10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13 Delft, The Netherlands, July 1-3, 2013

**Aerodynamic characteristics around the stalling angle of the discus **

**using a PIV **

**Kazuya Seo 1**

1

Department of Education, Art and Science, Yamagata University, Yamagata, Japan seo@e.yamagata-u.ac.jp

**ABSTRACT **

This paper describes the hysteresis in the aerodynamic properties of a discus near to its stalling angle. Wind tunnel tests
*were carried out with a full-size woman’s discus. The experimental aerodynamic data D, L and M were obtained from *
wind tunnel tests as functions of the angle of attack. It was found that the drag, lift and pitching moment coefficients,

*CD CL and CM, increase with increasing the angle of attack up to a stalling angle of 29-30. Beyond the stalling angle, *

*CL and CM* decrease suddenly and abruptly with increasing angle of attack. On the other hand, recovery from the stall

does not occur at the same stalling angle of 29-30 when the angle of attack decreases from the stall state; recovery
actually occurs at 25. The dependence of C*L and CM* on the angle of attack is almost the same when the angle of attack

is less than 24. Therefore, hysteresis occurs near the stalling angle. A laminar bubble region is observed in the upstream side of the discus at 28 during the process of increasing the angle of attack, and re-attachment occurs around the convex point of the discus. However, re-attachment does not occur at 26 during the process of decreasing the angle of attack.

**INTRODUCTION **

Discus throwing is a sport in which the thrower attempts to gain the longest flight distance. To determine the flight path
of a discus [1] when it is thrown, it is essential to know what aerodynamic forces are acting on it. We have measured the
aerodynamic forces acting on a women’s discus [2]. It was found that the lift coefficient decreases suddenly and
abruptly at the stalling angle. Therefore, we repeated the force measurements with fine intervals in terms of angle of
attack in order to elucidate the features of stalling in detail. As a result, it was found that hysteresis occurs around the
stalling angle. In this paper, the dependence of the aerodynamic coefficients on the angle of attack and the results of
**PIV measurements around the stalling angle will be shown. **

**METHOD **

A full-size discus was employed to determine the aerodynamic forces acting on it in a low-speed wind tunnel with a 0.7
m × 0.7 m rectangular nozzle. We used a commercially available discus (Super HM, Nishi athletics goods). Definitions
*of the characteristic parameters are shown in Figure 1. The wind speed, U, was set to 15, 20, 25 and 30 ms*-1_{. Since the }
*aerodynamic coefficients are independent of the spin rate on its axis of symmetry [2], it was set at ω=0 (non-spin) *
revolutions per second. The angle of attack, AoA, which is the angle between the discus planform and the direction of
the flight path, was also varied, from 0 to 90. The measurement interval for AoA was 1 around the stalling angle and
5 for the remainder of the range. Data were acquired over a period of 8 sec. using a three-component strut-type balance
(LMC-3531-50NS; Nissho Electric Works Co., Ltd.) and were recorded on a personal computer using an A/D converter
board with a sampling rate of 1000 Hz. Definitions of the aerodynamic forces are also shown in Figure 1. The drag and
*the lift are denoted by D and L, respectively, and the pitching moment is denoted by M. The ‘nose-up’ rotation is *
*defined as positive. The aerodynamic forces are converted into the drag coefficient CD, the lift coefficient CL* and the

*pitching moment coefficient CM*, as follows:

*A*
*U*
*L*
*CL*_{0}_{.}_{5}_{} 2 *(1) *
*A*
*U*
*D*
*CD* _{0}_{.}_{5}_{} 2 *(2) *

*Ad*
*U*
*M*

*CM* _{0}_{.}_{5}_{} 2 (3)

where is the density of air, A (= d2* _{/4) is the cross sectional area of the discus planform and d is the diameter of the }*
discus planform.

The measuring points denoted by P1, P2 and P3 for the pressure are shown in Figure 2. The measuring points are on the ‘pressure side’ when AoA is positive, and they are on the ‘suction side’ when AoA is negative.

