Introduction to Wind Tunnel

The basic concept and operation of subsonic wind tunnel was demonstrated in this experiment by conducting airfoil drag analysis on a NACA 0015 airfoil. The small subsonic wind tunnel along with apparatus such as, the manometer rake, the inclined manometer and the pitot – static tube were used with different baffle settings to record varying pressure readings. To achieve this objective, some assumptions were made for the lower range of subsonic flow to simplify the overall analysis.From the obtained aerodynamic measurements using a pitot-static tube mounted ahead of the airfoil at the test section, the actual velocity was determined and by relating it to the theoretical velocity, the velocity coefficient was calculated. The velocity coefficient varies for each baffle setting by a factor of decimals, thus the velocity coefficient can be used as a correction factor. Further, the coefficients of drag were calculated for the following angles of attack, 10o, 15o, and 20o and were co mpared with the published values. INTRODUCTIONThe wind tunnel is an absolute necessity to the development of modern aircrafts, as today, no manufacturer delivers the final product, which in this case can be civilian aircrafts, military aircrafts, missiles, spacecraft, and automobiles without measuring its lift and drag properties and its stability and controllability in a wind tunnel. Benjamin Robins (1707-1751), an English mathematician, who first employed a whirling arm to his machine, which had 4 feet long arms and it, spun by falling weight acting on a pulley however, the arm tip reached velocities of only few feet per second. 4] Figure 1: Forces exerted on the airfoil by the flow of air and opposing reaction on the control volume, by Newton’s third law. [1] This experiment will determine drag forces experienced by a NACA 0015 airfoil, subjected to a constant inlet velocity at various baffle settings with varying angles of attack.DATA ANALYSIS, THEORATICAL BACKGROUND AND PROCEDURE Apparatus in this experiment as shown in the figure 2, consisted of a small subsonic wind tunnel. The wind tunnel had an inlet cross-section of 2304 in2 and an outlet crosses section of 324 in2. A large compressor forced air from room) into the inlet through the outlet tunnel and back into the room. This creates a steady flow of air and a relative high velocity can be achieved in the test section. Instrumentation on the wind tunnel consisted of an inclined manometer and a pitot-static tube in the test section also a manometer rake behind the tested objet (airfoil NACA 0015). The manometer rake consisted of 36 inclined manometers; number 36 is used as a reference for the static pressure. All other manometer measures the pressure behind the object in the airflow. Figure 2: Wind tunnel set up with instrumentation [5]Before the experiment was performed the laboratory conditions were recorded, the room temperature was measured to be 22. 5 C (295. 65) and the atmospheric pressur e 29. 49 inHg (99853. 14Pa). Theory The setup of this experiment includes a NACA 0015 airfoil placed in the wind tunnel. Considering the cross-sectional area A1, velocity V1, and the density of air p1 at the inlet and similarly the cross-sectional area A2, velocity V2, and the density of air p2 at the outlet and by assuming that no mass is lost between the inlet-outlet section, we get the mass conservation equation, p1 V1 A1 = p2 V2 A2 (1).Further, the airflow can be assumed to be incompressible for this experiment due to low velocity, the equation (1) can be reduced to V1 A1 = V2 A2 (2), moreover, the air is assumed to be inviscid, the Bernoulli’s equation, p1+12? V12=p2+12? V22 (3) and the equation (2) can be reduced to Vth=2(p1-p2)/? 