Essay: Measuring Drag and Visualizing Flow Patterns Around Vehicle Model

Experimental Setup and Procedure
Equipment Used
• Vehicle model designed by students (wheels and axles provided)
• Vehicle model provided by TA for comparison
• Set of weights
• Force gauge
• Pitsco Airtech Scout Wind Tunnel with integrated drag sensor
• Pitot Static Tube
• 2 Pressure Transducers (including power supply) Range: +/- 10 IWC Accy: .8%
• Ruler (units in mm)
• Data Acquisition System DAQ NI 9215
• LabVIEW Software
• Dell Latitude Laptop
• DAQ to USB wire
Experimental Procedure
The overall purpose for this lab is for students to design, build, and test a vehicle to observe flow patterns and flow velocities as well as measure drag forces and coefficients. The vehicle could be made of any materials and constructed in anyway the students desired, so long as it followed the constraints set. This experiment required that students construct the vehicle model outside of the classroom. This lab experiment was conducted over multiple sessions to carry out all the necessary observations and testing. The first session focused on the calibration of the force gauge and drag sensor used in the lab trials. The following session was used to measure flow velocity and drag.
Vehicle design and construction was conducted on the schedule of the students. The requirements for the vehicle set by Mansy seen in the figure below are listed below in (Table 1 Appendices). For this experiment, cardboard was chosen for the vehicle model body for convenience, cost efficiency, and rigidity. The body was assembled using a hot glue gun and finished off with masking tape for extra security. The body was designed to be aerodynamic, with the front of the vehicle resembling a cone like one found on an airplane. With this aerodynamic geometry, the frontal area was kept to a minimum. The wheels were attached to the axles which were held to the bottom of the vehicle with pieces of curved cardboard. This allowed the wheel and axle assemblies to turn freely. Lastly, a piece of wire was made into a loop and attached to the front of the vehicle to hook on to the drag sensor. The vehicle CAD rendering is shown in (Figure 1).
Figure 1: Vehicle Rendering
During the first lab session for this experiment, calibration of the force gauge and drag sensor used for the lab trials was conducted. The procedure for these tests was done as follows:
1. Calibrating the force gauge
• The force gauges were zeroed with no force attached.
• A 10g weight was attached so that a tensile force was applied to the gauge tip and the force gauge reading was recorded. This process was repeated for weights of 20, 30, 40, 50, 60, 70 g.
• The data was plotted in Excel: force gauge readings (the x-axis) and weights (the y-axis.)
• A linear trend line was included in the plot and the equation was displayed. This is the force gauge calibration equation
2. Calibrating the drag force sensor with the force gauge
• The force gauge was connected to the drag sensor in the wind tunnel
• The force gauge and drag sensor were zeroed.
• 7 horizontal forces were applied, each between 0 and 100g in the direction of drag, on the drag sensor using the force gauge.
• Force gauge and drag sensor readings were recorded and plotted in Excel.
• Using the calibration equation for the force gauge found in the last test, the correct force acting on the drag sensor was calculated.
• The corrected force gauge values vs the drag sensor readings were plotted
• A linear trend line was included in the plot and the equation was displayed. This is the drag sensor calibration equation, where the actual force is a function of the drag sensor readings.
During the second lab session for this experiment, flow velocity and drag were measured. This test procedure was done in the following manner:
3. Measuring flow velocity and drag measurement
• The pressure transducers were connected to the Pitot static tube. One of the transducers measured dynamic pressure while, the other measured static pressure in the wind tunnel test section.
• A LabView VI (Appendices) was created to measure flow velocity. This VI measured voltage output of the pressure transducers, used the proper calibration equations of the pressure transducers to calculate flow velocity, and finally displayed the velocity value.
• The vehicle model was placed into the wind tunnel and connected to the drag sensor. The Pitot tube tip was adjusted to be in the middle of the tunnel test section. This is shown in (Figure 2).
