Fluid Mechanics II Lab Sheet
UNIVERSITI TUNKU ABDUL RAHMAN Faculty
:
Course
:
Year/ Semester Session
: :
Engineering and Science Bachelor of Engineering (Hons) Mechanical Engineering
Unit Code
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UEME3112
Unit Title
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Fluid Mechanics II
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Ms. Jaslyn Low Foon Siang
Lecturer 201305
Experiment 5: PRESSURE DISTRIBUTION ON CIRCULAR CYLINDER AND AIRFOIL Objectives: 1. To obtain and compare theoretical and experimental surface pressure distributions on a circular cylinder. 2. To obtain surface pressure distribution on an airfoil NACA 0012, and describes its significance in the wing design. Introduction: In many engineering applications, it may be necessary to examine the phenomena occurring when an object is inserted into a flow of fluid. The wings of an airplane in flight, for example, may be analyzed by considering the wings stationary with air moving past them. Certain forces are exerted on the wing by the flowing fluid that tend to lift the wing (called the lift force) and to push the wing in the direction of the flow (drag force). Objects other than wings that are symmetrical with respect to the fluid approach direction, such as a circular cylinder, will experience no lift, only drag. Drag and lift forces are caused by the pressure differences exerted on the stationary object by the flowing fluid. Skin friction between the fluid and the object contributes to the drag force but in many cases can be neglected. The measurement of the pressure distribution existing around a stationary cylinder in an air stream to find the drag force is the object of this experiment. Consider a circular cylinder immersed in a uniform flow. The streamlines about the cylinder are shown in Figure 1.
Figure 1. Streamlines of flow about a circular cylinder. The fluid exerts pressure on the front half of the cylinder in an amount that is greater than that exerted on the rear half. The difference in pressure multiplied by the projected frontal area
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Fluid Mechanics II Lab Sheet of the cylinder gives the drag force due to pressure (also known as form drag). Because this drag is due primarily to a pressure difference, measurement of the pressure distribution about the cylinder allows for finding the drag force experimentally. A typical pressure distribution is given in Figure 9.2.
Figure 2. Pressure distribution around a circular cylinder placed in a uniform flow. Shown in Figure 2a is the cylinder with lines and arrowheads. The length of the line at any point on the cylinder surface is proportional to the pressure at that point. The direction of the arrowhead indicates that the pressure at the respective point is greater than the free stream pressure (pointing toward the center of the cylinder) or less than the free stream pressure (pointing away). Note the existence of a separation point and a separation region (or wake). The pressure in the back flow region is nearly the same as the pressure at the point of separation. The general result is a net drag force equal to the sum of the forces due to pressure acting on the front half (+) and on the rear half (-) of the cylinder. To find the drag force, it is necessary to sum the components of pressure at each point in the flow direction. Figure 2b is a graph of the same data as that in Figure 2a except that Figure 2b is on a linear grid. Figure 3 shows the effect of separated flow and the failure of the boundary layer theory. In Figure 3, surface pressure distributions (Cp) for inviscid flow and boundary layer flow on a circular cylinder. The theoretical Cp is obtained using equation Cp = 1- 4 sin2 , while the experimental Cp is calculated using equation Cp = (p – p )/(1/2 V2), where p is the pressure on the surface of the cylinder, p and V are the pressure and velocity in the free stream, respectively. At the frontal and real stagnation points, Cp = 1. At the maximum-thickness point (cylinder shoulders), Cp = -3. Note that theoretical and experimental Cp’s coincide at = 0°. The actual laminar and turbulent boundary layer pressure distributions are surprisingly very different compared to theoretical predictions. Because of the boundary layer separation, the average surface pressure on the rear half of the cylinder is considerably less than that on the front half. Therefore, a large pressure drag is developed, even though (due to small viscosity) the viscous shear drag may be quite small. D’Alembert’s paradox is explained. No matter how small the viscosity, as long as it is not zero, there will be a boundary layer that separates from the surface, giving a drag that is, for the most part, independent of the viscosity.