1-A2A12 (4) in order to find the theoretical velocity. The pitot – static tube is used to calculate the actual velocity of the flow by using, Vact= 2(p2-p1)? (5). Furthermore, the velocity coefficient can be calculated using, Cv=VactVth (6).The pressure and shear stress acting on the NACA 0015 airfoil produces a resultant force R, which according to the Newton’s third law produces an equal and opposite reaction force. For this experiment, in the condition of lower range of subsonic velocity, it can be assumed that pressure and density will be constant over the airfoil thus, D=jj+1? (uo2-ui2)dy=-12? uj2+uj+12o-uj2+uj+12iyj+1-yj (7) can be used to calculate the drag and, CD=Drag12(? air*Velocity2*area) (8) can be used for calculating the coefficient of drag. Procedure Part 1, Variation of inlet cross section:In this first part we recorded the pressure behavior in the test section by decreasing the inlet area. After the safety instructions were given by the TA and a chart for the readings prepared on the white board the wind tunnel was turned on. Two students were taking readings simultaneously from the inclined manometer in the test section and the static pitot tube, the readings were recorded in table 1. Bet ween each reading the compressor was turned off due to the sound level, it was important to give the compressor some time after each start up to have the same conditions as in the previous measurement.Part 2, recording the wake profile of NACA 0015 For this part of the experiment the inlet area was fully opened and the airfoil first set to an angle of attack of 10, the wind tunnel was turned on and all 36 readings recorded (table 2) from the manometer rake. The measurement was repeated for an angle of attack of 15 and 20. RESULTS AND DISCUSSION The linear relationship between the V actual and the V theoretical approves of the theory that the velocity coefficient, Cv can be used as a correction factor for the theoretical velocity. This is further demonstrated in (Graph2). The calculated results are shown in table 1.The approximated literature values of the coefficient of drag for NACA 0015 airfoil were obtained from a NASA published report [3] for the 10o AoA, the percent relative er ror is 3. 1%, for 15o AoA, the percent relative error is 31. 0%, and for the 20o AoA, the percent relative error is 38. 7%. Increases in angle of attack lead to a more disturbed airflow behind the wing section. This disturbed airflow created more drag, these drag forces were clearly observable in table 3, 4. The angle of attack can be increased until the total drag forces become larger than the resultant lift- force; a wing is then no longer effective and stalls.The calculated drag forces are shown in tables 2-4. According to NASA, in their published report of Active flow control at low Reynolds numbers on a NACA 0015 airfoil, its is suggested that, by positioning the wake rake around 4. 5 times chord length behind wing to survey the wake. Further, two pressure orifices on opposite tunnel walls, aligned with the wake rake can be used to determine the average wake static pressure. This type of wake rake enables the wake to be surveyed with only a few moves of the wake rake, hence imp roving the measurements of drag using wake rake. 2] At large angles of attack, the upstream velocity of the airfoil can no longer be considered as the free-stream velocity, largely due to the miniature size of the wind tunnel relative to the NACA 0015 airfoil hence, the assumption that the uo max > ui is valid for this experiment.CONCLUSION Ergo, it is evidently seen in the graphs 1 and 2 that, the averaged velocity coefficient, Cv, 1. 