**Figure 1 ** Definitions of the characteristic
parameters.

**Figure 2 ** Measuring points for the pressure.

The 2D-PIV measurements were carried out on the centerline of the discus. Micro-droplet particles with diameters of
1μm were generated by an aerosol generator (PivPart40, PivTec), and were introduced into the flow from the sirocco
fan in the wind tunnel. A high repetition-rate pulsed ND:Yag laser (LDP-100MQG, Lee Laser) illuminated the
micro-droplet particles. A high-speed camera (Memrecam GX-8, Nac) was used to record tiff images at a sampling frequency
of 1000Hz. The wind speed was set at 20ms-1_{. Figure 3(a) shows a picture taken before the run, while Figure 3(b) shows }
a picture taken during the run.

**(a) Before the run; ** **(b) During the run **

**Figure 3 ** Experimental set-up of PIV measurement.
**RESULTS and DISCUSSIONS **

*The lift coefficient, CL, is shown in Figure 4 as a function of the angle of attack, AoA. The wind speed, U, is taken as a *

parameter. The closed triangles denote the data which is acquired in the process of increasing AoA from 0 to 35,
while the open circles denote the data which is acquired in the process of decreasing AoA from 35 to 0. It can be seen
*that CL* increases almost linearly with increasing AoA below 25. In the process of increasing from 0 to 35, C*L*

decreases suddenly and abruptly at 30 (29 for U=15m/s). This decrease is caused by the effects of stalling. Though the stall might be a ‘noise induced’ stall, which is very sensitive to small amounts of noise such as that caused by surface roughness or disturbance due to the introduced wind, the stalling angle is almost the same for all wind speeds. In the process of decreasing from 35 to 0, recovery from stalling occurs at 25 (24 for U=15m/s). Therefore, hysteresis occurs near the stalling angle.

*The dependence on AoA of the pressure coefficient, CP, is shown in Figure 5. The pressure coefficient, CP*, is defined as

the pressure divided by the dynamic pressure. The measuring points for the pressure are shown in Figure 2. The
measurements were carried out following a procedure from 0 to 90, from 90 to 0, from 0 to -60 and from -60 to
0. It can be seen that C*P* increases with increasing AoA in the range from 0 to 55 for P1, from 0 to 65 for P2 and
from 0 to 80 for P3. This is because there is an ‘in-flow’ directly into the measuring point. When AoA decreases from
90 to 0, C*P follows the same path with increasing AoA. On the other side, CP1* decreases with decreasing AoA in the

range from 0 to -28. It changes suddenly with decreasing AoA from -15 to -20. On the way back from -60 to 0,

*CP1* recovers from the stall at -25. Therefore, hysteresis occurs on the suction side. It can be seen that C*P2* also

decreases with decreasing AoA in the range from 0 to -30. Since C*P2 also changes suddenly with decreasing AoA *

from -27 to -28, the value of C*P2 is approaching that of CP1*. This implies that the region of the laminar separation

bubble extends from the measuring point P1 to P2*, because CP* is almost constant in the laminar separation bubble region

[3].
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 15 30 45
*C* *L*
AoA [°]
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 15 30 45
*C* *L*
AoA [°]
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 15 30 45
*C* *L*
AoA [°]
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 15 30 45
*C* *L*
AoA [°]

**(a) U=15m/s; ****(b) U=20m/s; ****(c) U=25m/s; ****(d) U=30m/s **

**Figure 4 ** The lift coefficient as a function of the angle of attack.

### -2.0

### -1.5

### -1.0

### -0.5

### 0.0

### 0.5

### 1.0

### 1.5

### 2.0

### -90

### -60

### -30

### 0

### 30

### 60

### 90

### CP1

### CP2

### CP3

*C*

*P*

### AoA [°]

**Figure 5 ** *The dependence on angle of attack of the pressure coefficient at U=20m/s. *

*The aerodynamic coefficients CL, CD and CM at U=20m/s are shown as a function of the angle of attack in Figure 6. *

Error bars that indicate the standard deviations for velocity are also shown. The closed triangles denote the data which
is acquired in the process of increasing AoA from 0 to 35, while the open circles denote the data which is acquired in
the process of decreasing AoA from 35 to 0. Since the difference in path is negligibly small above 35, the averaged
*values acquired by the back support are denoted by the open squares. It was found that hysteresis occurs for CL and CM*

near the stalling angle. The error bars near the stalling angle become longer. Since the induced drag coefficient is
*proportional to the square of CL [4], CD* also decreases just beyond the stalling angle in both processes.

