Domingo, C.

Fortuny, J.

Gallegos, J.M.

Orriols, G.

English

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Campaign of aerodynamic measurements in a wind tunnelDomingo, C.; Fortuny, J.; Gallegos, J.M.;Orriols, G. and Roset, M.Universitat Politècnica de Catalunya, UPC BarcelonaTECH(Under the supervision of Prof. D. Crespo and Dr. J.L. Gutiérrez)This paper introduces different ways to obtain aerodynamic results with the help of a wind tunnel.In Section I, the drag force on a cylindrical profile is measured with a scale and also computed frompressures measured at the surface of the cylinder, obtaining matching results. In Section II, liftand drag coefficients are computed for a symmetrical wing profile at different speeds and angles ofattack using two different methods; the dependence of the coefficients on the angle is found to fittheoretical models. Section III is devoted to measuring the wind speed at the wake of a cylinder bymeans of a hot wire anemometer in order to obtain a turbulence map and an indirect measure ofthe drag force, which narrowly fits the results from Section I.Keywords: wind tunnel, hot wire anemometer, winged profile, aerodynamics.I. CYLINDER PROFILEA. IntroductionThere are different methods to study the drag forceexerted by the wind on a cylinder. The following two arecompared in this section:1. Directly using the scale attached to the wind tunnel2. Using the partial forces measured with the PitottubeThe cylinder studied is 30 cm long and has a radius r =3.2 cm.B. MethodologyThe pressure has been measured for different orien-tations of the hole: between 0◦ and 180◦ every 10◦, 0◦degrees being the orientation where the wind points tothe hole. For every orientation there are 20 measuresevenly distributed during 10 s.The measures have been taken for ftunnel = 25 Hz,which means (assuming a linear relation between thespeed of the wind and the frequency) vwind = 16.66 m/s.To calculate the force (per unit of length) acting on thecylinder using the pressures on each angle, the followingexpression can be used:F =∫CP (θ) cos θdl =∫ 2π0P (θ)r cos θdθ ==∫ 3600P(2πα360)cos(2πα360)2πr360dα,where r is the radius and C is the circumference of thecylinder. Since there are a discrete number of measuresand even symmetry can be assumed:F ≈ 2πr36[P (0◦) + 217∑α=1P (10α) cos(10α)− P (180◦)]Assumptions to evaluate the error:1. α has an error of 0.5 degrees.2. the error of the measurement of P is its standarddeviation.3. the error of α and P are independent (the errorsquared is the sum of the squares)Thus:∆Fα =√(dFαdP∆P)2+(dFαdα∆α)2==2πr36√(∆P )2 cos2 α+(2π∆α360)2P 2 sin2 αC. Results0 50 100 150−0.25−0.2−0.15−0.1−0.050Angle αPressure(kPa)Pressure−0.500.51Forceperunitlength(N/m)Force per lengthFIG. 1. Pressure and force per unit length dependence respectto α2D. ConclusionsThe force obtained directly measuring with the scalewas 2.611 N. The force obtained by calculating the par-tial forces was (2.716± 0.365) N. Thus, a quite accurateresult is obtained. One of the possible causes for thislittle difference is the fact that the cylinder is finite.It is also interesting to observe in FIG.1 that not only thepartial pressure changes, but also the size of the standarddeviation does.II. WINGED PROFILEA. IntroductionIt is possible to study the lift coefficient, CL, and dragcoefficient, CD, of a winged symmetric profile (wingspanof 0.3 m and chord of 0.15 m) for different angles of at-tack and different velocities of the wind. This has beendone using an AFA TQ Equipment three component bal-ance that allows the measurement of the lift force, L, anddrag force, D, applied to the balance and a Pitot tube todetermine the velocity of the wind.By analyzing the pressure in different points of thewing it is also possible to estimate the drag and the liftwithout using the balance. This measurement will bepresented for a specific speed of the wind in order to com-pare the results with the ones obtained with the balanceand discuss the effect of having a finite wing (creation ofvortexes, for example – see [1]).B. MethodologyThe measurements were done for three different veloc-ities of the wind: 13 m/s, 27 m/s and 33 m/s that corre-spond to Reynolds of 2.3× 105, 4.8× 105 and 5.9× 105respectively. Therefore in all cases there were turbulentflow conditions.For every velocity of the wind the lift and the dragwere measured for angles of attack from −9◦ until 10.5◦making measures every 1.5◦. 