Lab 4 -- Fluid Dynamics: Week 2

Force Balance and Calibration

One way to measure the forces and moments acting on an object in a flow is to use a force balance.  A force balance utilizes one load cell for each directional component of force and moment.  When a force or moment is applied to an object mounted on a force balance a strain is created within the respective load cell.  The strain is then measured by a strain gage that is inside the load cell.  The strain gage then turns the amount of strain into a change in voltage.  Voltage is proportional to force therefore the measured voltage from the force balance can be turned back into the forces and moments that are acting on the object. 

            Over time the loads cells of the force balance will not read accurately and will “drift” from the real value.  Therefore, the force balance must be calibrated in order to remove the “drift” in the measured force and moments.  To calibrate the force balance, various known weights are attached in the direction of a single force component.  In order to see the “drift” in each component of the force or moment one force component or moment must be calibrated at a time.  The measured voltage or force is then plotted versus the known weight.  The plot will give the voltage for the known forces and moments and will also give the trend of the voltage versus force.  Since voltage is proportional to force the calibration curve will be linear. 

For this lab a 6 degree of freedom sting balance will be used to measure 3 forces and 6 moments during testing. Strain gauges measure the deflection of a metal beam within the device and use its material properties and geometry to determine how much force is being applied. Due to the design of the sting the measured forces and moments are coupled meaning several 6x6 calibration matrices are required to resolve the individual forces and moments alone. Below is the information required for calibration as provided by Aerolab.

-5.350000000E+00	2.609400000E+03	-2.004900000E+00	-2.471945340E+01	2.483178E+01	-3.547237E+01
-2.663700000E+03	4.842200000E+00	4.499100000E+01	3.739469363E+00	-2.683828E+01	3.031786E+01
-1.445100000E+00	9.355300000E+00	2.075600000E+00	2.226912819E+03	8.686581E+00	-4.108946E+00
-3.410500000E+01	-2.994600000E-01	-2.268900000E+03	1.127694119E+01	-7.119951E+00	1.742088E+01
-3.258611210E+02	2.871835546E+02	6.376038821E+00	-7.051597180E+01	2.689143E+03	-2.893483E+02
1.926350031E+02	1.230846765E+02	4.432376232E+02	5.799620650E+02	1.240966E+02	6.366004E+03

-4.310700E-04	4.162200E-05	4.1464000E-03	1.930190E-05	1.1705E-02	-4.0300E-06
1.777600E-04	-2.197400E-04	2.9586000E-05	3.219426E-03	-1.1115E-02	6.0100E-04
2.753000E-04	-4.667800E-05	2.8875000E-04	-2.825400E-04	6.7000E-04	7.1100E-05
9.488900E-05	-1.433400E-04	4.4672000E-04	-5.262300E-05	-8.7000E-04	1.7200E-04
-9.794820E-03	3.500444E-03	-1.0343479E-02	3.087124E-03	1.1290E-03	3.2408E-02
1.512935E-03	4.610287E-03	2.2939180E-03	3.355912E-03	-1.2160E-03	1.8670E-03

Channel order is N1, N2, S1, S2, AF, Rm.

Data Reduction

The calibration matrices are employed as follows:

Where:

= Force applied to the balance.

= Balance output resulting from applied force.

From this, N1, N2, S1 and S2 are reduced to N, S, Pm and Ym using:

Where L = distance between gage stations. In the case of the Syracuse balance,

this distance is 2.545 inches. The units used for calibration are pound-force for Forces and inch-pound-force for Moments.

Airfoil Theory

As fluid flows over the unique shape of an airfoil, a boundary layer forms on the surface. At a zero-degree angle of attack the boundary layer around a symmetric airfoil is equal on both sides of the airfoil, but if the airfoil has a non-zero angle of attack the surface velocity on top of the airfoil increases while the surface velocity on the bottom decreases. Similarly, for a non-symmetric airfoil at a zero degreesangle of attack the boundary layers on both sides of the airfoil are not equal. The non-symmetric boundary on the airfoil creates a circulation around the airfoil. The circulation increases the velocity on one side of the airfoil while it decreases the velocity on the other side. As seen in the Navier-Stokes equations, velocity is related to pressure. Therefore, on the higher velocity side of the airfoil pressure decreases while on the lower velocity side pressure increases. This pressure difference causes a net force on the airfoil. The net force can be broken up into components of lift and drag.

Figure 1: Forces and Pitching Moment on an airfoil

The lift is the force normal to the direction of the freestream velocity. The dimensionless parameter for lift per unit area is the coefficient of lift.

S is the wing area. From thin airfoil theory the lift produced by a symmetric airfoil is directly related to its angle of attack as approximated by the equation below.