-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 15 30 45 60 75 90
*C* *L*
AoA [°]
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 15 30 45 60 75 90
*C* *D*
AoA [°]

**(a) Lift coefficient; ** **(b) Drag coefficient; **

-0.05
0.00
0.05
0.10
0.15
0.20
0 15 30 45 60 75 90
*C* *M*
AoA [°]

**(c) Pitching moment coefficient **

**Figure 6 ** **The aerodynamic coefficients as a function of the angle of attack at U=20m/s. **

**(c) 35****; (d) 28****; **

**(e) 26****; (f) 25**

**Figure 7 ** **Velocity vectors on the suction side of the discus at U=20m/s. **

*The results of 2D-PIV measurements at U=20m/s are shown in Figure 7. The angle of attack increases from Figure7 (a) *
to (c) in the process of increasing AoA. The angle of attack decreases from Figure7 (d) to (f) in the process of
decreasing AoA. The flow direction is from the left to the right. The discus is located around the bottom in each picture.
It can be seen that the flow almost runs along the surface of the discus at 15 (Figure 7 (a)) and 28 (Figure 7 (b)) in the
process of increasing AoA, while boundary separation occurs at 35 (Figure 7 (c)). At 28 in the process of increasing
AoA (Figure 7 (b)), a low velocity region can be seen around the downstream side of the leading edge. This region
might correspond with the laminar separation bubble region. The velocity outside this low velocity region becomes
higher. Re-attachment occurs around the convex point of the discus (There are two circles on either side of the discus.
The edge of these circles is the convex point.). Since the regulations for discuses allow the diameters of these circles to
be changed in the range between 50 and 57mm, there is a possibility of changing the position of re-attachment. Since
the transition from the laminar flow to turbulent flow occurs far away from the discus surface at 35, it may happen that
the turbulent flow wedge cannot reach the surface again. Thus, there is no reattachment. At 28 (Figure 7 (d)) and 26
(Figure 7 (e)) in the process of decreasing AoA, boundary separation also occurs as it does at 35. Even if the angle of
attack in Figure 7 (d) is same value of 28 as Figure 7 (b), the velocity vectors are completely different. At 25 (Figure
7 (f)) in the process of decreasing AoA, recovery from the stall occurs.

**SUMMARY **

1. Hysteresis occurs around the stalling angle for both the lift and the pitching coefficients.

2. Stalling occurs at 30 in the process of increasing the angle of attack, while recovery occurs at 25 in the decreasing process.

3. The flow runs almost along the surface of the discus up to 28 in the process of increasing the angle of attack. 4. A laminar bubble region is observed in the upstream side of the discus at 28 in the process of increasing the angle

of attack.

**ACKNOWLEDGEMENTS **

**This work is supported by a Grant-in-Aid for Scientific Research (A), Japan Society for the Promotion of Science. **
**REFERENCES **

[1] Seo K., Shimoyama K., Ohta K., Ohgi Y. and Kimura Y. “Optimization of the moment of inertia and the release conditions of a discus” Procedia Engineering 34 (2012) pp.92-97.

[2] Seo K., Shimoyama K., Ohta K., Ohgi Y. and Kimura Y. “Aerodynamic behavior of a discus” Procedia Engineering 34 (2012) pp.170-175.

[3] Rinoie K. “Laminar separation bubbles formed on airfoils” Nagare 22 (2003) pp.15-22 (in Japanese). [4] John D. Anderson. “Fundamentals of Aerodynamics” 3rd ed. New York: Mcgraw Hill (2010)