0◦ mean that the wing is inhorizontal position and it was possible to fix this value bylooking at the angle for which there was no lift (the wingis symmetric). Positive angles correspond to a positivelift in the wing.In every measurement CL and CD can be found using:L =ρv∞2SCL2(1)D =ρv∞2SCD2(2)Where ρ is the density of the air. v∞ is the velocity ofthe air far away from the wing and is determined using−10 −8 −6 −4 −2 0 2 4 6 8 10 12−0.6−0.5−0.4−0.3−0.2−0.100.10.20.30.40.50.60.70.8Angle α (◦)CLcoefficient20 Hz40 Hz50 HzFIG. 2. CL coefficient dependence of angle α at a wind tunnelspeed corresponding to 20 Hz, 40 Hz and 50 Hz in the engine.the proportional relation between the frequency of rota-tion of the engine and the speed of the wind. S is thesurface of the wing.For the wind speed of 13 m/s CD and CL were alsocalculated using the 20 pressure sensitive probes alongthe chord. This was done approximating L and D in asimilar fashion that we did with the cylinder. In this caseit is useful to approximate the wing with an attack angleof α as two planes with inclination α (for the upper andlower surfaces). Doing this considerations:D =∑lower surfacePi∆xi sinα−∑upper surfacePi∆xi sinαL =∑lower surfacePi∆xi cosα−∑upper surfacePi∆xi cosαwhere ∆xi have been adjusted taking into considera-tion the distribution of the probes along the wing. Usingthis expressions it is possible to obtain CL and CD asexplained in (1) and (2).C. Results and DiscussionFIG. 2 and 3 show the values we have obtained for thelift coefficient CL and the drag coefficient CD at anglesranging from −10◦ and 10◦ approximately. Each colorcorresponds to one of the velocities. Errors in FIG. 2 and3 have been computed considering a precision of 1 m/s forvelocities, and the errors for velocity and forces have beenassumed independent.For a fixed angle, we observe that CL and CD giveapproximately the same value for the three speeds thatwe have studied. This confirms that CL and CD are welldefined physical variables.3−10 −8 −6 −4 −2 0 2 4 6 8 10 1200.010.020.030.040.050.060.070.080.090.10.110.12Angle α (◦)20 Hz40 Hz50 HzFIG. 3. CD coefficient dependence of angle α at a wind tunnelspeed corresponding to 20 Hz, 40 Hz and 50 Hz in the engine.As observed in 2, CL depends linearly with respect toα. The lines of the linear fit of the experimental pointshave the following equations. For 20 Hz: y = 3.0516x +0.0099, for 40 Hz: y = 3.0749x + 0.0349 and for 50 Hz:y = 3.0218x− 0.0394 (in this case the equations considerthat x is in radians).Tanking into account [2] the slope of CL respect to αfor a finite wing should satisfy:dCLdα=2π1 + 2π/πAR= π (3)Since AR = 3015 is the relation between the wingspanand the chord of the profile. Therefore the values of theslopes coincide with this theory.The CD curve is approximately symmetrical with re-spect to α = 0. This is consistent with the fact that,disregarding the effect of gravity, the air flow must bethe same setting the wing profile at angle α and at angle−α for all α. That is because the wing has an horizontalplane of symmetry. It can also be seen that CD increaseswhen |α| increases. This is reasonable, as a higher angleof attack means that a large surface is facing the air flow,which results in a higher drag force and higher CD.Using the second method, FIG. 4 presents the plotobtained for the drag coefficient and the one obtainedfor the lift coefficient.Considering that x is in radians, the equation obtainedfor the linear plot is: y = 3.6028x − 0.078. In this case,the value of the slope is bigger than the slope calculatedusing the balance (see FIG. 2). This can be explainedsaying that some of the effects of a finite wing were ne-glected in this measurement (since the pressure probesare in the middle of the wing). For an infinite wing theslope should be 2π (from (3) and making AR to infinity)so it makes sense that the slope is between π and 2π.−10 −8 −6 −4 −2 0 2 4 6 8 10 12−0.6−0.5−0.4−0.3−0.2−0.100.10.20.30.40.50.60.70.8Angle α (◦)CLcoefficientCL0.000.010.020.030.040.050.060.070.080.090.100.110.12CDcoefficientCDFIG. 4. CL and CD coefficient dependence of angle α at awind tunnel speed corresponding to 20 Hz according to pres-sure measurments.D. ConclusionsAs a conclusion, both methods can be used to obtainthe variation of the drag and lift coefficients for smallangles of attack, where the dependence is linear. It isalso observed that using the pressure measurements, thestart of non-linearity can be observed around 11◦ but nomeasures where done after this value.Another observation is that the value of the slope us-ing the pressure method is bigger than using the balancewhich means that the values are different for small andbig angles but give us the same result around 4◦-6◦. Weexpect this result to appear due to the presences of vor-texes