As determined by thin airfoil theory the lift-curve slope is 2π. Drag is the force which opposes the freestream direction. The dimensionless parameter of drag per unit area is the coefficient of drag.

Pressure drag is a major source of the drag on an airfoil. The pressure drag is due to the component of the pressure difference which is parallel to the freestream. This drag increases exponentially as lift increases. Like a bluff body the airfoil will cause a momentum deficit in the flow but unlike the bluff body the airfoil is a streamlined body, therefore the drag caused by this momentum loss is small compared to the pressure drag. As the angle of attack of the airfoil is increased the boundary layer stays attached to the surface of the airfoil until a certain critical angle of attack is reached. At this point the boundary layer on the top of the airfoil begins to separate from the trailing edge of the airfoil. If the angle of attack continues to be increased separation creeps up the airfoil from the trailing edge and then the boundary layer completely detaches from the top of the airfoil resulting in a condition known as stall. Stall quickly results in a large spike in drag and sudden loss of lift.

The net force also produces a moment about the airfoil. The dimensionless parameter for the moment per unit area is the coefficient of moment.

Here x is the mean chord length of the airfoil. At the leading edge of the airfoil the moment has a negative slope as the lift increases. There is a point on the airfoil where the moment is zero no matter the magnitude of lift. This point is called the mean aerodynamic center and is located approximately at the quarter chord. Attached are the characteristic curves of the airfoil.

2-D vs. 3-D Objects

In the test section of the wind tunnel the flow can either be two dimensional or three dimensional. If the test object spans across the entire test section the object is considered to have an infinite span and therefore the flow is approximated as two dimensional. An object in a two dimensional flow has less drag than a three dimensional flow. This is due to the fact that there is more boundary layer separation on the object in a three dimensional flow than in a two dimensional flow. In two dimensional flow, separation occurs on just the top and bottom of the object while in three dimensional flow separation occurs on the top, bottom, and the sides. The greater boundary layer separation leads to a greater amount of pressure drag upon the object. Additional energy is lost at the 3-D tips in the form of trailing vortices. So although the two dimensional object has greater frontal surface area the increased amount of pressure drag of the three dimensional object is much greater than the increased profile drag.

Figure 2: Bluff Bodies in a flow (top view of test section)

Figure 3: Cylinder mounted on force balance (side view of test section)

Boundary Layer

With flow over any solid object the velocity of the fluid in direct contact with the body goes to zero.  This is called the no slip condition which occurs due to the viscous forces that act between shearing fluid/wall layers. Since fluids deform easily wall friction physically forces a parabolic boundary layer profile (as seen in the figure below).  Moving away from the wall flow begins to return to the freestream velocity.  The distance from the wall of the object to the location where the flow returns to 99% of the freestream velocity is call the boundary layer thickness.  In the boundary layer region, the flow is unsteady and rotational therefore the Bernoulli’s equation does not hold in this region.   Since Bernoulli’s equation is invalid and the full Navier-Stokes equation is difficult to solve, the flow in the boundary cannot be solved for.  The thickness of the boundary layer grows as the flow travels downstream along the wall.  Further downstream the boundary layer makes a transition from laminar to turbulent.  The difference between the laminar and turbulent boundary layer is that the turbulent has a steeper gradient.  The thickness of the boundary layer, δ, is at the point where the local velocity is 99% of the freestream velocity. 

Figure4.  Boundary Layer over a flat plate

Trip into Turbulence

The reason why golf balls have dimples is to trip the boundary layer into being turbulent. As seen in Figure 5, pressure drag is lessened when the laminar boundary layer trips into a turbulent boundary layer (NOTE: This is only true for a blunt body). At this point the boundary actually stays attached to the surface of the sphere longer thus producing less pressure drag upon the sphere. To induce a turbulent boundary layer a small disturbance is place on the surface of the sphere ahead of the separation point.

Figure 5: Laminar vs. Turbulent Boundary Layer

Equipment

• Closed loop wind tunnel
• Pitot-static tube
• Aerolab 6 DoF Sting Balance
• Clark Y airfoil
• Daytronic System 10 DataPac
• Pressure Systems 9010 Optomux
• 5x 4.8cm O.D. Cylinder
• Lengths: 10.5”, 18”, 20”, 22”, and 24”
• Pitot tube rake
• Thermometer
• Labview

Procedure

Part 1: Boundary Layer

1. The wind tunnel will be run at 30 Hz.
2. Place the boundary layer rake in the 1^st hole in the middle of the test section. Ensure the tubes are parallel to the freestream flow.

3. Connect the tubes to the pressure scanner.
4. Acquire pressure data using the labview VI and manual record the temperature data.