063 can be used as the correction factor for the theoretical velocity. Further, the accurate (4-32) drag forces were calculated to be 2. 72 N, 13. 46 N, and 46. 4 N for the following angles of attack, 10o, 15o, and 20o. Moreover, the drag coefficient were also calculated based on the observed data and than were directly compared with the literature values. For the 10o of angle of attack, the percent relative error was very minimal at 3. 1% however; the drag coefficients for the 150 and the 20o were not very accurate, with the percent relative error of 31. 0% and 38. 7% respectively. This can be improved by implementing a smaller airfoil, so that the proportion of the wind tunnel covered by the airfoil is significantly smaller.Also, the skin friction losses along the edges of the wind tunnel may very well be taken into the account to achieve greater accuracy. Finally, it can be concluded that, as the angle of attack of the airfoil increases, the drag force will also increase due to the effect of flow separation. REFERENCES [1] Walsh, P. , Karpynczyk, J. , â€Å"AER 504 Aerodynamics Laboratory Manual† Department of Aerospace Engineering, 2011 [2] Hannon, J. (n. d. ). Active flow control at low reynolds numbers on a naca 0015 airfoil. Retrieved from http://ntrs. nasa. gov/archive/nasa/casi. ntrs. nasa. gov/20080033674_2008033642. pdf [3] Klimas, P.C. (1981, March). Aerodynamic characteristics of seven symmetrical airfoil section through 180-degree angle of attack for use in aerodynamic analysis of vertical axis wind turbi nes. Retrieved from http://prod. sandia. gov/techlib/access-control. cgi/1980/802114. pdf [4] Baals, D. D. (1981). Wind tunnels of nasa. (1st ed. , pp. 9-88). National Aeronautics And Space Administration. [5]Fig. 1, Wind tunnel set up with instrumentation, created by authors, 2012 APPENDIX Sample Calculations Note: AoA = ANGLE OF ATTACK. Sample calculations part 1, Baffle opening 5/5: Conversion inH2O to Pa (N/m2): 1 inH2O=248. 2 Pa (at 1atm) ?2inH2O ? 248. 82 PainH2O=497. 64 Pa Theoretical velocity: Equation (4): Vth=2(p1-p2)/? 1-A2A12 , where p1-p2=497. 64 Pa, A2=2304 in2, A1=324 in2, ? Density air (ideal gas law) laboratory conditions; 22. 5 C (295. 65K), 29. 49 inHg (99853. 14Pa): ? =pRT=99853. 14Pa287JkgK(295. 65K)? 1. 1768 kgm3 ?Vth=2(497. 64pa)/1. 1768kgm31-2304 in2324 in22=29. 37m/s Actual velocity: Equation (5):Vact= 2(p2-p1)? where p1-p2=522. 52 Pa, ? =1. 1768 kgm3 ? Vact= 2(522. 52Pa)1. 1768 kgm3=29. 80 m/s Velocity coefficient: Equation (6): Cv=VactVth=29. 8029. 37=1. 0 15 Sample Calculations Part 2, Angle of attack 10o, tube 1For dL, tube number 36 served as a reference pressure for all readings: 26. 4cm – 9. 2cm = 17. 2cm or 0. 172m Pressure difference, equation (7): ?p=SG*? H2O*g*L*sin? =1*1000kgm3*9. 81ms2*0. 172m*sin20o=577. 06 Pa Velocity, equation (8) note; pressure difference previously calculated: V1=2*SG*? H2O*g*L*sin air=2*577. 06 Pa1. 1768kgm3=31. 32 m/s Drag force, equation (9), for ui a velocity away from the tunnel wall was chosen to achieve a more realistic drag force: D=jj+1? (uo2-ui2)dy=-12? uj2+uj+12o-uj2+uj+12iyj+1-yj=-121. 1768kgm3(31. 32ms)2+( 31. 5ms)2o-2(31. 