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AIRFOIL DRAG BY WAKE SURVEY USING LDV 1 Purpose This experiment introduces the student to the use of Laser Doppler Velocimetry (LDV) as a means of measuring air flow velocities. The section drag of a NACA 0012 airfoil is determined from velocity measurements obtained in the airfoil wake. 2 Apparatus (1) .5 m x .7 m wind tunnel (max velocity 20 m/s) (2) NACA 0015 airfoil (0.2 m chord, 0.7 m span) (3) Betz manometer (4) Pitot tube (5) DISA LDV optics (6) Spectra Physics 124B 15 mW laser (632.8 nm) (7) DISA 55N20 LDV frequency tracker (8) TSI atomizer using 50cs silicone oil (9) XYZ LDV traversing system (10) Computer data reduction program 1

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AIRFOIL DRAG BY WAKE SURVEY USING LDV

1 Purpose

This experiment introduces the student to the use of Laser Doppler Velocimetry (LDV) as a means ofmeasuring air flow velocities. The section drag of a NACA 0012 airfoil is determined from velocitymeasurements obtained in the airfoil wake.

2 Apparatus

(1) .5 m x .7 m wind tunnel (max velocity 20 m/s)

(2) NACA 0015 airfoil (0.2 m chord, 0.7 m span)

(3) Betz manometer

(4) Pitot tube

(5) DISA LDV optics

(6) Spectra Physics 124B 15 mW laser (632.8 nm)

(7) DISA 55N20 LDV frequency tracker

(8) TSI atomizer using 50cs silicone oil

(9) XYZ LDV traversing system

(10) Computer data reduction program

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3 Notation

A wing area (m2)b initial laser beam radius (m)bo minimum laser beam radius at lens focus (m)c airfoil chord length (m)Cd drag coefficientda elemental area in wake survey plane (m2)d drag force per unit spanf focal length of primary lens (m)fo Doppler frequency (Hz)I detected signal amplitude (V)l distance across survey plane (m)r seed particle radius (m)s airfoil span (m)v seed particle velocity (instantaneous flow velocity) (m/s)U wake velocity (m/s)Uo upstream flow velocity (m/s)α Mie scatter size parameter/angle of attack (degs)δy fringe separation (m)θ intersection angle of laser beamsλ laser wavelength (632.8 nm for He Ne laser)ρ air density at NTP (1.225 kg/m3)τ Doppler period (s)

4 Theory

4.1 Introduction

The profile drag of a two-dimensional airfoil is the sum of the form drag due to boundary layer sep-aration (pressure drag), and the skin friction drag. Usually the profile drag is determined from forcemeasurements made using a mechanical balance attached to the model. In the two-dimensional case(where the airfoil spans the tunnel - wall to wall), the profile drag may also be determined from mo-mentum considerations by comparing the velocity ahead of the model with that in its wake; this methodis used here and presupposes the flow is incompressible.

Momentum changes can be derived from velocities obtained from a pressure rake or a hot wire surveyacross the wake. Both these techniques are compromised because they require the insertion of a phys-ical body into the flow, resulting in a disturbance of the velocity field. In addition these instrumentsrequire auxiliary calibration with inevitable loss in accuracy.

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The laser Doppler method for measuring flow velocities is based only on geometrical parameters, whichare readily determined, and hence requires no corroborating calibration. With commercially availableinstrumentation flow velocities from 1.5 mm/s to 4000 m/s can be measured with a spatial resolutionof ≤1 mm3. Photon impact provides the only possible flow perturbation and this is negligible for allcurrent systems. Optical access is of course mandatory, either by direct transmission of the laser beamsor via a monomode fiber optic link.

4.2 Derivation of Cd from Wake Survey Data

Consider the two-dimensional wing in a steady, non-turbulent, incompressible flow with an incidentvelocityVo, Fig. 1.

The air that passes over the airfoil suffers a loss of momentum and this loss is related to the profile dragper unit spand as follows:

d =1

s

[Mass

sec× (change in velocity)

](1)

d =1

s

∫ ∫ρV da(Vo − V ) (2)

In Eq. 2,V is the wake velocity at the elemental areada in the plane which is perpendicular to the airstream. Integration is carried out over the entire plane.

