position of pressure taps (mm)

Transcription

1 Cp To: Anderson A., Professor From: Knepple, R., Fluids Lab Trainee (initialed electronically (2/28/13): R.K.) Partners: Muehlek E., Xie, L. Date: 2/20/13 Subject: Aerodynamics of Mercedes CLK: Surface Pressure Effects Summary This memo reports on the surface pressure distribution along the body of a Mercedes CLK. Figure 1 depicts the distribution of Pressure Coefficients (Cp) and surface pressure trends along the length of the car. The experiment confirmed that as Cp increased or decreased, the pressure (in Pa) followed the same pattern. These Cp values ranged from 0.217±0.058 to 1.103±0.090 at 20 Hz wind tunnel motor frequency and 0.327±0.019 to 1.098±0.050 at 40 Hz wind tunnel motor frequency. There was very little variation between Cp values at 20 Hz and at 40 Hz, as confirmed by Figure 1. The wind tunnel velocities were 14.76±0.28 m/s for the 20 Hz setting and 31.26±0.14 m/s for the 40 Hz setting. Experimental Procedure In order to obtain the necessary pressure values along the surface of the car, a 1/8 th full scale model of the car with pressure taps along the surface was placed in the wind tunnel. The model had 13 tygon tubes attached to different pressure taps. We took 100 readings by a pressure transducer for each of these pressure taps for when the wind tunnel motor frequency was at 20 Hz and when it was at 40 Hz. These voltage values were then converted to pressure values and analyzed. More details can be seen in Attachment D. Pressure Coefficient Results The Pressure coefficient (Cp) of each point can be seen in the Figure below: X Actual (mm) Position 5 front of car hood windshield 145- top trunk Behind car position of pressure taps (mm) Cp-40Hz Cp-20Hz Figure 1: Cp Values along the length of the car for 40 Hz and 20 Hz and their physical position on the car. Note: there are uncertainty bars on all of the data but some are smaller than the markers on the graph.

2 Uncertainty Analysis: Velocity and Cp Uncertainty analysis was done on both velocity values and Cp values; both processes can be seen in Attachment C. Using pressure and density, the uncertainty for the velocity at 20 Hz was ±0.28 m/s and ±0.14 m/s at 40 Hz. To do uncertainty analysis on Cp values velocity, pressure difference with uncertainty in both the calibration of the pressure transducer and within the data considered, and density as well as their uncertainties were considered. The Cp uncertainty values ranged from to for 20Hz and to and can be seen fully in Attachment B. Since the µcp values were small for most of the points, our data is reliable for analysis. For some positions, however, the µcp value was high (for example at 165mm the µcp was 14.5%) showing that there was a larger error associated with these readings, most likely due to either movement of the tygon tubes or not enough motor settling time between readings. Pressure Results and Discussion The surface pressure along the car at 20 Hz varied from Pa to Pa. At 40 Hz the surface pressure varied from Pa to Pa. Although different in values, the pressures acted similarly along the model at both frequencies and can be seen in Figure 3a and 3b of Attachment A. The highest pressure was at the front of the car when Cp was 1; this is the stagnation point. Another stagnation point existed in between the hood and the windshield at 80mm along the model. Between mm (hood of the car) as well mm (trunk) the pressure increases. From 80 to 122 mm the pressure decreases. For mm the pressure graph essentially flattens out and therefore the pressure remains constant in this region. For positions behind the car the pressure graph stops increasing and begins to act unpredictably; this is the zone of separation where our previously made assumptions no longer apply. Discussion: Pressure and Cp relationship Theoretically, Cp is proportional to the surface pressure in a constant free stream velocity and our figures and data show this trend. For both data sets, however, there is a point in the 40 Hz data at the 122 mm mark where both pressure and Cp values increased while it was expected to instead decrease. This peak was most likely caused by experimental error such as not waiting for the system to settle between readings. As such this deviation was not included in the analysis. Closing This experiment demonstrated how the pressure along the surface of the car increased and decreased depending on the shape and location being analyzed. The surface pressure distribution along the car proved the relationship between Cp and pressure: as Cp increased, pressure increased and as Cp decreased, pressure decreased. Despite differing pressure ranges, ( Pa at 20 Hz and Pa at 40 Hz) the Cp results for both motor frequencies were nearly identical, proving the same trends occur even at different air speeds. I recommend that more data should be taken with more wait time between trials to obtain higher accuracy and lower µcp values. If you have any further questions or concerns please contact me at kneppler@garnet.union.edu.

