTION
Except for some on-line measurements which will be described next, all data reduction wasperformed subsequent to testing.
On-Line Data Examination
At each test condition on-line measurements were made of power spectral density functionsof the difference in voltages between the two probe filaments. For an ideal X-probe, reference 2shows that this voltage difference is proportional to the measured flow normal to the probe axis.In addition, on-line measurements were made of power spectral density functions of the stingaccelerations. These spectra were characterized by prominent peaks at the frequencies of vibrationof the sting. The voltage-difference spectra were examined for peaks at these same frequencies,but none were found. Had such peaks been found, the conclusion would have been made that the
motion of the sting was responsible for those peaks and that contamination existed. However,because this condition did not exist, it was judged that no contamination existed.
Turbulence-Velocity Time Histories
Total-velocity time histories were determined from filament voltage time histories byemploying the calibration procedure discussed previously. Turbulence-velocity time histories werethen obtained from the total-velocity time histories by subtracting the mean from the velocitycomponents.
Standard deviations of each component of tunnel turbulence were computed from theturbulence-velocity time histories. The turbulence levels, expressed as a percentage of tunnelvelocity, were computed by dividing the standard deviations by the corresponding tunnelvelocities.
Turbulence-Velocity Power Spectral Density Functions
Power spectral density functions of the vertical and lateral components of tunnel turbulencewere computed from the turbulence-velocity time histories using the Blackman-Tukey method(ref. 3). In this method an estimate of the autocorrelation function for each time history iscomputed first. These autocorrelation functions were chosen to have 512 lags. Next, for eachautocorrelation function, a Hanning lag window was employed and an estimate of the powerspectral density function was computed.
When the resulting power spectral density functions exhibited the characteristic inflectionsin the spectra at frequencies approaching the Nyquist frequency, aliasing was determined to bepresent in the digitized data.
Use of Unconstrained Optimization to Approximate Measured Spectra
An important objective of the program was to determine the values of parameters o_,[3, T,and n within the following assumed simple analytical expression which approximates the measuredtunnel-turbulence power spectra at each test condition
1 + 13f2¢(f) = oc
0+::(1)
5
Thisexpressionwaschosenbecauseit is consistentwith andhaspropertiessimilar to thefamiliarDrydenandVon l_trm_tnformsof atmospheric-turbulencepowerspectra.In choosingequation(1),theauthorshopedto usetheirunderstandingof thefamiliar formsof atmospheric-turbulencepowerspectrato interpretthecharacteristicsof thetunnel-turbulencepowerspectra.
An important property of equation (1) is its asymptotic behavior. At low values offrequency the value of ¢ asymptotically approaches a constant value, and at high values offrequency the value of ¢ asymptotically approaches zero as the negative 2(n-1) power offrequency. On a log-log plot, these low- and high-frequency asymptotes am straight lines withslopes of zero arid negative 2(n-l), respectively. At intermediate values of frequency there is atransition between the low- and high-frequency asymptotes in the vicinity of a frequency whichwill be referred to as the break frequency, fb. The quantity fb is defined to be the frequency atwhich the low- and high-frequency asymptotes intersect and is expressed as
(2)
Before the presence of aliasing was detected, the authors had conceived a straightforwardprocedure, which employed unconstrained optimization, to determine the parameters oc, 13,_,, andn. In this procedure these four parameters were the design variables and the objective function wasbased on the difference between equation (1) and the measured power spectrum, over thefrequency range of zero to the Nyquist frequency. The procedure assumed that there was noaliasing present in the measured data, therefore, _ in equation (1) is referred to as the u,mliasedspectral model.
The objective function was the sum, over the frequency range from zero to the Nyquistfrequency, of the square of the differences of the logarithms of the unaliased spectral model and themeasured spectrum
Obj=Z log[m(f)]} (3)
The difference in logarithms of spectra, rather than the difference of spectra, was chosen totbrce the optimizer to work as hard in the high-frequency region as it does on other portions of thespectrum. Because aliasing was discovered before optimization was performed, equation (3) wasnever employed, but an alternate form, to be described next, was employed.
"Eliminating" Aliasing
After the presence of aliasing was detected, the spectral model was modified to reflect thepresence of aliasing. The design variables were the same but the objective function was based onthe difference between the analytical expression, as specified in equation (4), and the measuredpower spectrum. The new analytical expression is referred to as the aliased spectral model and iscomprised of the sum of all unaliased spectral segments (each segment based on eq. (1)) betweenzero and 1000 Hz, but "folded" about frequencies zero and the Nyquist frequency, fN (refs. 3 and5).
l+13(f + 2kfN) 2_^(f)=___a , , (4)
k [l+y(f+2kfN)2]"
for k = 0, .i- 1, _:2, _:3 ....
6
Whenaliasingisconsidered,theexpressionfor 0A(f) in equation (4) replaces ¢(f) in theobjective function yielding,
Obj = _ {log[Omeas (f)]- log[0 A (f)]}2f
(5)
Parameters a, 13,y, and n were obtained during the optimization procedure. The Appendixto this paper describes the composition of equation (4) and provides an illustration of its validationto turbulence spectra.
Quantities Which "Define" the Turbulence
. Equation (1) may be rewritten in a form identical to the Dryden and Von K.4rm,Sn forms ofreference 4, in terms of quantities V (velocity), L (turbulence integral scale length), and a
{.turbulence standard deviation). Both forms of atmospheric-turbulence power spectra may beexpressed in the following form
,.. (2/tL'_2 f2
¢(f) =G22L 1 + P t---V) (6)
== l+y' f2
In comparing equations (l) and (6) term by term the following relationships are apparent:
o22Lot - (7)V
^,/2xL_ 2
,(2xL'_ 2
(9)n=n
Quantities 13'and _' are nondimensional. A nondimensional break frequency may bedefined as
(10)
_f2.L , ft--£-J "= (11)
Equations (1) and (6) both define the turbulence, but equation (6) will be used exclusivelyfor the remainder of this paper because it is identical in lbrm to the Dryden and Von Kfirm,'fn
forms. Therefore, knowledge of quantities a, L, lY, y', n, and r b is required to define the
turbulence. These quantities are computed in the lbllowing manner: parameters et, fl, y, and n aredetermined using equation (5) as the objective function; quantity o is computed from theturbulence-velocity time histories; and quantity V is known from the test conditions. With these
7
six quantities known, quantity L is computed using equation (7); quantities lY and _ are computed
using equations (8) and (9), respectively; and fb is computed using equations (2) and (11).