Part 2: Airfoil

LabVIEW Program: Force_Balance_Airfoil.vi

1. Place airfoil on sting balance in the wind tunnel, secure using the set screws.
2. Turn on the wind tunnel at 30 Hz or 45 Hz.
3. Adjust angle of airfoil to -10 degrees using the model positioning system. Acquire force and moment data from the computer.

4. Note the temperature after each data recording.

5. Increase angle of attack by 2 degrees
6. Repeat until an attack angle of 18 degrees.
7. Now engage flaps and slats.
8. Repeat steps 4 to 6.
9. Measure airfoil chord, length, and depth.

Part 3: Cylinders

LabVIEW Program: Force_Balance_Cylinders.vi

1. Record the length and outside diameter of each of the cylinders.
2. Before recording data with a cylinder in the flow, run the program (with the tunnel at 25 Hz) without a cylinder mounted. This should be labeled “Cylinder 0”
3. Insert first cylinder, labeled with the number 1, into the wind tunnel. Cylinder must be perpendicular to the flow.
4. Turn on wind tunnel at 30 Hz.
5. Measure and record the drag produced from the cylinder as well as the temperature inside the tunnel.
6. Repeat the drag measurements for the rest of the cylinders.

Questions

USE +/- 2% for the Force Data Uncertainty!!!

Part 1: (Boundary Layer)

• Plot flow velocity (m/s) as a function of distance (mm) from wall (profile should look something like Figure 2) and compare results at upstream and downstream locations (1^st and 2^nd tunnel holes). —One graph!
• What happens to the velocity of the air as you get closer to the wall? Why?
• Does the velocity in the center of the test section change with distance downstream?  If so how much does it vary and why does it vary? Hint: think continuity!
• What actually happens to the boundary layer profile as you move down stream? What actual physics is responsible for this phenomenon?

Part 2: (Airfoil)

• Plot all 6 forces and moments vs angle of attack. Include both Reynolds numbers for both “clean” (no flaps or slats) and “dirty” (with flaps and slats) configurations on a single plot.
• Plot coefficient of lift vs. angle of attack. Plot coefficient of drag vs. angle of attack. Plot coefficient of drag vs. coefficient of lift. Plot coefficient of moment vs. angle of attack. Plot coefficient of moment vs. coefficient of lift. Include all 4 tests on a single plot.
• What is the Reynolds number for each tunnel run?
• What is the slope of the coefficient of lift vs. angle of attack (otherwise called lift-curve slope) at each tunnel speed? Is the measured value close to the theoretical lift curve slope for a thin airfoil?
• What angle of attack did the tuffs visibly separate from the surface of the airfoil? Does this value agree with what your data says?
• Why do the tuffs separate from the airfoil (there is a lot to discuss here. Hint: stall)?
• Does the Reynolds number affect the lift, drag and moment by the airfoil? If so, WHY and how are these quantities affected?

• Does the angle of attack of the airfoil change the freestream velocity of the wind tunnel? If so, explain why (think continuity, again)?

Part 3: (Cylinders)

• What is the Reynolds number?
• What is the coefficient of drag on each of the cylinders?
• Which cylinder had the highest coefficient of drag? Why?
• Compare and explain the difference between “2-D flow” and “3-D flow.”
• How does the coefficient of drag of Cylinder 1 compare to the coefficient of drag obtained from the wake measurements from Part I of the lab?
• How does your drag coefficients compare to published data?

Tips-

• Be consistent with units (convert to SI right in the beginning, find appropriate conversions, and stick to them throughout calculations)
• Clearly label all graphs and tables (so that it is immediately obvious what trend is trying to be conveyed).
• If trying to compare results from two similar experiments combine plots onto one graph (consolidation and/or direct comparison of results is very effective method of presentation).
• Pay attention to neatness of graphs and tables (i.e. white background, thick dark axes, thick colored trendlines, appropriately scaled axes, # of digits, etc).
• Address all questions posed in each lab concisely including all directly relevant information. You may address additional concerns for completeness.
• Do NOT attach any raw data anywhere in lab (only averaged data and short samples may be included when necessary)---No treestumps!
• Read outside sources for additional context (Wikepedia (online) is a great source for basic information when lost but use with caution, it can be misleading). Reference websites when necessary, it is easy enough.
• Reference any FIGURES, PICTURES, ETC used in your report directly under the figure. We read the same websites, books, and reports that you do. Save yourself from trouble and write a reference if you didn’t create it yourself!
• Get started on calculations immediately after lab, this is a long one!

References

-Fox, McDonald & Pritchard, Introduction to Fluid Mechanics, 6th edition, John Wiley & Sons Inc., 2004

-Ira Abbott and Albert von Doenhoff, Theory of Wing Sections, Dover Publications, 1959

-Wikipedia.org

-Van Dykes book of Fluid Motion

-www.airfoiltools.com

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