• The flow velocity of the wind tunnel was raised to its maximum and allowed to stabilize for about 5 seconds. Flow velocity read from the VI and the drag value at the maximum velocity were recorded.
• The flow velocity was then reduced slightly and brought back up to maximum velocity and allowed to stabilize for 5 seconds. The flow velocity and the drag force were recorded. This process was repeated 4 times, resulting in a total of 5 velocity and drag force pairs including the previous step.
• Next, the effects of hysteresis were observed. The velocity was reduced by one speed setting at a time on the wind tunnel. This was repeated until the lowest speed setting above zero was reached.
For each setting, a velocity and drag force measurement was taken for a total of 5 recordings in this decrease of speed. Then the wind tunnel was raised by one speed setting at a time until reaching maximum velocity again. In this increase of speed, a total of 5 velocity and drag force measurements were collected. The wind tunnel could equalize for 5 seconds for each adjustment. Once steady, the velocity and drag force were noted
• The student vehicle model was removed from the wind tunnel and replaced by the model provided by the TA. The wind tunnel was set to maximum velocity and the drag force and speed were recorded for comparison purposes. Frontal area of this vehicle was also noted
• Lastly, the student designed vehicle model was placed in a wind tunnel equipped with a fog machine and black light to observe flow visualization. The velocity and drag force were collected and a video of the flow visualization was recorded.
Figure 2: Wind Tunnel
V) Results and Discussion
Table 1: Calibration Results and Regression Analysis
Force Gauge Calibration
Drag Force Sensor Calibration
Actual
Mass (g)
Force Gauge Mass (g)
Force Gauge Measurement (g)
Drag Measurement (N)
Actual Force (g)
10
9.6
6.8
5
6.418
20
19.5
26.4
25
25.907
30
29.5
48.5
47
47.881
40
39.3
33.1
33
32.568
50
49.6
15.6
15
15.168
60
59.4
50.8
50
50.168
70
69.1
23.9
23
23.421
Standard Error of Fit: .5585
The above table displays the results from the calibration of both the force gauge and the drag force sensor. When performing regression analysis, plots were formed of the data above in the form of force gauge readings vs. weights for the calibration of the force gauge and actual force vs. drag measurement for the drag force sensor calibration. When incorporating a linear fit of both plots respectively, the linear regression equations were and . (Equation 1) was utilized to further regression analysis by calculating the standard error of fit. The plots shown below are of the calibration plots.
The table below outlines measurement results from testing of the car in the wind tunnel made by the members of the group. It includes max flow velocity of the wind tunnel, the drag measured at max speed, and the drag coefficient at max speed with respect to the group’s vehicle and the provided vehicle by the lab TA.
Table 2: Results of Wind Tunnel Testing
Max flow velocity in the wind tunnel (m/s)
15.30
Drag at max speed, group vehicle (N)
7.11
Drag coefficient at max speed, group vehicle
.4650
Drag coefficient at max speed, provided vehicle
1.015
Using excel and the plotting function, we can create functions relating the measured drag to the flow velocity of the wind tunnel. This is done so by creating a linear fit and adding a regression line to display the relationship between the two variables. When doing so the regression line is yielded for both vehicles tested. The functions relating drag and flow velocity for the group-made vehicle and the lab-provided vehicle are and , respectively.
Table 3: Quantifying Hysteresis of Wind Tunnel
Trial
Wind Tunnel Setting
Velocity (m/s)
Drag (N)
1
6
15.300
19
2
5
11.740
15
3
4
10.18
7
4
3
7.820
5
5
2
1.490
2
6
2
2.320
3
7
3
7.550
5
8
4
9.960
7
9
5
11.860
13
10
6
15.27
18
To relate drag coefficient of the acquired data to Reynolds number, Reynolds number was first calculated for each trial using (Equation 4). This equation is the ratio of the product of density, velocity of the air flow, diameter of the wind tunnel (.16 m) and dynamic viscosity of air. An equation was acquired to illustrate the relationship between the drag coefficient and Reynold’s number for both models used throughout this experiment. The equations relating the two variables for the group-made vehicle and the lab-provided vehicle are and , respectively. Below are the illustrations of the regression analysis along with the linear regression.