RESULTS AND DISCUSSION
Table 1 contains a summary of the results which are discussed in this section of the paper.Also included in the table are the tab point, corresponding tunnel velocity, and dynamic pressurefor each entry.
Turbulence-Velocity Standard Deviations
The standard deviations, which are a measure of the intensity of tunnel turbulence, werecomputed for the vertical and lateral components of tunnel turbulence. The vertical component isplotted in figure 11 (a) as a function of tunnel velocity and in figure 11 (b) as a function of dynamicpressure; the lateral component is similarly displayed in figure 12. As expected, the standarddeviations tended to increase with both tunnel velocity and dynamic pressure, although thestandard deviations of the vertical component were slightly greater than those of the lateralcomponent. The maximum standard deviation for the vertical component was about 3.5 fps; forthe lateral component, about 3.1 fps.
Some discrepancies in the data were noted. For the vertical component of tunnel turbulenceat a tunnel velocity of 500 fps three sample records were obtained, resulting in three significantlydifferent values of standard deviation. At a tunnel velocity of 300 fps there appears to be acondition of low turbulence intensity for both components of tunnel turbulence. These discrep-ancies were investigated but no apparent reason for them was found. These will be investigatedfurther in the next phase of the program.
Also plotted in figures 11 and 12 are the linear least squares estimates constrained to passthrough the origin. The correlation coefficient, r, of each estimate is indicated on the plot.For both components of tunnel turbulence, the correlation coefficient is somewhat greater when thedata are plotted as a function of dynamic pressure, suggesting a slightly stronger linear relationshipwith dynamic pressure than with velocity.
Tunnel turbulence is frequently expressed as a percent of tunnel velocity. The data offigures 11 and 12 were normalized by tunnel velocity and then replotted in figures 13 and 14.For the vertical component, the percentages ranged from about 0.2 % to about 0.8 % of tunnelvelocity. For the lateral component the percentages ranged from about 0.3 % to about 0.6 %.The figures also include linear least squares estimates.
Turbulence-Velocity Power Spectral Density Functions
Figure 15 (a-k) contains eleven log-log plots of the power spectral density functions of thevertical component of tunnel turbulence for the different tab points and tunnel velocities. Figure 16(a-j) contains ten similar plots for the lateral component. To aid in comparing the power spectra thescales on all 21 plots were kept identical.
Each plot contains the following:
(1) An estimate of the power spectral density function computed from theturbulence-velocity time history.The estimate is characterized by jaggedness and by aliasing.It is labeled on the plot as "measured spectrum."
(2) Thealiasedspectralmodel(eq.(4)),obtainedbyperformingtheoptimizationprocedure.It isgenerallydifficult to seethismodelrepresentationontheplotbecauseitpassesthroughthemiddleof themeasuredspectrum,anindicationof thesuccessof theoptimizationprocedure.It is labeledon theplotas"aliasedspectralmodel."
(3) Theunaliasedspectralmodel(eqs.(1)and(6)),obtainedbysubstitutingintoequation(1) theoptimizedvaluesof theparametersfromthealiasedspectralmodel.Thismodelisalwaysbelowthecorrespondingaliasedspectralmodelfor allfrequencies.It is labeledon theplotas"unaliasedspectralmodel."
Themeasuredspectraexhibit trendswith increasingtunnelvelocityconsistentwiththecorrespondingtrendsfor standarddeviation.For instance,astunnelvelocityisincreasedfrom 100fps to 500fps thereisaboutanorder-of-magnitudeincreasein thestandarddeviationfor bothcomponentsof turbulence.Thereis alsoaboutanorder-of-magnitudeincreasein the low-frequencyvaluesof themeasuredspectra.
Forthepresentapplication,anindicationof theamountof aliasingpresentin ameasuredspectrumis thedifferencein themagnitudesof thelow-frequencyasymptotesof thealiasedandunaliasedspecu-almodels.A relativelysmalldifference,asin figures15(a)and 16(a),indicatesarelativelysmallamountof aliasing.A relativelylargedifference,asin figures15(j)and 16(g),indicatesarelativelylargeamountofaliasing.Themeansquareratio(MSR)providesaquantitativemeasureof theerrorpresentin thepowerspectradueto aliasing;thesmallertheMSR,thegreatertheerror. TheMSR istheratioof theareasundertheunaliasedandaliasedpowerspectrafrom thelowestfrequencyto theNyquistfrequency.For thetwentyonespectraobtainedin thepresentstudy,theratiosrangedfrom 0.624to 0.861.
Quantities Which "Define" the Turbulence
Figures 17 and 18 contain plots, as functions of tunnel velocity, of the quantities whichdefine the turbulence. Figure 17 displays the quantities for the vertical component of tunnelturbulence; figure 18, the lateral component. The quantities plotted are or, 13',v', the ratio fl'/_,', n,
L, and fb. Where appropriate, for comparison with atmospheric turbulence power spectra, the
values of the quantities from the Dryden and Von Kfinn,4n forms are indicated on the plot.Each plot contains a least-squares line through the data.
Because the general trends in con'esponding data in figures 17 and 18 are very similar, thefollowing discussion applies to both the vertical and lateral components of tunnel turbulence.
Amplitude ix.- Figures 17(a) and 18(a) show variations of a with tunnel velocity,variations which have a similar character to those of a in figures 1 l(a) and 12(a). (From equation(7), for a given velocity and a given value of L, ct is proportional to the square of a.) The least-squares line in these plots was constrained to pass through the origin.
Coefficient _'.- Figures 17(hi and 18(b) show variations of 13' with tunnel velocity.
The least-squares line has a very shallowpositive slope, indicating that the value of 15'is verynearly constant with tunnel velocity. Corresponding values of_' from the Dryden and VonK,'trm,'tn forms, 3 and 4.781, respectively, are about an order of magnitude larger than the valuesof 15'from tunnel turbulence. This discrepancy in _' may be related to the physical restraints thatthe tunnel walls impose on the flow, restrai!us that are not present in the atmosphere.
.C,.o_edligl_lL_.-Figures17(c)and 18(c)showvariationsof _,'with tunnelvelocity. Theleast-squareslineherealsohasavery shallowpositiveslope,alsoindicatingthatthevalueof,/isvery nearlyconstantwith tunnelvelocity. Correspondingvaluesof _ from theDrydenandVonK_'rrffm forms, 1 and 1.793, respectively, are about two to four times larger than the values offrom tunnel turbulence. This discrepancy in V' may also be related to the physical restraints thatthe tunnel walls impose on the flow, restraints that are not present in the atmosphere.