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The drag coefficientCd is obtained from Eq. 2 thus:

d =1

2ρV 2

o cCd (3)

Cd =2d

ρcV 2o

(4)

Cd =2

scV 2o

∫ ∫V (Vo − V )dA (5)

Since the airflow is two dimensional, the span-wise integration does not depend on the integrand.If da = dl × ds then

∫ ∫da = s

∫dl wheredl is a differential length vertically across the wake,

perpendicular to the span direction of the wing:

Cd =2

cV 2o

∫l

V (Vo − V )dl (6)

For numerical integration purposes Eq. 6 may be approximated by:

Cd ≈2

cV 2o

∑i

Vi(Vo − Vi)∆li (7)

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4.3 Experimental Drag Data

The shape of the wake velocity profile is a function of the survey plane location as indicated in Fig. 2(taken from Bairstow, [1]):

Bairstow also cites experimental evidence indicating that Eq. 6 may be used to obtain accurate (to±2%) estimates ofCd for survey plane locations from .042c to .98c behind the trailing edge of the airfoil(at zero angle of attack).

For the Aerospace Laboratory experiment, using the notating of Fig. 2, the wake velocity equals thefree stream velocity for n/c≤ 0.25, therefore traverses of± 5 cm normal to the trailing edge shouldprove adequate for good survey data if the airfoil is used at small attack angles.

It is difficult to estimate the total drag of an airfoil accurately from purely theoretical considerations dueto variations in skin friction and air stream turbulence. The NACA 0012 airfoil used for this experimenthas a smooth Mylar finish promoting the formation of an attached boundary layer; therefore a first order

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estimate ofCd may be obtained using Fig. 3 (Batchelor, [2]).

Figure 3

Additional information on wing characteristics may be found in a text describing NACA airfoils byAbbott and Von Doenhoff, [3], from which Fig. 4 has been extracted. An excellent catalog of lowReynolds number data is available, for reference only, in the Aerospace Laboratory [4]. The bestavailable text for descriptions of wind tunnel testing techniques is Pope, [5].

Figure 4

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4.4 The Laser Doppler Method

The description of the laser Doppler technique given here is necessarily brief and simplified; onlythe pertinent features of the method are described so that the student may grasp the fundamentals.Because the method is contemporary and has such great potential for use in flow diagnostics, studentsare encouraged to read from some of the references cited. Several copies of the text by Durstet. al.areavailable for short term loans from the laboratory.

The Dual Beam or Differential Doppler system is used for the flow measurements in this experiment;it differs from the Reference Beam mode in providing a real fringe pattern in the probe volume orobservation region (where the beams intersect), and the phenomenological interpretation is easier tounderstand. In fact there is a real or virtual fringe pattern formed in either the reference or dual beamsystem, thus the explanation offered here serves as an interpretation for both operating modes.

Figure 5. Basic LDV optical system (differential mode)

In Fig. 5a, two equal intensity intersecting beams derived from the same laser are made to intersectforming an approximately ellipsoidal volume which will contain interference fringes perpendicular tothe plane of the figure and throughout the region common to the two beams.

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A particle (usually smaller than the fringe spacingδy) will scatter light as it traverses the fringe volume.For an isotropic scatterer, the scattered radiation may be observed from any direction and, for a particlemoving normal to the fringes and through the center of the probe volume, will resemble the waveformshown in Fig. 5c.

The intensity profile of the overlapping beams (usually Gaussian for a TEM laser beam) determines theshape of the outer envelope in Fig. 5c and the modulation depth is a function of the fringe contrast andthe particle size. If the fringe spacing is known, then the vector component of the particle’s velocitynormal to the fringes can be determined from the modulation frequency.

It should be noted that a directional ambiguity exists with the laser Doppler system depicted in Fig. 5,since the Doppler scatter signal alone contains insufficient information to determine the propagationdirection of the scattering particle. This uncertainty can be removed by several techniques which givethe sense of the flow velocity while retaining all the features just described. Usually the directionalambiguity is removed by using a Bragg acoustic modulator or a rotating diffraction grating to impart afrequency bias to one of the beams. This bias - much higher than the maximumfD anticipated - resultsin a fringe pattern that moves continuously in one direction. The Doppler frequency then observed willbe less for a particle moving in the same sense as the fringe motion and vice versa.