5m/s)2i0. 01m=0. 07 N Total drag force, summation lead to:Dtotal = 9. 04 N, however due to the boundary layer along the inner walls of the wind tunnel a more accurate summation is the sum of the values of tubes 4-32 which results in a total drag force of 2. 72 N. Coefficient of Drag Equation (9), for the drag force the more accurate summation of tube 4-32 was used : CD=Drag12(? air*Velocity2*area)=2. 72N12(1. 1768kgm3*31. 50ms2*(0. 1524m*1. 00m)=0. 031 To compare the Cd to a value found in literature the Reynolds number is required: Re=? air*V*cViscosity=1. 1768kgm3*31. 50 m/s*0. 1524m1. 789*10-5kgs*m=315782. 35 Observation and Results for Part 1Table 1, Observations/Results part 1| Baffle Opening| Inclined Manometer (inH2O)| Pa ( x 248. 82 Pa/inH2O)| Pitot Static (inH2O)| Pa ( x 248. 82 Pa/inH2O)| V theoretical (m/s)| V actual (m/s)| Cv| 5;5| 2. 00| 497. 640| 2. 10| 522. 52| 29. 37| 29. 80| 1. 015| 4;5| 1. 80| 447. 876| 1. 90| 472. 75| 27. 87| 28. 35| 1. 017| 3;5| 1. 15| 286. 143| 1. 25| 311. 02| 22. 27| 22. 99| 1. 032| 2;5| 0. 45| 111. 969| 0. 46| 114. 46| 13. 93| 13. 95| 1. 001| 1;5| 0. 05| 12. 441| 0. 08| 19. 905| 4. 64| 5. 82| 1. 252| Table 1: The theoretical velocity was calculated using the eq. (4) and the actual velocity was calculated using the eq. 5) from the obtained pressure data from the hand held pitot tube. The velocity coeffic ient, Cv, was calculated using the eq. (6). Note: The sample calculations are given in the appendix section of this report. Graph 1: The results from Table 1 were used to create the plot of V actual Vs. V theoretical. Graph 2: The plot of the velocity coefficient and the actual velocity. From the plot, it can be clearly seen the very minute difference between the velocity coefficient values. Observation and Results for Part 2 Table 2, Observations/Recordings part 2, Angle of attack 10 | Fluid length in tube ( ±. 1cm), Inclination 20|Tube Nr. | L (cm)| dL (cm)| Pressure (Pa)| u (m/s)| Drag force (N)| 1| 9. 2| 0. 07| 0. 07| 0. 07| 0. 07| 2| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 3| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 4| 9. 0| -0. 07| -0. 07| -0. 07| -0. 07| 5| 8. 8| -0. 13| -0. 13| -0. 13| -0. 13| 6| 8. 8| -0. 13| -0. 13| -0. 13| -0. 13| 7| 8. 8| -0. 07| -0. 07| -0. 07| -0. 07| 8| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 9| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 10| 9. 0| -0. 03| -0. 03| -0. 03| -0. 0 3| 11| 8. 9| -0. 03| -0. 03| -0. 03| -0. 03| 12| 9. 0| -0. 03| -0. 03| -0. 03| -0. 03| 13| 8. 9| -0. 07| -0. 07| -0. 07| -0. 07| 14| 8. 9| 0. 64| 0. 64| 0. 64| 0. 64| 5| 11. 0| 1. 68| 1. 68| 1. 68| 1. 68| 16| 12. 0| 1. 01| 1. 01| 1. 01| 1. 01| 17| 9. 0| -0. 03| -0. 03| -0. 03| -0. 03| 18| 8. 9| -0. 03| -0. 03| -0. 03| -0. 03| 19| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 20| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 21| 9. 0| -0. 03| -0. 03| -0. 03| -0. 03| 22| 8. 9| -0. 07| -0. 07| -0. 07| -0. 07| 23| 8. 9| -0. 07| -0. 07| -0. 07| -0. 07| 24| 8. 9| -0. 10| -0. 10| -0. 10| -0. 10| 25| 8. 8| -0. 10| -0. 10| -0. 10| -0. 10| 26| 8. 9| -0. 03| -0. 03| -0. 03| -0. 03| 27| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 28| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 29| 9. 0| 0. 00| 0. 00| 0. 00| 0. 00| 30| 9. 0| 0. 00| 0. 00| 0. 0| 0. 00| 31| 9. 0| 0. 07| 0. 07| 0. 07| 0. 07| 32| 9. 2| 0. 34| 0. 34| 0. 34| 0. 34| 33| 9. 8| 0. 34| 0. 34| 0. 34| 0. 34| 34| 9. 2| 0. 07| 0. 07| 0. 07| 0. 07| 35| 9. 0| 5. 84| 5. 84| 5. 84| 5. 84| 36| 26. 4| 0| Reference| 0. 