]_Jg.._L__.- Figures 17(d) and 18(d) show variations of the parameter ratio 13'/'/' withtunnel velocity. The least-squares line again has a very shallow positive slope, indicating, again,that the value of lYh' is very nearly constant with tunnel velocity. Corresponding values of 13'/_/from the Dryden and Von K_rfftn forms, 3 and 2.667, respectively, are about three times largerthan the values of fl'/_ from tunnel turbulence.
Fdllig.Rgllldl.- Figures 17(e) and 18(e) show variations of the exponent n with tunnelvelocity. The least-squares line is essentially horizontal, indicating that the value of n is constantwith tunnel velocity. Corresponding values of n from the Dryden and Von Kfirrn_n forms, 2 and1.833, respectively, are extremely close to the values of n from tunnel turbulence.
Normalized break frequency, fb." Figures 17(t) and 18(f) show variations of fb
with tunnel velocity. The least-squares line again has a very shallow positive slope, indicating,
again, that the value of fb is very nearly constant with tunnel velocity. Corresponding values of
fb from the Dryden and Von K_ndn forms, 1.732 and 1.345, respectively, are extremely close to
the values of fb from tunnel turbulence. From equation (11), for a constant normalized break
frequency and a constant value of L, the (unnormalized) break frequency will be proportional totunnel velocity.
Integral scale length. L.- Figures 17(g) and 18(g) showvariations of L with tunnelvelocity. The least-squares line has a very shallow positive slope, indicating that the value of L isvery nearly constant with tunnel velocity. Typical values of L from the Dryden and Von KSnnfmforms are 1000 and 2500, respectively. For atmospheric turbulence the quantity L is interpreted asthe average diameter of the largest eddies in the atmosphere (ref. 4). If a similar interpretation weremade for tunnel turbulence, the largest eddies could not be larger than the test section size.For tunnel turbulence, as indicated in figures 17(g) and 18(g), the value of L was about 4 feet,more than two orders of magnitude below the typical values for atmospheric turbulence, but, moreimportantly, smaller than the 16-foot test section size and therefore consistent with theinterpretation of integral scale length and eddy size.
All of these so called "defining" quantifies exhibit only small differences with measurementdirection, suggesting that the turbulence within the test section of the TDT may be isotropic, i.e.,
independent of direction.
CONCLUDING REMARKS
Preliminary measurements of the vertical and lateral velocity components of tunnelturbulence were obtained in the Langley Transonic Dynamics Tunnel test section using a constant-temperature anemometer equipped with a hot-film X-probe. For these tests air was the testmedium. Test conditions included tunnel velocities ranging from 100 to 500 fps at atmosphericpressure. Standard deviations of vertical and lateral turbulence velocity components weredetermined and power spectra were computed. Both components of turbulence generally increasedwith tunnel velocity. In terms of percentages of tunnel velocity, the intensity of the tunnel
10
turbulencerangedfrom about 0.2% to 0.8% for the vertical component, and ranged from about0.3% to about 0.6% for the lateral component. Unconstrained optimization was employed todetermine the values of parameters within simple analytical expressions for the power spectra.When data were discovered to be aliased, the spectral model form was modified to account for and"eliminate" the aliasing. Excellent agreement between the modified model and the measuredvelocity spectra was achieved. The parameters completely define the power spectral densityfunction of turbulence for each component of turbulence at each tunnel velocity. From theseparameters break frequency and integral scale length were determined at each test condition.These quantities were compared with those of Dryden and Von KLmafin atmospheric-turbulencepower spectra.
11
APPENDIX
THE ALIASED SPECTRAL MODEL
This appendix offers more information about the aliased spectral model, equation (4) in themain body of the paper:
Aiiased Spectrum Defined in Terms of Unaliased Spectrum .........
Assume that a random process exists whose (unaliased) power spectrum is expressed byequation (1) from the main body of the paper, repeated here as equation (A1)
1 + 13f2¢_(f) = a (A1)
(1+_2) n
The range of frequency, f, in equation (A1) is zero to infinity. When this equation isplotted in a log-log format, it has a shape as shown by the unaliased spectrum of figure A1.
Assume also that a sampled record of this random process (with Nyquist frequency, fN)has been obtained and that a power spectrum has been computed from the sampled record.Assume, further, that this computed power spectrum exhibits evidence of aliasing, notably a"curling up" at frequencies approaching fN. This aliased spectrum has a shape as shown by thealiased spectrum of figure A1
As shown in such references as 3 and 5, an aliased power spectrum, over its frequency
range of zero to fN contains all the power of the unaliased power specmam, over its fr_uencyrange of zero to inanity. The aliased power spectrum may be expressed as an infinite folded"
sum of spectral segments of the unaliased power spectrum. Equation (4) from the main body ofthe paper expresses this sum and is repeated here as equation (A2)
•,-, 1 +13(f + 2kfN) 2
0^ (f)= _ [1 + T(f + 2kf_)2]"
(A2)
for k = 0, -T-l, :r2, :r3 ....
The range of frequency, f, in equation (A2) is zero to fN.
Figure A2 contains a sketch illustrating the composition of an aliased spectrum in terms ofthe sum of the folded segments of its corresponding unaliased spectrum. For ease in visualizing asum, figure A2 is in linear-linear format. In the figure, the aliased and unaliased spectra are labeledand the folded segments are seen folding back and forth between zero and fN. While the sumactually includes an infinite number of segments, for purposes of illustration, only three segmentsare shown in the figure, corresponding to k=0, k=-l, and k=+l in equation (A2). Each segmenthas a bandwidth, or frequency range, equal to fN. The contribution to the sum from eachsuccessive segment becomes successively smaller. This fact raises the question: Recognizing thatthe 1000 Hz low-pass filter imposes an upper limit of 10 segments, how many folded spectral
segments are required to converge to the measured spectrum?
12
FigureA3 illustrates the results from a study that was performed to determine the numberof folded spectral segments to include in the optimization procedure. Figure A3 is a magnifiedview of the high-frequency portion of the power spectrum in figure 16(g), chosen because itcontains a significant amount of aliasing. The various dashed curves in the figure representincreasing numbers of spectral segments included in equation (A2). The lowest dashed curvecorresponds to k=-I in equation (A2) (or, the primary spectral segment plus one additional spectralsegmen0; the highest dashed curve corresponds to k=-5 (or, the primary plus nine additionalsegments). These two extremes correspond to upper limits of frequency of 2fN and 10fN,respectively. The upper limit of 10fN is seen to give the best agreement between the aliasedspectral model and the measured spectrum, and for this reason, 10f N was chosen as the upper limitfor all optimizations. In figure A3 the smooth solid line below the lowest dashed line is the
unaliased spectral model, corresponding to the aliased spectral model with upper limit of frequencyof 10fN.
