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Airfoil Drag by Wake Survey Using Ldv

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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 sep- aration (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 mo- mentum 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 suit- able size and buoyancy is adequate for monitoring high turbulence velocities or any rapidly changing flow perturbation.
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