Figure 3: Regressions Analysis, Group Vehicle
Figure 4: Regression Analysis, Lap-Provided Vehicle
When comparing the results obtained in this experiment to real-world applications, it is important to note that since the drag force and velocity of air in the wind tunnel are independent variables, we can justify our results using the theoretical density of air to calculate our theoretical coefficient of drag. The theoretical density of air at room temperature and atmospheric pressure is 1.184 Kg/m3. Therefore, by using (Equations 2 & 3) we can calculate the theoretical coefficient of drag to be 0.48095. When compared to our measured coefficient of drag, at 0.4650, the measured coefficient of drag is within 1% of the theoretical value. The calculations just performed were taken at a room temperature of 25 C, most closely resembling our lab conditions. The percent error was calculated using (Equation 5).
Figure 5: Flow Visualization
The above illustration is the flow visualization of the group-made vehicle. It is seen that stream flows uninterrupted around the vehicle, following the contours of the body. The wind tunnel was set at setting 2 so the flow stream can be visualized easily. No turbulence is observed in the rear of the vehicle. The front appears to have no “slicing effect” as the stream flows around it acting as a downward force on the front of the vehicle. When performing the calibration of the force gauge and the drag force sensor, two equations were yielded to best conduct the experiment further. The equations were stated before in the paragraphs above. The force gauge sensor calibration was then used to perform regression analysis and find the standard error of fit which was calculated to be 0.5585.
The results for the vehicle testing by the group were then acquired and compared to that of a control vehicle provided to the group by the lab TA. The results of the wind tunnel testing include a max flow velocity of 15.30 m/s, a drag of the group’s vehicle at max speed of 7.11 N, and a calculated drag coefficient of the group’s vehicle of 0.4650 compared to that of the provided vehicle which yielded a drag coefficient of 1.015. This proves the vehicle made by the group members has a lower coefficient of drag and thus a lower drag force. The functions relating drag and flow velocity for the group-made vehicle and the lab-provided vehicle are and , respectively.
A relationship between the drag coefficient and Reynold’s number was then asked to be drawn and the resulting equations were for the group’s vehicle and for the second model provided by the lab TA. The experimentally acquired coefficient of drag was calculated to be very close to that of a theoretical value calculated from a theoretical density. The experimental yielding a value of 0.4650, was within 1% of the theoretical at a value of 0.48095. This proves little error was encountered during our experiment and the calibration of the force gauge and drag sensor was performed accurately. The results are tabulated below in Table 4.
When performing this experiment multiple errors were encountered. The first and most important is the accuracy of the wind tunnel tuning knob. When adjusting the intensity of the flow velocity in the wind tunnel, the knob proved to be not constant with regards to repeatability. The knob featured smooth transitions into the quantified flow velocities while one with distinct tactile positions would yield more precise results. Another variable leading to error in the experiment is the placement of the pitot static tube in the wind tunnel. The pitot static tube needs to be placed as close to the vehicle as possible, however the design of both the tube and wind tunnel made for some difficulty. Flow velocities and other variables measure through the LabVIEW software may be skewed because of this. Human error is present in the form of LabVIEW operation. Pausing and stopping at certain times could have made for slightly random results. And at last our wind tunnel glass was damaged (missing a piece) so that could have affected the results.