Validation of Aiiased Spectral Model
To validate the procedure for "eliminating" aliasing, a numerical test was performed on aDryden power spectral density function deliberately aliased by creating a sampled analyticalautocorrelation function. For a theoretical and unaliased Dryden power spectrum, expressed in theform of equation (6), the values of lY, V', and n are 3, 1, and 2, respectively. For thisnumerical test, values of o, L and V were arbitrarily chosen to be 2, 4, and 400 respectively.Therefore, from equations (7), (8), and (9), the values of a, 13,and _, were 0.0800, 0.01184, and0.00395 respectively.
Using the optimization procedure on this deliberately aliased spectrum, the unconstrainedoptimizer determined the values of a, 13,"t, and n to be 0.0802, 0.01210, 0.00406, and 1.98,respectively. Because the largest difference between these values and the theoretical values wasonly 3%, this numerical test was judged to successfully validate the procedure.
ACKNOWLEDGMENTS
The authors wish to acknowledge the data reduction effort of Kurt M. Hitke of the
UNISYS Corporation and the helpful suggestions of Anthony S. Pototzky of the LockheedEngineering & Sciences Company.
REFERENCES
1. Lueptow, R. M.; Breuer, K. S.; and Haritonidis, J.H.: Computer-aided Calibration ofX-probes Using a Look-up Table. Experiments in Fluids 6, pp 115-118, Springer-Verlag,1988.
2. Nystrom, Lowell D.: Anemometry. Technical Bulletin TB5. TSI Incorporated, Oct, 1970.
3. Otnes, Robert K.; and Enochson, Loren: Applied Time Series Analysis. John Wiley andSons, Inc., 1978.
. Houbolt, John C.; Steiner, Roy; and Pratt, Kermit G.: Dynamic Response of Airplanes toAtmospheric Turbulence Including Flight Data on Input and Response. NASA TR-199,1964.
5. Bendat, Julius S.; and Piersol, Allan G.: Random Data. Second edition. John Wiley andSons, Inc., 1986.
13
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100
90
80
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50
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30
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i i
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it!!
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1
Tunnel velocity, 500 fpsI
O. I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Math number
1.1 1.2 1.3
Figure 9. Transonic Dynamics Tunnel operating boundary in air.Open circles denote test conditions.
23
3.5
2.5
>
,n 2c_
i.5
0>
(I.5
(1
Range cpitch an
stinggles
V=550
v---450fps
V=250fp$
fps
Fps
V=50 fps
//
I 1 t 1111 I111 IIII Illl I I _L_=L _. _J.___ _J____L__
0 11.5 1 1.5 2 2.5 3 3.5
Voltage for filament with positive attitude angle
Figure 10. X-probe calibration voltage grid.
24
This page left blank intentionally.
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25
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28
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°.,,_
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.....¢
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,4
o_
O. 1
Vehvcity
spectrum,(fps)2/Hz
{}.{)1
().iX) I
().()(X)I
1
• . !.H
....... !.....i
....... ;.....j
_J
!1
!i
I
iiii!ili::
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--, ,7
i!
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f _
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l! !........ ? " " f ii : i .... i...... _-..iiii i ! i
().!
...... i:i!!_,.._........_.......::.._..++._ ..................._....+.+.._..._.,...,............_......._..,..;.... ,:_i_i_?_:_i_:_:_:i_i:i::_i!:::!._
...................:_...+.+..__._._._............_......._.....,....,:.,:.,_........................_ ......._.................. i----.i.+-._----:.._._............!.......i.-.--_.... .i-i-,_,1_............_.......i,,-,.!....44._-........... :.... :-- _ ...!.--;.
_ Measured spectrum._-!.4.__............ ,.'....... _-.--.:,-.-
i i Unaliased spectral model :::.::::::::::::::::::::::::::::::::::::!._......... _.i-.:,.__............_.......i.....i-..._.
Ii i!ii i .............._----_--.;..i-- ..!+i ............ _...... _-_,i .........................
_ii_..........._ i_i_' _ '_+-i-+--_+_--_:_,_-_-.+.+_--,._.._._..._............_......._....,..........................._....i.... _._._..........................,:..... i-s-_..-i............i......*----_.---..................._....._..+.s.'_............i......._..---_.... _-_.-:,--_............_.......i,...-_....
i_!_;: /! "Y i i .!.i !....................._....,:..+._.............._......_....._.....
............. .......i...-.i-.-i..._........ i......._•.--',.... _.'.-'-._............_-......i..--.i....
?iil i ili i llil.................. •:--.--L..L..I..._. ,_ ............ !..... "...................... :-,-.;.-,:-.._..-_.....÷ ............ :.......... L:.._.. ,,'............ ;........ :-.-..:..._-.. 4-
'_ , ' .;.yyyy. ........ _-...._...i-.._.--_-÷+ ............ :...... : " +':"_• _............ _....... _-'"-i-"-_"
": : ..... : _N[J, ........ i -'---_ i _
I 10 1(X)
Frequency, Hz
(a) Tunnel velocity 100 fps (tab point 104).
Figure !5. Power spectral density functions of vertical component of tunnelturbulence.
30
0.I
Velocity
spectrum,
(rps)2/l-lz
0.O1
O.(Mll
O.(R_I
.................. t ......... i,.÷.4,
I
I
o
I
I
I
....................]?._.:b...:..,_.-_
: - ! i:j:i
! i :; i
_ii i............i.....................i........:"_'_-'_............i........................:........":.._._.._.............:.......................+......._...[.!........_ _._._................._.......i...!6..!..........._......
............i........._.._._,._...........i.......
I).i
............ .:'"';_;U: "":'"¢'"
+ i .............. .q .................i. '_ ...................i.............
: • ,::
....:,.._......._.: ..................!............_..
..: . ..:.,.,._ .................. .:............ ,..,.._.....:.._,_._..................._............_..
....................................._.....;.i.:..._................... _.......,.....÷ _÷i "i ......._....
...._...._.._.!."_.................._..............
....i.... i * i :_................!.............
....:......_..*.!..i...................!.......,.....
:
! I0
: : : ; , .
_: __,._T_q:_::-._
............_-...... !-..-.!..._---L.
............_......._....._..._.._..
............_......._....+..÷.+..
