Airfoil Drag by Wake Survey Using Ldv

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 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 coefficient da elemental area in wake survey plane (m2) d drag force per unit span f 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 beams λ 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 separation (pressure drag), and the skin friction drag. Usually the profile drag is determined from force measurements 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 momentum considerations by comparing the velocity ahead of the model with that in its wake; this method is used here and presupposes the flow is incompressible.

Momentum changes can be derived from velocities obtained from a pressure rake or a hot wire survey across 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 instruments require auxiliary calibration with inevitable loss in accuracy.

2 The laser Doppler method for measuring flow velocities is based only on geometrical parameters, which are readily determined, and hence requires no corroborating calibration. With commercially available instrumentation flow velocities from 1.5 mm/s to 4000 m/s can be measured with a spatial resolution of ≤1 mm3. Photon impact provides the only possible flow perturbation and this is negligible for all current systems. Optical access is of course mandatory, either by direct transmission of the laser beams or 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 incident velocity Vo, Fig. 1.

The air that passes over the airfoil suffers a loss of momentum and this loss is related to the proﬁle drag per unit span d as follows:

1 Mass d = × (change in velocity) (1) s sec

1 ZZ d = ρV da(V − V ) (2) s o

In Eq. 2, V is the wake velocity at the elemental area da in the plane which is perpendicular to the air stream. Integration is carried out over the entire plane.

3 The drag coefﬁcient Cd is obtained from Eq. 2 thus:

1 d = ρV 2cC (3) 2 o d

2d Cd = 2 (4) ρcVo

2 ZZ Cd = 2 V (Vo − V )dA (5) scVo

Since the airﬂow is two dimensional, the span-wise integration does not depend on the integrand. If da = dl × ds then RR da = s R dl where dl is a differential length vertically across the wake, perpendicular to the span direction of the wing:

2 Z Cd = 2 V (Vo − V )dl (6) cVo l

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

2 X C ≈ V (V − V )∆l (7) d cV 2 i o i i o i

4 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 of Cd 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 the free stream velocity for n/c ≤ 0.25, therefore traverses of ± 5 cm normal to the trailing edge should prove 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 due to variations in skin friction and air stream turbulence. The NACA 0012 airfoil used for this experiment has a smooth Mylar finish promoting the formation of an attached boundary layer; therefore a first order

5 estimate of Cd may be obtained using Fig. 3 (Batchelor, [2]).

Figure 3

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

Figure 4

6 4.4 The Laser Doppler Method

The description of the laser Doppler technique given here is necessarily brief and simpliﬁed; only the 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, students are encouraged to read from some of the references cited. Several copies of the text by Durst et. al. are available 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 or observation region (where the beams intersect), and the phenomenological interpretation is easier to understand. In fact there is a real or virtual fringe pattern formed in either the reference or dual beam system, 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 intersect forming an approximately ellipsoidal volume which will contain interference fringes perpendicular to the plane of the ﬁgure and throughout the region common to the two beams.

7 A particle (usually smaller than the fringe spacing δy) 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 particle moving normal to the fringes and through the center of the probe volume, will resemble the waveform shown in Fig. 5c.

The intensity proﬁle of the overlapping beams (usually Gaussian for a TEM laser beam) determines the shape of the outer envelope in Fig. 5c and the modulation depth is a function of the fringe contrast and the particle size. If the fringe spacing is known, then the vector component of the particle’s velocity normal 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 propagation direction of the scattering particle. This uncertainty can be removed by several techniques which give the sense of the ﬂow velocity while retaining all the features just described. Usually the directional ambiguity is removed by using a Bragg acoustic modulator or a rotating diffraction grating to impart a frequency bias to one of the beams. This bias - much higher than the maximum fD anticipated - results in a fringe pattern that moves continuously in one direction. The Doppler frequency then observed will be 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:

λ δy = θ (8) 2sin 2

Doppler frequency:

2vsin θ f = 2 (9) D λ

Focus diameter at the 1/e2 intensity level:

2fλ 2b = (10) o πb

Focal volume dimension at the 1/e2 intensity level:

bo ∆x = θ (11) sin 2

8 bo ∆y = θ (12) cos 2

∆z = 2bo (13)

Fringe visibility:

I − I V = max min (14) Imax + Imin

4.5 Experiment LDV System

Figure 6. LDV arrangement

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

9 Small diameter scatter particles must be used to follow the tunnel ﬂow faithfully; only a seed with suitable size and buoyancy is adequate for monitoring high turbulence velocities or any rapidly changing ﬂow perturbation. The TSI seed generator uses high pressure air to produce silicone oil droplets with a diameter dispersion centered around 1-2 µm. This particle size results in a maximum system frequency response 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, its size and the wavelength of the exciting radiation. Figure 7 shows some polar scatter proﬁles for various values of the size parameter (α = 2πr/λ), where r is the particle radius. Because α is approximately 5 for the current experiment the scattered radiation will be predominately in the 180o, or forward, direction.

10 In general the seed diameter should be less than the fringe spacing to ensure maximum signal modulation 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 to remove 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 proportional to fD. The particle (viz flow) velocity is readily obtained by applying the appropriate normalization factor derived from Eq. 9. The tracker has the capability of adjustment so that the flow velocity could be 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 of quantum (shot) or thermal (Johnson) origin, is always present along with the actual Doppler scattering signal. Usually the signal-to-noise ratio (S/N) is sufﬁciently large for the tracker to lock on to the Doppler signal. However, in situations where the S/N ratio is marginal, the tracker may be triggered by noise and present a spurious output. The tracker must always therefore be used with discretion since it is 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 visually monitor the detector signals as they exit from the low pass ﬁlter - a high speed storage oscilloscope is provided 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 (5 m/s), take simultaneous readings with the LDV and the pitot tube.

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

11 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 cm from its trailing edge.

(d) Record the Doppler frequencies over a vertical traverse that encompasses the whole wake (2 mm increments 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 whenever possible. There will be variations in the Doppler frequency at each height setting; you should record the maximum and minimum values as well as the mean; also plot the upper and lower bounds for your report presentation.

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

5.3

The tunnel velocity (without the airfoil inserted) is constant for the traverse ranges employed; you should 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 correlation coefﬁcient the most suitable parameter for evaluating the agreement between the two techniques? If the correlation coefﬁcient was .9999998 how would you present the results to illustrate the differences between the two techniques?

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

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

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

(d) Comment on all sources of error you perceive in the experiment; some areas you may wish to consider 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 in fD. (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 variety of fields than discuss any one area in great detail.

7 Preparation

(1) There is considerable scatter in the drag data for the NACA 0015 when α ≥ 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, NTIS DE 82-021712 (1982).

13 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.

14 APPENDIX

The optical constants for the Aerolab LDV system are:

Beam interaction angle θ = 5.648 degrees Focal length f = 0.593 m Laser wavelength λ = 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 airfoil as a function of angle of attack.