Table 4: Final Results Summary
Force Gauge Calibration Equation
Drag Force Sensor Calibration Equation
Standard Error of Fit
0.5585
Max flow velocity in the wind tunnel (m/s)
15.30
Drag at max speed, group vehicle (N)
7
Drag coefficient at max speed, group vehicle
0.4650
Drag coefficient at max speed, provided vehicle
1.015
Function relating drag and flow velocity (group vehicle)
N
Function relating drag and flow velocity (lab vehicle)
Function relating drag coefficient and Reynold’s Number (group vehicle)
Function relating drag coefficient and Reynold’s Number (lab vehicle)
Experimental and theoretical drag coefficient with percent error
Experimental: 0.4650
Theoretical: 0.48095
Percent Error: 0.449%
VI) Conclusion
The “Measuring Drag and Visualizing Flow Patterns Around Vehicle Model” experiment was helpful and very informative. It focused on understanding the fundamental principles of aerodynamics and introduced the practicality of how to calibrate pressure transducers. The aerodynamic principles were modeled with a group-built vehicle and a small-scale vehicle (provided by the teaching assistant). Both vehicles were tested using a wind tunnel and a VI given by the TA. Multiple things were computed for each model at various flow velocities including velocity, density, dynamic pressure, static pressure, and drag. The coefficient of drag for both vehicles was determined by calibrating and plotting the values of the force gauge and drag force sensors. The calibration equations were used for both sensors (Equation 1). Next, the max flow velocity in the wind tunnel was computed. Then the students found the drag coefficient at max-speed for both models. The max flow velocity in the wind tunnel lead to 15.30. After the wind tunnel flow velocity was achieved the drag coefficient at max-speed for the group-built model and the small-scale model resulted in 0.4650 and 1.015 respectively (Equation 2 & 3). As seen from the given values of drag coefficient that the group-built model has a lower coefficient of drag than that of the small-scale. The relationship between the drag coefficient and the Reynold’s number for both vehicle models were compared using the following equation for the group-built model and for the small-scale model (Equation 4). The resulting theoretical coefficient of drag was computed to be 0.48095. In conclusion, since both values of drag coefficient are within 1% the encountered error during the experiment was very minimal. This lead to an accurate calibration of the force gauge and drag force sensor. Overall, this was a very well-organized lab but there are a few things that would make it even more fun and enhance the learning experience. First, the wheel we were given didn’t have rubber or any type of grip to hold onto the ground so we experienced some lateral movement when the velocity in the wind tunnel. Also, the building requirements were vague, particularly surrounding the “cabin”. This lead to an unfair advantage when some groups ignored it leading to a significantly more aerodynamic car.
VII) Appendices
Table 1
Vehicle Dimension Constraints
Cabin exterior
32 mm width x 30 mm height x 60 mm length mm
Minimum ground clearance
10 mm
Wheelbase
100 mm
Distance between right and left wheels
34.3 mm
Minimum load capacity
1000 gm
Additional Constraints
• Vehicle body at a length greater than cabin length
• Minimum 4 wheels
• Circular flat horizontal loading surface on top with diameter =10 mm
• Wire connector loop at the front of vehicle, max diameter =1.5 mm
Equations
Equation 1: Standard Error of Fit
Equation 1a:
Equation 2: Coefficient of Drag
Equation 3:
Equation 4: Reynold’s Number
Equation 5: Percent Error
References
[1] Mansy, Hansen, 2017, “EML 3303C and EAS 3800 MECHANICAL ENGINEERING
MEASUREMENTS, BERNOULLI PRINCIPLE – (GROUP REPORT) SPRING
2017”, UCF
[2] Figliola, Richard S. and Donald E. Beasley. Theory and Design for Mechanical Measurements. 5th ed. New York, NY: John Wiley & Sons, 2011. Print.
[3] M. Pachlhofer, “Darcy-Weisbach friction calculation in StormCAD and SewerCAD,” Bentley Communities, 20-Feb-2014. [Online]. Available: https://communities.bentley.com/products/hydraulics___hydrology/w/hydraulics_and_hydrology__wiki/12247.darcy-weisbach-friction-calculation-in-stormcad-and-sewercad. [Accessed: 22-Apr-2017].