............i-...... _..,.._,.,-L4..
............_......_....+..+..!..
............_.......!.....!..._..._..
............ _....... _.....|.
............ _•...... _.,,,._..._..._,.
............_.......i....._•..$..L._ .--____._--.___:.!............i......_--._.-.N.-l-.i-I............i......_...._-..i.._.-
............i......_•_
............._...... _'"'_'"'i"i"
............. _...... _...._ ...... ;..
.............i......i....i..._.z......................_-i-i-i
............_.......__*h_l
,:I:il............ ._....... !...-._-.._..L.
.........................i_L
........................i'--'!"!"f'i-
..................i.... k.?.i..1..i.,
.......................bTTT_.
.................... _........ -;.--L-',-i.._"
...................-H-!-ltii ili!,
100
Frequency, Hz
(b) Tunnel velocity 200 fps (tab point 68).
_" " Figure 15. Continued.
31
ILl
Vch_ityspcclrum,(l'ps)2/I-Iz
0.01
().(X)I
O.(XX) I
...............i I i ................'..... :. ,,, ' " ..................i_,.,,i.,+, i _...i-._ '
lii!I • iii !! _!............... ; __-_-_............_......_--._ -_ ..........._.......i.--..i..i.,_- :._............:......._.-..._.,.i,. !........................
i i ! _i
F,'equency, Hz
(c) Tt, nncl velocity 200 fps (tab point 2(X)).
Figurc 15. Continued.
32
O.I
Velocity
spectrum,
(fps)2/Hz
0.01
II.O01
O.(}(X)i
!........... I ......
......... :. .,i
.......... 1 ...... I
.......... ,...... i
" ....... ! -. 1
; I
........i •I......... i ......
......... ! ....
, !
(1. I I !0 100
Frequency, Hz
(d) Tunnel velocity 250 fps (tab point 81).
- - - -Figure 15. Continued.
33
O.I
Velocityspectrum,(l'ps)2/tlz
0.()I
().(X)l
O.O(k) I
I
i iiiii !............ _ ......
i !
'I
Frequency, Hz
(c) Tunnel velocity 3(X) fps (tab point 94).
Figure 15. Continued.
34
+
.................-+i.,.................................._......i'.'!."h ............_......_....
............._......_+.: ...:..........._......_....
..............._......._..! .._............_......_.....
................_......._.._.....: ..........._......_....
•,.,................+......+.._................++.....+......................+.......i.+.+.....+ ............_ ....
............i..........1 I!_-i-...........i.......i.....velocity......i.......!i!............!.......!....
(fPs)21H_ .............i.....i! _!...........-
O.Ol ..........+i......................: i
O.(X) I
0.0001
==============================................ !.. ,.i,.+_l
............_. ,il Unaliased spectral model
............. L.._..._ Aliased spectral modeli !1
................. _ ....... i...:. .iA............ , ...... ;.-.-J... i-.4J..i ............................. +........ <..._. ...+............ <....... <.......................+......+..... _..+.'.+............................. i........ V+.+ "t't ............ i....... i"''''P,'"'+''''': +'; .............
................ +........_ +...i • .<.,, ........... i....... i....... ....I +"+'+'+..............................+.....I-..++.}. r.i.+...........i.......i-----_.....":..+..i.+............................ _....,-..i--.+.. I.:.: ............ + ...... +...+: .-+.+<..,>.....,
: t . .
-,- -4.-+- +--4....d .-;-:..... "-- '
(). I 1 10 100
Freqt,ency, Hz
(f) Tunnel Velocity 350 fps (tab point 115).
Figure 15. Continued.
• +,
,+4+-_.
,. <+,.+,,.<..+,,.,I--,,
,-.c..+,
• .+.¢.
..+.<.
_._+.+.
.<..+.
++;..t-
• ,t- .+,.
-.+o,I.
.¢,+.,.
--+-,t-
-+..r.
..+.+.
.< ....
. ,.+ .+.+
+++.-:,..
.... <.
.++....
,.++..+._
35
O.I
Velocity
spectrum,(fps)2/Hz
O.()l
().(X)!
O.(XX)I
iilitl!iiliii_iiiiiI_iI!i!iiiH!ii!!!!!!ii!iiii!i!iliii!ii_
uC,ai"i :i:c; :P;_ttlr,:lmodelF ..........
!! li! iiiittiiii!iii i!i!!l!iJiiIiiiiiiiii!ili!Yitiii
1).1 I 111
....... _.-.._-._.._..
....... i.-..-,_..A-.-!..:
.......i--"i'"+-'!-"
....... :_....._..... !
....... _....,: ..... !
....... L.-._ ..... :..
....... 7---¢ ..... !."
_.-...._..._--
...... W'"_"':._._............. _....... <........... ,._
......i--i .... i_! ............. ......_................
.......iiii!ii......!iii!i'.'..'.".'i"'.'-i'_'.'.i'_i'.'l.'.i_'Y,'.'".'.'.'!'_.'._i,'_!_'!"i'__]......i...+.._......._..............!.....!"_ i_" "I
..........i i!li_!_..........._.....i! _!_;I
I(X)
Frequency, Hz
(g) Tunncl velocity 400 fps (tab point 128).
Figure i 5. Continued.
36
1
0.1
VelocitySl_Ctrum,
(fps)2/Hz
0.01
0.001
O.(XX)I0.1 I
Frequency, Hz
10 100
(h) Tunnel vekxcity 450 fps (tab point 141).
Figure ! 5. Continued.
37
0.1
Vch_:ityspectrum,(fps)2/tlz
0.()1
O.(XX)I
::!
i ¸!1_
!!i!
__j_ Mcasu|'cd spectrum
Unaliased spectral model
Aliascd speclral model
• 4 .i...:..
().1 1
I............. '.. .......
i.............i.......
i............ ¢ ........
10
....Ti]
100
Frequency, Hz
(i) Tunnel velocity 5(X) fps (tab point 154).
Figure ! 5. Continued.
38
0.1
Velocityspectrum,(fps)2/Hz
0.01
O,(X) I
O.(XX) 1
! .... "----4- -
...........i ......t:1 t
! !
::::::::::::::::::::::::.......... 4" ...... ( .....
................... ....
.......... ÷ ...... ¢ .....
........... i ............
........... i ............
.......... _. ...... 4- ....
........... 4- ...... _ ........
...................... )..,
............i.......!.. _.
.......... i ...... i _-
.......... •_...... i-. -.i-..
.......... _....... i' "_."