3 Acknowledgements Ellen Muehleck, Lutao Xie and Zac Hertel References [1] Anderson. Ann. MER 331 Fluid Mechanics Lab. "Race Car Aerodynamics Project." Union College, Attachments A) Figures B) Data Analysis Results C) Uncertainty Calculations D) Experimental Procedure

4 Cp Attachment A: Figure In order to better understand the figures below, a table of the length along the car from the front of the car and its corresponding position phrase that we are familiar with can be seen below. Table 1: Position along the car. X (mm) Actual Position 5 front of car hood windshield top trunk 250 Behind car Cp-40Hz Cp-20Hz position of pressure taps (mm) Figure 2: Cp Values along the length of the car for 40 Hz and 20 Hz and their physical position on the car. Note: there are uncertainty bars on all of the data but some are smaller than the markers on the graph.

5 Surface Pressure(Pa) Position (mm) 20HZ Figure 3a: Pressure differentials across the surface of the car at 20 Hz wind tunnel motor frequency. The uncertainty bars are present but are smaller than the graph markers and therefore not easily observed on the figures. Surface Pressure(Pa) Position (mm) 40HZ Figure 3b: Pressure differentials across the surface of the car at 40 Hz wind tunnel motor frequency including the outlier. The uncertainty bars are present but are smaller than the graph markers and therefore not easily observed on the figures. Note: There was 1 outlier at 122 mm taken out from the data. It was most likely caused by not waiting long enough for the wind tunnel to increase speed. Figure 2 and b showed the pressure difference along the length of the car model. The pressures acted similarly along the model at both frequencies. The highest pressure was at the front of the car when Cp was 1; this is the stagnation point. Another stagnation point exists in between the hood and the windshield at 80mm along the model. Between mm (hood of the car) as well as mm (trunk) the pressure increases. From 80 to 122 mm the Pressure decreases. For mm the pressure graph essentially flattens out and therefore the pressure remains constant in this region. For positions behind the car the pressure graph stops increasing and begins to act unpredictably; this is the zone of separation where our previously made assumptions no longer apply. Figure 1 and 2 together demonstrated that the pressure coefficient is proportional to surface pressure at constant freestream velocity.

6 Attachment B: Data Analysis Results The table below represents the analysis done on data collected at 20 Hz motor frequency and 40 Hz motor frequency. Table 2: Experimental and calculated major results 20Hz 40Hz Position (mm) ΔP (Pa) δdp ("H2O) Cp µv µcp δcp ΔP (Pa) δdp ("H2O) Cp µv µcp δcp NA NA NA NA NA NA Velocity m/s m/s

7 Attachment C: Uncertainty Analysis For the uncertainty analysis of the Cp values, first density had to be found. This was done by using the following equation: (1) Where P is the atmospheric pressure ( Pa), R is the Gas Constant (287 J/Kmol) and T is Temperature (296K). The density was found to be 1.19kg/m 3. Then we found the uncertainty in this value (2) Where P is atmospheric pressure, R is the gas constant, is the uncertainty in temperature (1 0 ) and is the uncertainty in atmospheric pressure. We found to be kg/m 3. To find the velocity of the air from the wind tunnel at different frequencies, Equation 3 derived from Bernoull s Equation was used: (3) Where Po is the pressure found at the pitot probe, P is the atmospheric pressure and ρ is the density found with equation 1. Next, the uncertainty in velocity was found using Equation 4: ( ) (4) Where v is the velocity found per frequency with Equation 3, is the pressure difference of the pitot probe (in inches of water), was found using Equation 2, and was found using Equation 1. To find for this equation, we had to account for the standard deviation of the values as well. Therefore: (5) Where δ Pcalibration was a given (0.02 inches of water) and the standard deviation of the pressure (stdev) was found to be for 20 Hz and for 40 Hz. To find velocity δ P of the pitot probe was used. Combining these uncertainties with their corresponding values gives velocities of the air in the wind tunnel of 14.76±0.28 m/s at 20 Hz and 31.26±0.14 m/s at 40 Hz. To find the uncertainty values for Cp, equation 6 was used: ( ) ( ) (6)

8 Where all of the values were found before. These values can be seen in Figure 2 and in the tables in attachment B.

9 Attachment D: Experimental Procedure [1] To perform this experiment, we obtained cars that had pressure taps, or small holes in the surface of the model to which tygon tubes are attached and are used to read pressure distribution. Figure 4: Top view of the car and the locations of the pressure taps We first placed the car in the wind tunnel as seen in Figure 5. Figure 5: The Mercedes CLK in the Union College Wind Tunnel

10 Tygon tubes 1 through 9 out of the bottom of the model were attached to different channels of the pressure transducer. We turned the wind tunnel to 20 Hz and let it stabilize for a minute. Using DAQ system software, we took 100 readings for each channel, waiting a minute in between channel switches. We noted that the first channel (channel zero) was actually attached to the pitot probe (seen in Figure 5). Once we completed Channel 9 readings, we replaced channels 1 through 3 with tubes and took 100 readings for each of these 3 channels. This process was repeated for 40 Hz. We compiled and analyzed the data, which can be seen in Attachment B. I affirm that I have carried out my academic endeavors with full academic honesty Signed: Rebecca Knepple, Lutao Xie, Ellen Muehleck (2/28/13)