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Fluid Mechanics II Lab Sheet
Figure 3. Surface pressure distributions (Cp) for inviscid flow and boundary layer. Similar concepts hold for the airfoil as well. The flow past an airfoil at zero angle of contact (the angel between the upstream flow and the axis of the object) is shown in Figure 4a, while the flow past the same airfoil at a 5° angle of attack is shown in Figure 4b. Over the front portion of the airfoil, the pressure decreases in the direction of flow (favorable pressure gradient), while the pressure increases in the direction of flow (adverse pressure gradient). If the adverse pressure is not too great, the boundary layer fluid can flow into slightly increasing pressure region (from C to the trailing edge in Figure 4a) without separating from the surface. However, if the adverse pressure gradient is too large, the boundary layer will separate from the surface as indicated in Figure 4b.
Figure 4. Flow visualization photographs of flow past an airfoil: (a) zero angle of attack, no separation; (b) 5° angle of attack, flow separation. 3
Fluid Mechanics II Lab Sheet Materials and Apparatus: A wind tunnel is really a fairly simple device. Most designs feature each of the five components described below. The overall design creates high-speed, low-turbulence airflow through the test section and allows researchers to measure the resulting forces on the model being tested.
Straighteners: Nozzle: Test Section: Diffuser:
The purpose of the straighteners is to straighten the airflow. The nozzle takes a large volume of low-velocity air and reduces it to a small volume of high-velocity air without creating turbulence. The test section is where the test article and sensors are placed. The diffuser slows the speed of airflow in the wind tunnel.
The wind tunnel used in this experiment has a multipurpose 30×30×45 (w×h×l) cm Plexiglas test section. The air flow is generated by using a centrifugal fan. Air is drawn by the centrifugal fan into the settling chamber through a faired inlet and passes through a rectangular screen flow conditioning section before being accelerated through the contraction section into the test section. The flow then passes through the diffuser section into the centrifugal fan and is discharged into the room. The test-section air velocity control is accomplished by a variable frequency inverter. Figure 5 is a schematic of the side view of the circular cylinder. The cylinder is placed in the test section of the wind tunnel which is operated at a pre-selected velocity. The pressure tap labeled as #1 is placed at 0° directly facing the approach flow. The pressure taps are attached to a multi-tube inclined U-tube manometer board. Only the first 10 taps are connected. The manometers will provide readings of pressure at 15° intervals. For two different approach velocities, measure and record the pressure distribution about the circular cylinder. An airfoil NACA 0012 is also mounted in the test section. However, only the first 7 taps are connected.
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Fluid Mechanics II Lab Sheet
Figure 5. Schematic of the experimental apparatus used in this experiment. Procedure: (1) The relationship between the fan frequency and air speed (i)
Level and zero the inclined manometer. Record the room temperature and barometric pressure. (ii) Connect the tubing to the inclined manometer from the pitot-static tube. Ensure the connection is done properly. (iii) Switch ON the wind tunnel, adjust the fan motor frequency to 35 Hz. Run the motor. Allow the flow in tunnel stabilize for about 1-2 minutes. (iv) Loosen the screw of the pitot-static tube, move the pitot-static tube to the center of the test section. Ensure the measuring point of the tube is in-line with the air flow. Tighten back the screw. (v) Record the dynamic pressure from the incline manometer. (Reminder: The reading of the inclined manometer is fluctuating, kindly take the average reading). (vi) Record all the readings in Table 1. (vii) Repeat the whole experiment with different fan motor frequencies (i.e., 5 Hz increment) until 50 Hz. (viii) Using the equations provided, compute the maximum air speed for each fan motor frequency value. (2) Pressure distribution on circular cylinder (i)
Place the test model holder stand on top of the test section. Place the counter weight on the rear part of the test model holder stand. (ii) Connect the tubing to the respective pressure port of the cylinder. (iii) Place the cylinder into the test section. Insert the circular cylinder’s holder rod to the hole provided at the test model holder stand via the slot. Tighten the set screw using screw driver. Ensure the first pressure port is in parallel direction of the air flow before tightening it. (iv) Insert the tubing to the slot of the top test section. Close all the windows of the test section with respective cover.