............ ("...... !"-"_"q-'!" -.!-_ ............. _'...... _-.-.-"......]! Fq.4 "i............ i.......
........... i....... _'-"-b-'!"!-' -'!'_ ............. _'...... _.---':,...... i"!"_ "_............ i.......
............. _....... :.....:...:..:....:A.: ........... $ ...... ,i.....: ...... i"i"_' -i............ _.......
............._.......:.--.-"..:-.:-.--:-+:............._......_.--.-:...... i.-_--_
.............'.......".-..+.._._....:.*_............._......i..-.._...... i-.i.-_-_............_.......
....................!...--i...i..!...i-_i............."......_...,_.......... i............_......
.................... ,--.'.F.-!..'.". "!'÷i ............. )...... _----q--"
.................................. _ ............. L ....,[ ......... _............ (.......
.................. _...._-._..;.-_.-i-,_............!.......i-..-_.... _.............i.......
................... i.-..i.-_.._-._..i_............_,.......".-..._.... _.............i.......
.................. : ....... .",":"i ":':......................... :.....
_,_I_ Measured spectrum ......_.......
Unaliased spectral model
Aliased spectral model
.............,..... i.--.-i...... i..i-.: .i............!.......
............. i ...... _.-..._...... :..:.._. ...................
............. ) ...... _.....! ...... _...'.._ .......
............. ."....... b--.') ..... 4-..)+
............._.......i,.--_..... _.-_.i................................!...... !.,.,._..... ';-._-i....................
I 10 100
Frequency, Hz
(j) Tunnel velocity 500 fps (tab point 173).
Figure 15. Continued.
39
1 _-"; g I
..........._......;...-.:,-._..,i.-!.... i........... _...... i,.-.-:.._ .i._i.............. _...... _.....!. 4 ._.._....
........... ._...... _....._...i..._.._....
............ _...... _.....:..._.,.L.! .... i
........... _,...... _-....... _. _....
/............ _...... i---.-:.--_.--_.i..l. -!0.I
..........._......_.._-.._.!..:....[
Velocity i
;pectrum,(fps)2/Hz
-i--_............!......,_....
-i.-_............._......*.....i-i ! i
_=_:::i:::!::l:-:.-._............,_......",.....
...._--.-_.4..-.._.:-_............ _....... ,....
spectrum,
0.01
0.(}()I
O.(XX)I
...... r .... _ , !.,_
..... _..... _.,._
.... _...... _'-":" ", i i
............i......._'""_."__"_
,:........._.......!-'-'_'"i-'$'_..........._.......i....,_.,.i._-_..........._......_-,-i_.i-i
....... i....i? ........i_il............_......i....
¢1_1_ Measured spectrum
Unaliased spectral model
Aliased spectral model
i .......... ¢......
•i............. i......
().1 1 I() 100
Frequency, Hz
(k) Tunnel vch}city 5(}0 fps {tab point 196).
Figure 15. Concluded.
40
0.1
Velocity
spectrum,(fps)2/Hz
0.01
O.{R)I
o.{x )l
m,--m:/--
f o
1........... }.................
............ {............ +...
: i! .
} i :
i !............ 1............ +..
............ { ....... t.o.._...
.... --t.: i im............_......:.....:...
: 1
..........._..........i
........... :. ........ $..
. --! -L._°.......... !...........
p
......... ! ....... !,,,
..........i...........i.-......... !.......... _,.
..........i .........{-
: E
............ : ........... 4--............ ! ......... e......... 4, .... ;
F
.......... ,i. ...... !...:
.......... i.---
,..,_...:.4 :.
,..t..._ ._._.
• : i _'_
! i {{
O.1
Velocityspectrum,(fps)2/Hz J
0.01
0.001
O. O(X)1
........... + ...... 1' -' 'i"
...........- ......_., .i..
...........+......_-. -i--
,..+..+._,
.......... i iii ! E! [ !i : :
.......... Measured spectrum
Unaliased spectral model
...... i ......_ - _ _ Ahascd spectral model
I ilFi:i _ =_
_ i . i i ; i i i :: i_:: i i i i _ i !
l .......... _.......;._;, _,- ....... _.......i,,.._.,.i,.i...!,:'..i............"......"..... :............"........... i...i............ 4 ...... _.,,.,:.-, ; : _ ........ _....... :.....:-.:--:- .: ............ _ ...... _...... :..... _............ !"+
........... : ....... ;...,.i. .... _-i. : ........ .:...... L..i.-,4..i • 4 ........... :....... :..... i--":_"" ....... :'"+
.......... •, ......_. _.... _ _ ; ......... _..... i _ i _.... _.......... _ _............_................
.......... ._...... i.--.:-., " :-_ .......... i....... : ' ' • , 4 _............ _............. _--q-
........ :....... ;, "_. i ', : ............ :...... ; i i............. _.......... 4-4.
..........._.... i i..... . ._ii+ : _ i _ ! .....! t
0.1 I 10 100
Frequency, Hz
(b) Tunnel velocity 15(1 fps (tab point 217).
Figure 16. Continued.
42
O. I
Velt_ity
sl_ctmm,(fps)2/Hz
0.01
0.001
O.(R_I
Frequency, Hz
(c) Tunnel velocity 200 fps (tab point 216).
Figure 16. Continued.
43
17,-'--
0.1 .........
Velocity iiiiiiiiiii
spectrum,(fps)2/Hz ........
0.01 .........
O.(X)! iiiiiiiill
O.O(X) 1 .....
......+.... _'-i""+!'i............_"......_......."'"""
...... _..... !.................... %...... _....... ,...:....
......+.... ;.+ -i.i.i............+......i...............
......_....,.i-.,.i.i-!............*......_..............
.....i.........i ..!.i.i............_......._......4--÷+i iil
......'_.... TI!:I.._!.!.L.:.......,:......._.... "'*''_"
......+.........i'---_'i'!............._......_......._'-÷':-
......:_......._..,._+'_............J,......_......._.".:.
......_.......... LL_............:........_.....i...._..+.:.
.... :........................... >.
1
..... + ....
..... )e ....
...... t" ....
_I_ Measured spectrum
Unaliased spectral model
Aliascd spectral model
! ili
(). I I 10
i---_-q-"............... !...... _..-.,_.....i.-.-%._..............._.......L-.._-..-!I..._.-L_.,._.............:.......i....._....i
i..._.,:..!...- ............ i ...... -:,.---_.--:
I...L÷._..._ ............ _...... ._.._._....i
i..- .':'- .-_ ...................... :'..--_ ...... i
i.,,:._..:...: ............ :....... L...._..,.:-,
i.._...................._......._,...,_,...i..! ii i............................