disturbing the pressure measurements.III. HOT WIRE ANEMOMETERA. IntroductionAs a last experiment, two hot wire anemometer probeswere used with a double aim: on one hand obtaining anestimate of the turbulence of the wind in the wake ofa cylinder; on the other hand, having a third measurefor the drag force of the cylinder, complementing thosefound in Section I.A Constant Temperature Anemometer (CTA) hasbeen used. This device can measure the speed of theair from the voltage required to maintain the tempera-ture of a thin metal wire constant, as it is cooled by thewind. This voltage is then translated to a speed provideda calibration process has been performed. Note that thedevice can only detect the modulus of the velocity, butgives no information about its direction, in contrast tothe Pitot tube; in contrast, it is more precise.45 10 1510152025Speed (m/s)Height(cm)0 20 40 60 80 100Turbulence (%)FIG. 5. The speed detected by the CTA is plotted in blue,with error bars corresponding to the standard deviation. Theturbulence intensity behind the cylinder is also shown in blueas a percent. Both are represented as a function of heightfrom the ground of the tunnel. The projection of the positionof the cylinder is included in black as a reference.B. MethodologyTwo CTAs are introduced in the wind tunnel: one iskept fixed in a position that is not affected by the pres-ence of the cylinder; the other one is placed in differentvertical positions centered behind the cylinder, so thatwe can record wind speeds at different heights relative tothe center of the cylinder. These heights are controlledby a ruler placed on top of the chamber.The tunnel frequency of 25 Hz, as in Section I B, whichcorresponds to a wind speed of roughly 17 m/s. A soft-ware is used to convert the measured voltages into speeds,after providing it with calibration data. It will be set torecord 1024 measurements at a frequency of 1 kHz.In order to compute the drag force exerted on the cylin-der by the wind, by the law of action-reaction it is enoughto compute the rate of change of the loss of momentumof the air: F = −∆ṗ. Assuming a steady flow, we haveF = −∆(ṁv) =∫Sρ(v2∞ − v2)dS, (4)where S is a transverse section of the tunnel, v∞ is thespeed before interacting with the cylinder and v is thespeed after the cylinder.C. ResultsThe average speed detected by the anemometer placedfar from the cylinder was 15.49 m/s with a standard de-viation of 0.50 m/s. This corresponds to a turbulence of3%.The speed as a function of height for the secondanemometer is represented in FIG. 5 together with theturbulence. Notice that the standard deviation, andhence also the turbulence intensity, of the velocities whenthey are close to zero is underestimated by the mea-surements, because all are taken as positive since theanemometer cannot detect their direction. Therefore theturbulence plotted in FIG. 5 might be smaller than thereal one.The value of the drag force computed from (4) by con-sidering 1 cm-wide strips of area is (3.67± 1.04) N. Theerror comes essentially from quadratic propagation of thestandard deviations in the speed.D. ConclusionsThe obtained value for the drag force is significantlyhigher than the ones found in Section I D but still com-patible. This is comprehensible, since those were directmeasurements of the dynamics of the cylinder, and thisis an indirect measurement of the effect it produces inthe wind. Possible sources of error include loss of speedin the heating of the gas and the assumption that themeasured velocity is in the direction of the tunnel, whichneed not be the case and with a hot wind anemometer itis not possible to check.It is also observed that the cylinder displaces the airgoing towards it creating a very turbulent regime (withmore than 60% turbulence intensity) behind it.IV. ACKNOWLEDGEMENTSWe would like to close this paper by thanking Dr. Cre-spo and Dr. Gutiérrez for their help with this project,assuring us the measurements were correct, indicating ushow to analyze data properly and supporting us with allthe material we needed.We also thank the Faculty of Aerospace Engineering ofCastelldefels (EETAC) for letting us do the experimentswith their wind tunnel. Finally we would like to thankDr. Pere Bruna for the learning opportunity.[1] Milne-Thomson, L. M. Theoretical aerodynamics, 1966. [2] J. D. Anderson, Fundamentals of Aerodynamics, McGraw-Hill, pp.380 (2001)

Campaign of aerodynamic measurements in a wind tunnel

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Campaign of aerodynamic measurements in a wind tunnel

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