00| 0. 00| Total drag force (1-35)| 9. 04| Total drag force (4-32)| 2. 72| Coefficient of drag calculated| 0. 031| Coefficient of drag literature| 0. 030| Table 3, Observations/Recordings part 2, Angle of attack 15 | Fluid length in tube ( ±. 1cm), Inclination 20| Tube Nr. | L (cm)| dL (cm)| Pressure (Pa)| u (m/s)| Drag force (N)| 1| 8. 2| 0. 06| 0. 06| 0. 06| 0. 06| 2| 8| -0. 01| -0. 01| -0. 1| -0. 01| 3| 8| -0. 01| -0. 01| -0. 01| -0. 01| 4| 8| -0. 04| -0. 04| -0. 04| -0. 04| 5| 7. 9| -0. 08| -0. 08| -0. 08| -0. 08| 6| 7. 9| -0. 04| -0. 04| -0. 04| -0. 04| 7| 8| -0. 01| -0. 01| -0. 01| -0. 01| 8| 8| -0. 01| -0. 01| -0. 01| -0. 01| 9| 8| 0. 19| 0. 19| 0. 19| 0. 19| 10| 8. 6| 0. 49| 0. 49| 0. 49| 0. 49| 11| 8. 9| 0. 49| 0. 49| 0. 49| 0. 49| 12| 8. 6| 0. 39| 0. 39| 0. 39| 0. 39| 13| 8. 6| 0. 56| 0. 56| 0. 56| 0. 56| 14| 9. 1| 1. 40| 1. 40| 1. 40| 1. 40| 15| 11. 1| 2. 51| 2. 51| 2. 51| 2. 51| 16| 12. 4| 2. 74| 2. 74| 2. 74| 2. 74| 17| 11. 8| 2. 40| 2. 40| 2. 40| 2. 40| 18| 11. 4| 2. 00| 2. 00| 2. 00| 2. 00| 9| 10. 6| 1. 47| 1. 47| 1. 47| 1. 47| 20| 9. 8| 1. 06| 1. 06| 1. 06| 1. 06| 21| 9. 4| 0. 79| 0. 79| 0. 79| 0. 79| 22| 9| 0. 63| 0. 63| 0. 63| 0. 63| 23| 8. 9| 0. 49| 0. 49| 0. 49| 0. 49| 24| 8. 6| 0. 39| 0. 39| 0. 39| 0. 39| 25| 8. 6| 0. 32| 0. 32| 0. 32| 0. 32| 26| 8. 4| 0. 26| 0. 26| 0. 26| 0. 26| 27| 8. 4| 0. 26| 0. 26| 0. 26| 0. 26| 28| 8. 4| 0. 26| 0. 26| 0. 26| 0. 26| 29| 8. 4| 0. 26| 0. 26| 0. 26| 0. 26| 30| 8. 4| 0. 26| 0. 26| 0. 26| 0. 26| 31| 8. 4| 0. 26| 0. 26| 0. 26| 0. 26| 32| 8. 4| 0. 32| 0. 32| 0. 32| 0. 32| 33| 8. 6| 0. 56| 0. 56| 0. 56| 0. 56| 34| 9. 1| 0. 56| 0. 56| 0. 56| 0. 56| 35| 8. 6| 6. 30| 6. 0| 6. 30| 6. 30| 36| 26. 2|   0. 00| Reference  | 0. 00  | 0. 00  | Total drag force (1-35)| 19. 55| Total drag force (4-32)| 13. 46| Coefficient of drag calculated| 0. 145| Coefficient of drag literature| 0. 100| Table 4, Observations/Recordings part 2, Angle of attack 20 | Fluid length in tube ( ±. 1cm), Inclination 20| Tube Nr. | L (cm)| dL (cm)| Pressure (Pa)| u (m/s)| Drag force (N)| 1| 8| 0. 16| 0. 16| 0. 16| 0. 16| 2| 7. 6| 0. 03| 0. 03| 0. 03| 0. 03| 3| 7. 6| 0. 03| 0. 03| 0. 03| 0. 03| 4| 7. 6| 0. 03| 0. 03| 0. 03| 0. 03| 5| 7. 6| 0. 03| 0. 03| 0. 03| 0. 03| 6| 7. 6| 0. 03| 0. 03| 0. 03| 0. 03| 7| 7. 6| 0. 03| 0. 3| 0. 03| 0. 03| 8| 7. 6| 0. 09| 0. 09| 0. 09| 0. 09| 9| 7. 8| 0. 16| 0. 16| 0. 16| 0. 16| 10| 7. 8| 0. 23| 0. 23| 0. 23| 0. 23| 11| 8| 0. 50| 0. 50| 0. 50| 0. 50| 12| 8. 6| 1. 17| 1. 17| 1. 17| 1. 17| 13| 10| 2. 37| 2. 37| 2. 37| 2. 37| 14| 12. 2| 3. 58| 3. 58| 3. 58| 3. 58| 15| 13. 6| 5. 39| 5. 39| 5. 39| 5. 39| 16| 17. 6| 7. 21| 7. 21| 7. 21| 7. 21| 17| 19| 7. 88| 7. 88| 7. 88| 7. 88| 18| 19. 6| 7. 88| 7. 88| 7. 88| 7. 88| 19| 19| 7. 04| 7. 04| 7. 04| 7. 04| 20| 17. 1| 5. 73| 5. 73| 5. 73| 5. 73| 21| 15. 1| 4. 09| 4. 09| 4. 09| 4. 09| 22| 12. 2| 2. 44| 2. 44| 2. 44| 2. 44| 23| 10. 2| 1. 37| 1. 37| 1. 37| 1. 37| 4| 9| 0. 66| 0. 66| 0. 66| 0. 66| 25| 8. 1| 0. 29| 0. 29| 0. 29| 0. 29| 26| 7. 9| 0. 23| 0. 23| 0. 23| 0. 23| 27| 7. 9| 0. 23| 0. 23| 0. 23| 0. 23| 28| 7. 9| 0. 19| 0. 19| 0. 19| 0. 19| 29| 7. 8| 0. 19| 0. 19| 0. 19| 0. 19| 30| 7. 9| 0. 19| 0. 19| 0. 19| 0. 19| 31| 7. 8| 0. 19| 0. 19| 0. 19| 0. 19| 32| 7. 9| 0. 46| 0. 46| 0. 46| 0. 46| 33| 8. 6| 0. 50| 0. 50| 0. 50| 0. 50| 34| 8| 0. 29| 0. 29| 0. 29| 0. 29| 35| 8| 6. 40| 6. 40| 6. 40| 6. 40| 36| 26. 2| 0| 0. 00| 0. 00| 0. 00| Total drag force (1-35)| 51. 30| Total drag force (4-32)| 46. 64| Coefficient of drag calculated| 0. 489| Coefficient of drag literature| 0. 300|