............!......._...._.-'-i
I00
4-_-i
-¢--..I
.'.-._-I
-'., -,-I
-._-.-:-_
..i.e..t
Frequency, Hz
(d) Tunnel velocity 25(i) fps (tab point 215).
Figure 16. Continued.
44
O.!
Velocity
Sl_Ctmm,(fps)2/Hz
O.Ol
0.001
O.(X)O!
- _ i J,
........... i........ ,i----.i-.
..........._......._.....:..
...........i.......i.-,-_-
...........i......._-...i..
...........i.......i-...-_..
...........i.......i..-+.
........................ ) ..
........... _....... ÷.....)..
........ : ....... L..,_..
........... !-...... _- ,.i,.,
............ :...... ¢" "i""
........... i ....... L...L.
....... t--4 -I
............!.......!....4.-
...........i......._..-..}.-............ _,...... i.,-.,!-..
.......... i ...... i"" ")-
.........._.......i...;.
........... ¢ ..... i..'"i-."
..........._......_...+..
•*;-'.;"!.............. i....... _...._..._.4. ..i.i-............ !....... !-----;..... 4.-i.!..i- ............ !.......... ,---_--_--_-: -..;._.4.4..,.'.: .............. :....... i-...4-.4..i. ..i-i............. "....... i...--i ..... .i...i.!..i ............. i.......... _...-i..i.-,.4 .............................. ...i..4-..i._._i.............._......___+ '_............_........_"_....__"_............._.........._i__":'"_""""'"''""'":"_":'.._;.:.............._......._..:..._._.•_:............!......._....4....._.._.i-4............_..........i-..-i-.,-.'.'..i...._..._.i.......i........}.;..;._i..............i......._.,+._i_............,......._.-_....._._._.............i..........i+,.,...................................i..:"i'
, , : : :
-i..._.: .............. }....... ;..-.i...,_--;- ..!4 ............ i....... !-..-4 ..... .i..4-i..i. ........... !.......... i-.--;--_.-_.,,................................. ],.¢-_.-
.i._.._ .................... ;....i-.-_.,:)...i, ............ !....... ;.-.-4 ..... *.,i.i- ._............. :-.......... _--.-_...... _,.i ...................... :........ _.._.,_.
-(--÷.i .............. .'........ ).,--¢.-_.-). ..!._ ............ :....... _-----_..... +..).i.._ ............. :.......... _-...).- -.}._.i-: ............ :....... :........ ¢.+--_-, ._-: ............ ;....... _ ,--i...$.-;. ..:i ............ "....... i.-...; ..... .L.LI..i ............. _.......... ,i-..-,....;.i ._.-:............ .."....... i........ {"_."i"
.... ;-,., .-¢-
._._._............._......._........._-.!.._i............._......_.....i.....i..i...L.._............_.......i ....i-.i-.i.
............... i...i....i..is..,............_......s........r'_v
• i..,;.: ............... _....... i....., ,.;.,L..,'...:,i. ............ .; ....=_....4 ..... _...L_.., ............. i.. $.-.L- .-i.._.i.i ............ i....... .:........ _..,i...i..! : ......._....:.'!'+": : ....._ _......._-,;,._-..... •- -
-._* ........................'.-.,...*..:...:.._....................;.--..._.....*..,.-._.........................._""i............i............_..._.+.:.• :--:. _............. _....... :..-..:-..:-.:-..-:-,': ............ ->...... (..--._..... i..!-,). ";............ _.......... ".... ")')............ ) ...... "_......... .:-'i'.i-i--+-_............. _.......i--,-i-.-+--i.--i..:.;............_......."-..-.i.....+..i+-i............._....... " " '
.... }...: ............. ; ...... .;......... L,i..i.
..........................."'_v'_'r""" ...........................i.+-i.
i , , ,I -- -- Unaliascd spectral model l i li......................_....._...L....i.i............i.......i........i.4..i.--- Aliased spectral mode :.::.::.!:!!.!:.........,-..-:.....,............:.......................:.'.:.:.:....._..._...._-._._.r............_......_.........i..i..i.
•-_--i - A --i,';- ....... -L---" ...... "--i-_
......................... i:: iltiIi ......"..........................."• -_._;
0.1 I I() I(X)
Frequency, Hz
(e) Tunnel velocity 300 fps (tab point 214).
Figure 16. Continued.
45
O. !
Velocity
spectrum,(fps)2/Hz
0.01
0.001
0.(_)01
Frequency, Hz
(f) Tunnel velocity 350 fps (tab point 213).
Figure 16. Continued.
46
O.1
Velocity
spectrum,
(fps)2/Hz
0.1)!
O.(X) I
0.0001
................_........L._ •.,.'.4.x............;.......:...__...
.................i........iI.i.!.*.........................i-..
.................. i........ i...;.. ,;.,_.4............. i....... !'""_'"'
1
........... 1 ....... ! .....
........... , ....... ° .....1........... ....... ! .....
.......... q....... _ .....
........... I ...... ,t- .....
........... F ..... _......
! ....
.........i._............_......."--'i"+':-'i-*_
............................i"'"i"'i"_"i'_....................:............,:,.
..._.,.._. _............ _............ L..._....'..
.._.-.-:.. ,t............ _....... i-'-'-!'-"_'-" "!"|-._.,..,._............_.......i....-_-..._--_..b,
............................ i....!....!.._.._:._._
......_........................_...._...._.._.._..+._
i ii i.......... :............ :....... L..._.,..'...._..;.
..... •- ................ _....... _'"'_-'"i'- 1ilt'-4--•
........ _............_.......i.....i...._..--i.:_
.........i............i......._.-.-,:-.--i----4.-i-
...................._.......iiii_
..... _..... :............ :....... _.,..i,,,,:,- --_--F
.....iIO.I I I0 I00
Frequency, Hz
(g) Tunnel velocity 4(X) fps (tab point 212).
Figure 16. Continued.
47
O.1
Velocity
spectrum,(fps)2lHz
O.Ol
O.(X)l
(),(XX)I
.... t
I........... I
............. i i-i ..............•.......:'1: ............:..........._+ _+............. _....... _...-.,_--._..... "-_ ............. ; ...... _ .--!...._.--.:--_.... _............ i........... _---i-- ---:--i-
............... b..i. _ :, ;_.; ............ _...... i.. _..... i,. '.,.:.............. :,....... b.--_----_.... ;-: ............. _....... _--.-J.- ,b,:.._..... :,............ :............ _...i...._..:.