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Fluid Mechanics II Lab Sheet (v)
Connect all the tubing to the multi-tube inclined U-tube manometer. Ensure the connection is correct whereby the first port should be connected to the first U-tube manometer and so on. (vi) Switch ON the wind tunnel. Set the fan motor frequency to 35 Hz. Allow the flow in the tunnel stabilize for 1-2 minutes. (vii) Measure the pressure differences for all the U-tube manometers. Record the readings in Table 2. (Reminder: The reading should be negative reading). (viii) Repeat the experiments with different fan frequencies (40, 45 and 50 Hz). (ix) Plot the graph of pressure differences against pressure point. (3) Pressure distribution on airfoil NACA 0012 (i)
Place the test model holder stand on top of the test section. Place the counter weight on the rear part of the test model holder stand. (ii) Connect the tubing to the respective pressure port of the airfoil NACA 0012. (iii) Place the airfoil into the test section. Insert the airfoil’s holder rod to the hole provided at the test model holder stand via the slot. Tighten the set screw using screw driver. Ensure the airfoil is in parallel direction of the air flow before tightening it. (iv) Insert the tubing to the slot of the top test section. Close all the windows of the test section with respective cover. (v) Connect all the tubing to the multi-tube inclined U-tube manometer. Ensure the connection is correct whereby the first port should be connected to the first U-tube manometer and so on. (vi) Switch ON the wind tunnel. Set the fan motor frequency to 35 Hz. Allow the flow in the tunnel stabilize for 1-2 minutes. (vii) Measure the pressure differences for all the U-tube manometers. Record the readings in Table 3. (Reminder: The reading should be negative reading). (viii) Repeat the experiment with different fan frequencies (40, 45 and 50 Hz). (ix) Plot the graph of pressure distributions against pressure points. Equations: (i)
The Pitot formula, V =
2( Pstagnation − Pstatic )
ρ
, where V = air speed (m/s), Pstagnation =
stagnation or total pressure (Pa), Pstatic = static pressure (Pa), and = air density (kg/m3). (ii) The manufacturer’s formula, V = 1096.2 Pv / ρ , and ρ = 1.325 × PB / T , where V = air speed (ft/min), Pv = velocity pressure (inches of water), = air density (lb/ft3), PB = barometric atmospheric pressure (inches of mercury), T = absolute room temperature (indicated temperature (°F) + 460). (iii) The dynamic viscosity ( ) can be calculated using Sutherland’s relation. For SI units, 1.4578 × 10 −6 × T 1.5 µ= T + 110.4 where T is the room temperature in Kelvin.
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Fluid Mechanics II Lab Sheet
Results and Discussion: (1) Pressure distribution on circular cylinder (i) Plot the pressure distributions against pressure points and describe the pressure points with a diagram. Discuss the pressure distributions on the circular cylinder. (ii) Using the equations provided, compute the experimental Cp = (p – p )/(1/2 V2) and compare with theoretical Cp = 1- 4 sin2 . Also, compare both Cp profiles with those shown in Figure 3. You need to obtain the data of maximum air speed for various fan motor frequencies from another group doing the Experiment 1 on the same day. (2) Pressure distribution on airfoil NACA 0012 (i) Plot the graphs of pressure distributions against pressure points and describe the pressure points with a diagram. Discuss and interpret the finding from the graph. Laboratory Report 1. This is a GROUP report. DO NOT COPY, or you will not obtain any mark. However, you will share the data with your group members. 2. Attach the ORIGINAL spreadsheets and plots containing the experimental data with your report. You need to describe them properly. 3. Provide a sample calculation. Coordinate with your group members to avoid presenting the same sample calculation. 4. Your report should include: Objective, Introduction, Methods and Apparatus, Procedures, Results and Discussion, and Conclusions and Recommendations.
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Fluid Mechanics II Lab Sheet
Table 1 Fan Motor Frequency (Hz) 35 40 45 50 Table 2 Points
Dynamic Pressure (in. water)
Maximum Air Speed (m/s)
35
Fan Motor Frequency (Hz) 40 45 Total Pressure (mm water)
50
35
Fan Motor Frequency (Hz) 40 45 Total Pressure (mm water)
50
1 2 3 4 5 6 7 8 9 10
Table 3 Points 1 2 3 4 5 6 7
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