Some useful parameters which relate to the LDV geometry illustrated in Fig. 5 are given below:

Fringe spacing:

δy =λ

2sinθ2

(8)

Doppler frequency:

fD =2vsinθ

2

λ(9)

Focus diameter at the1/e2 intensity level:

2bo =2fλ

πb(10)

Focal volume dimension at the1/e2 intensity level:

∆x =bo

sinθ2

(11)

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∆y =bo

cosθ2

(12)

∆z = 2bo (13)

Fringe visibility:

V =Imax − Imin

Imax + Imin

(14)

4.5 Experiment LDV System

Figure 6. LDV arrangement

The optical arrangement employed for measurements in the Aerospace Laboratory 50× 70 cm windtunnel is shown in Fig. 6. The LDV is configured to operate in the forward scatter mode, i.e., thescattered radiation is detected by ‘looking’ into the oncoming laser beams.

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Small diameter scatter particles must be used to follow the tunnel flow faithfully; only a seed with suit-able size and buoyancy is adequate for monitoring high turbulence velocities or any rapidly changingflow perturbation. The TSI seed generator uses high pressure air to produce silicone oil droplets with adiameter dispersion centered around 1-2µm. This particle size results in a maximum system frequencyresponse of about 10 kHz. Because the oil evaporates very slowly only minute quantities are required,the closed circuit tunnel permitting continuous recirculation of the seed.

Figure 7

The polar distribution and polarization of the scattered light are functions of the seed refractive index, itssize and the wavelength of the exciting radiation. Figure 7 shows some polar scatter profiles for variousvalues of the size parameter (α = 2πr/λ), wherer is the particle radius. Becauseα is approximately5 for the current experiment the scattered radiation will be predominately in the 180o, or forward,direction.

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In general the seed diameter should be less than the fringe spacing to ensure maximum signal modula-tion depth and an optimum signal-to-noise ratio.

4.6 Detection and Processing of the Scattered Signal

The forward scattered radiation is detected by the photomultiplier in Fig. 6 and then low pass filtered toremove the ‘pedestal’ component of the composite waveform shown in Fig. 5. A DISA 55N20 tracker(similar to a phase lock loop) is subsequently used to provide a digital output which is proportionalto fD. The particle (viz flow) velocity is readily obtained by applying the appropriate normalizationfactor derived from Eq. 9. The tracker has the capability of adjustment so that the flow velocity couldbe displayed directly, but this mode will not be used in this experiment for the reason stated below.

The current state of the art for Doppler signal processing equipment is such that electrical noise ofquantum (shot) or thermal (Johnson) origin, is always present along with the actual Doppler scatteringsignal. Usually the signal-to-noise ratio (S/N) is sufficiently large for the tracker to lock on to theDoppler signal. However, in situations where the S/N ratio is marginal, the tracker may be triggered bynoise and present a spurious output. The tracker must always therefore be used with discretion since itis imperative that its output unequivocally correspond to the Doppler frequency being sampled.

A good technique for ensuring that only viable Doppler signals are being processed is to visuallymonitor the detector signals as they exit from the low pass filter - a high speed storage oscilloscope isprovided for this purpose.

5 Experimental Procedure

5.1

(a) Remove the airfoil from the test section.

(b) With the tunnel set at its slowest setting (5m/s), take simultaneous readings with the LDV and thepitot tube.

(c) Repeat (b) for a number of flow velocity settings, up to the maximum tunnel speed. Record sufficientdata to ensure that a valid statistical comparison can be made between the two methods.

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5.2

(a) Set the tunnel flow to approximately 10 m/s.

(b) Install the airfoil section in the test section (α = 0 deg).

(c) Position the LDV probe volume at the same height as the airfoil’s horizontal chord line and 15 cmfrom its trailing edge.

(d) Record the Doppler frequencies over a vertical traverse that encompasses the whole wake (2 mmincrements are adequate). Always use discretion when interpreting the tracker output (see Sec. 4.6).