......... _..... _ ,_ ................... _...... _....... _..:..:. . ........... _....... _-..._..,_ .... _.¢. ............ _....... _.....___..¢,._...._ ............ _....... _....!..._.._..
............ _ '_* ..........i'i'......._ _...............! [ ) !_tj_!i_f.!.......i ii i!H............i.......i !+ii .... !............_......4 i} ii -
ILl ! !0 I(X)
Frcclucncy, Hz
(h) Tunnel velocity 450 fps (tab point 2()5).
Figure 16. Continued.
48
O. I
Velocity
spectrum,(fps)2/Hz
0.01
().0() I
().(XX)I
100
__~ i.
....... ! ....
...... ,4- ....
1
1
...... ,4- ....
...... ,t ....
--.+.H_4---*.-*.--t.*4_,._ii'"..._. L._.;.I
i_lil
...$.._...._.,:M
....i--i--_-+l.'i.-i"_.+l._..-:_- _-._
"ii'il
"L_
.--i.q.-_--.-,
...._..?.._._._
...o...._.._._.,_
:::.:_.:.-_:::_:......,kt..._.._.,....,
"'TT"...{.._..
•..i..i.-I -_.1{!':1
Frequency, Hz
(i) "Funnel velocity 450 fps (tab point 211).
Figure 16. Continued.
49
O. ! I I0 1O0
Frequency, Hz
(j) Tunnel velocity 500 fps (tab point 204).
Figure 16. Concluded.
50
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55
Power
spectrum
z
Aliased spectrum(eq. A2)
p-- Unaliased
L _ n,,*_l ¢ , , ,,,HI t
fN
Frequency
Figure A I. Aliascd aml unaiia_d spectral Irclationships.
i i i till|
56
o
|
II
z_
57
0.03
N
>
0.02 ...i........
O.Ol
0.009 '_ ........".......
0.008 ........_.......i
0.007 -----_
0.006
I
0.005
i8 I0
Aliased spectral model to 10OO Hz
Measured spectrum
901)
800
700 Hz
i 600
!
500
400 Hz"
Aliased spectral model to 200 HzI
E
20
1Unaliased spectral modelbased on 1000 Hz
t _ !
50
Frequency, Hzz
=
Figure A3. Enlarged high-frequency Segment of spectrum.
lOO
58
Form Approved
REPORT DOCUMENTATION PAGE oM8Noo7o4-o188
PuDirC reO(}r_it_ Dut_3en for thls ccliect_on Of infcr_at#o_ .S _tlrr_ate_ [o _.erage _ hour De" r_.3rse, _nc_L;alng the _.=*_ge for revlPw.n_ instt.JctJons, sear;h_r_ ex,5%_n_ 5_[3 _.c,_r¢_'_
I gathering 3no maintaining %he _lata neeo.e_, and cOrnple_lng anO rev,ewmg :he col_e_cn of mfc'_-_a_._'_ S_nd :2rnments rec)a-dm_ th_s bJaen est;matc :" in, :,t'_r as c)ec_ Of th'_coliect on of nforrnat on nc ud n_ $ugge,_t=on_ tor r(_uctng th_s Outoen tc _asratncjton Heacla_arlers Ser,_ce% _rteC_ora_e TOt l_f-_'f_&tlOr_ O_:l_ra[_Or_ and ned-r%, I_ __ ;e! ersJr
Daw_ H_ghwa_, 5ude _2_ Admgton, _',_. 22202-4302. _nc_ to the Office O_ Mar_ageme _', ,_n0 Buclget oaDe_,v_rk Red_ on Prote:t (O?_a.O 88 , _ a_h:'_ton, __C 20503
I. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
March 1993 Technical Memorandum
4. TITLE AND SUBTITLE S. FUNDING NUMBERS
Characteristics of Vertical and Lateral Tunnel Turbulence
Measured in Air in the Langley Transonic Dynamics Tunnel WU 505-63-50-15
6. AUTHOR(S)
Robert K. Sleeper, Donald F. Keller, Boyd Perry I11,and Maynard C. Sandford
7. PERFORMING ORGAN'IZATION NAME(S) AND ADDRESS(ES)
NASA Langley Research CenterHampton, VA 23681-0001
9. SPONSORING/MONITORING AGENCY NAME(S) ANI_"ADDRESS(ES)
National Aeronautics and Space AdministrationWashington, DC 20546-0001
8. PERFORMING ORGANIZATIONREPORT NUMBER
10. SPONSORING / MONITORINGAGENCY REPORT NUMBER
NASA TM-107734
11. SUPPLEMENTARY NOTES
Similar material to be presented at the Forum on Fluid Measurements and Instrumentation to beheld during the AS/vIE 3rd International Symposium on Thermal Anemometry, June 20-24, 1993,in Washington, DC.
12a, DISTRIBUTION ,'AVAILABILITY STATEMENT 12b DISTRIBUTION CODE
Unclassified - Unlimited
Subject Category 09
13. ABSTRACT (Maximum 200 words)
Preliminary measurements of the vertical and lateral velocity components of tunnel turbulencewere obtained in the Langley Transonic Dynamics Tunnel test section using a constant-temperature anemometer equipped with a hot-film X-probe. For these tests air was the testmedium. Test conditions included tunnel velocities ranging from 100 to 500 fps at atmosphericpressure. Standard deviations of turbulence velocities were determined and power spectra werecomputed. Unconstrained optimizati9 n was employed to determine parameter values of a generalspectral model of a form similar to that used to describe atmospheric turbulence. These para-meters, and others (notably break frequency and integral scale length) were determined at each testcondition and compared with those of Dryden and Von K_,'rn_m atmospheric turbulence spectra.When data were discovered to be aliased, the spectral model was modified to account for and"eliminate" the aliasing.
14. SUBJECTTERMS
Wind-tunnel turbulence; Transonic Dynamics Tunnel; turbulence measurementsturbulence spectra; turbulence velocity; vertical and lateral turbulencecomponents; hot-film anemometers
J7. SECURITYCLASSIFICATION18 SECURITYCLASSIFICATION19. SECURITYCLASSIFICATIONOFREPORT OFTHISPAGE OFABSTRACT
NSN 7540-01-280-5500
15. NUMBER OF PAGES
5916. PRICE CODE
A0420. LIMITATION OF ABSTRACT
Unclassified UnclassifiedStandard Form 298 (Rev 2-89)Prescrd:)e_ by ANSi 5tcl l]g-I82gB-_02