(e) Rough plot and examine your data, additional measurements should be taken if required to suffi-ciently define the curve — this is a good experimental procedure which should be employed wheneverpossible. There will be variations in the Doppler frequency at each height setting; you should recordthe maximum and minimum values as well as the mean; also plot the upper and lower bounds for yourreport presentation.

(f) Repeat these procedures with the airfoil set toα = 8 degs.

5.3

The tunnel velocity (without the airfoil inserted) is constant for the traverse ranges employed; youshould check that this is so by suitable measurements on an empty test section.

DO NOT LOOK DIRECTLY INTO THE LASER BEAM

DO NOT ADD SEED UNLESS YOU HAVE RECEIVED INSTRUCTIONS

DO NOT CHANGE THE PHOTOMULTIPLIER H.T. SETTING

6 Presentation of Results

(a) Plot and discuss the velocity relationship between the manometer and the LDV. Is the correlationcoefficient the most suitable parameter for evaluating the agreement between the two techniques? Ifthe correlation coefficient was .9999998 how would you present the results to illustrate the differencesbetween the two techniques?

(b) Plot your wake surveys, append error bars to indicate the observational scatter. State the Reynolds

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number. Comment on the rationale of data smoothing and its justification.

(c) Using the raw frequency information calculateCd for the upper and lower bounds of your data forboth α = 0 and 8 degs. You may count squares, integrate numerically or use any other method, butdetail your procedure and estimate the errors incurred.

(d) Comment on all sources of error you perceive in the experiment; some areas you may wish toconsider are:

(i) Do boundary layer effects contribute significantly to errors in your results?(ii) Can meaningful drag measurements be obtained from a wake survey conducted when the

airfoil is near stall?(iii) Suggest two methods for determining the fringe spacing in the focal volume? — This is

obviously a key parameter in the measurement accuracy of the technique.(iv) Does the seed size, its density and concentration affect the results in this experiment?

When would these parameters be significant?(v) What type of averaging should be applied to obtain the ‘correct’ mean frequency at each

height? Think carefully and consider the origin of the scatter infD.(vi) Comment on other possible applications of the LDV technique. Make your discussions

BRIEF. It is more important here that you recognize the application potential in a varietyof fields than discuss any one area in great detail.

7 Preparation

(1) There is considerable scatter in the drag data for the NACA 0015 whenα ≥ 10 degs (see Appendix).What is the most likely reason for this behavior?

(2) Attempts have been made to use LDV on board aircraft for the detection of CAT (Clear Air Turbu-lence). Suggest as many reasons as you can why this is a difficult application for the technique.

8 References and Bibliography

1. Bairstow, L.,Applied Aerodynamics,Longmans Green (1946).

2. Batchelor, G. K.,an Introduction to Fluid Dynamics,Cambridge University Press (1979).

3. Abbott, I. H., and Von Doenhoff, A. E.,Theory of Wing Sections,Dover Publications (1959).

4. Miley, S. J.,A Catalog of Low Reynolds Number Airfoil Data for Wind Turbine Applications,NTISDE 82-021712 (1982).

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5. Pope, A.,Wind Tunnel Testing,John Wiley and Sons (1954).

Some LDV Information Sources

(See the instructor for the SHORT term loan of some useful material.)

Drain, L. E.,The Laser Doppler Technique,John Wiley, Toronto (1980).

Durst, F., Melling, A., and Whitelaw, J. H.,Principles and Practices of Laser Doppler anemometry,Academic Press, Toronto, 2nd Ed. (1981).

Schlichting, H.,Boundary Layer Theory,McGraw-Hill, 7th Ed. (1979).

Laser Velocimetry Systems,Thermo Systems, Box 43394, St. Paul, MN 55164, USA.

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APPENDIX

The optical constants for the Aerolab LDV system are:

Beam interaction angleθ = 5.648 degreesFocal length f = 0.593 mLaser wavelengthλ = 632.8 nm

Conversion: V (in m/s) = 6.422× frequency (in MHz)

Below is data collected by students in this laboratory for the drag coefficient on the NACA 0015 airfoilas a function of angle of attack.

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