Sound Source Measurement of a Semi-Circular Cylinder in a Uniform Flow by Particle Image Velocimetry

In this paper, the measurement of an aerodynamic sound source for a semi-circular cylinder in a uniform flow is described using Particle Image Velocimetry (PIV). This experimental technique is based on vortex sound theory, where the time derivative of vorticity is evaluated with the aid of two sets of standard PIV systems. The experimental results indicate that the sound source for the semi-circular cylinder is located around the shear layer near the edge of the semi-circular cylinder. The sound source intensity and the area are reduced in the semi-circular cylinder compared with those of a circular cylinder. This result indicates that the aerodynamic sound of the semicircular cylinder is smaller than that of the circular cylinder, which supports the microphone measurement result.


Introduction
The aerodynamic sound from a bluff body in a stream is an important topic of interest in fluid and environmental engineering.Many research papers have been published on the aerodynamic sound from a bluff body, such as circular and rectangular cylinders, which are summarized in review papers [1]- [3].However, there have been fewer publications on semi-circular cylinders [4]- [6], despite the industrial importance of the design of wing mirrors for automobiles [7], Savonius wind turbine rotors [8], and so on.Takizawa et al. [4] studied the aerodynamic characteristics of a semi-circular cylinder by measuring the pressure distribution on the wall surface.Later, Fujita [5] investigated the aeroacoustic characteristics of two-dimensional cylinders of various cross-sectional configurations and showed that the rounded corners in front of the bluff body are effective at improving the aeroacoustic characteristics of the bluff body.Such a body shape looks similar to the geometry of a semi-circular cylinder.More recently, Yamagata et al. [6] studied the aerodynamic characteristics of a semi-circular cylinder and showed the aerodynamic/acoustic characteristics of a semi-circular cylinder at various angles of attack.It is found that the drag forces and the Sound Pressure Level (SPL) of the semi-circular cylinder are lower than the circular cylinder at certain angles of attack; this suggests that a semi-circular cylinder has superior aerodynamic/acoustic characteristics.
In order to investigate the sound source measurements from bluff bodies, experimental methods, such as acoustic impedance [9] [10], microphone array [10] [11], cross-correlation [12]- [16], and a method based on time-resolved Particle Image Velocimetry (PIV) [17]- [20] have been reported in literature.Although these experimental methods allow the localization of the aerodynamic sound sources, the last two methods can simultaneously evaluate the sound source and velocity field, which is useful for understanding the generation mechanism of aerodynamic sound.Recently, a method using two sets of standard PIV systems has been reported for the localization of the sound source from a circular cylinder in a uniform flow [21].This method allows the evaluation of the sound source without relying on the high-speed PIV system; thus, it is well suited for the detection of the sound source from a bluff body of complex geometry for industrial applications, though the applications have not yet been reported.
The purpose of this study is to examine the sound source distribution of a semi-circular cylinder in a uniform flow using two sets of standard PIV systems.Particular attention is placed on the visualization of the sound source distribution related to the noise production mechanism of the semi-circular cylinder by comparing it with that of the circular cylinder.

Theoretical Background
According to vortex sound theory [22] [23], the acoustic sound p a can be expressed by the following equation assuming a low Mach number: Here, c is the speed of sound; φ is the velocity potential; r is the distance from the sound source; t is time; u is the velocity vector; V is the volume of interest; x i is the position of interest; and ω is the vorticity vector.The vector product of vorticity and velocity in Equation ( 1) is called the Lamb vector, and the time derivative of the Lamb vector times the gradient of the velocity potential is the sound source intensity.In this paper, a planar PIV measurement is applied to the flow around the semi-circular cylinder, so the measurements are limited to a two-dimensional cross section perpendicular to the cylinder axis.Then, the time derivative of the Lamb vector in Equation ( 1) can be reduced to the following equation: Here, ω z is the vorticity in z-direction; u is the stream wise velocity; and v is the normal velocity.Therefore, Equation (2) shows the sound intensity distribution of the aerodynamic sound generated from a bluff body.It should be mentioned that the velocity potential of a semi-circular cylinder is numerically obtained by solving the Laplace equation together with the Neumann boundary conditions on the wall and outer boundaries.

Experimental Method
The experiment was performed in an acoustic open-jet wind tunnel, which has been described in Ref. [21].The test section is 190 × 190 mm and 600 mm long.A semi-circular cylinder of 15 mm in diameter was placed horizontally 300 mm downstream of the contraction nozzle exit at the mid-height of the wind tunnel.The semi-circular cylinder was placed axisymmetric to the stream with the convex side facing upstream, as shown in Figure 1, where the sound pressure level (SPL) was found to be lower than that of the circular cylinder [6].The experiment was performed at a mean free-stream velocity of U 0 = 30 m/s, which corresponds to a Reynolds number of Re (=U 0 d/ν) = 3 × 10 4 , where d is the diameter of the semi-circular cylinder; U 0 is the free-stream velocity; and ν is the kinematic viscosity of the working fluid (air).Note that the mean freestream velocity in the test section was uniform within an accuracy of ±1%, and the freestream turbulence level was about 1%.
The time-derivative measurement of the Lamb vector in Equation ( 2) is performed using two sets of standard PIV systems, which are illustrated in Figure 1.Each PIV system consists of Nd:YAG lasers (50 mJ/pulse with 15 pulses/sec), two CCD cameras (1280 × 1024 pixels with 12 bits), and a pulse generator, as described in Ref. [21].
Figure 2 shows the timing chart of the illumination and imaging for the two pairs of

Sound Spectrum
The sound spectrum of the semi-circular cylinder was measured using a microphone with a diameter of 12.7 mm, which was located over the cylinder at a vertical distance of 500 mm. Figure 3 shows the sound spectrum of the semi-circular cylinder in a uniform flow compared with that of a circular cylinder.It is found that the sound spectrum of the semi-circular cylinder has a peak spectrum around 400 Hz, while that of the circular cylinder is around 370 Hz.The Strouhal number of the semi-circular cylinder, St (=fd/U 0 ) = 0.21, is slightly larger than that of the circular cylinder, 0.19.It is clear that the peak sound pressure level (SPL) of a semi-circular cylinder is lower than that of a circular cylinder, and the reduction effect is observed in the lower frequency range of the spectrum.These results suggest better aeroacoustic performance for a semi-circular cylinder compared with a circular cylinder.width downstream of each cylinder, which is narrower for the semi-circular cylinder than for the circular cylinder.It should be mentioned that the mean velocities of the shear layer from the edge of the semi-circular cylinder penetrate into the wake region and modify the wake structure such that the width and length of the wake are reduced in the semi-circular cylinder compared with the circular cylinder.Corresponding to this change, the accelerated mean velocity region over the semi-circular cylinder becomes shorter than that over the circular cylinder.In order to visualize the sound source intensity distribution, the RMS sound source intensity is evaluated based on 600 instantaneous velocity fields measured at 4 Hz in the flow around the semi-circular cylinder.The results are compared with those of the circular cylinder, which are shown in Figure 6(a) and Figure 6(b), respectively.Although the main feature of the sound source intensity distribution of the semi-circular cylinder looks similar to that of the circular cylinder, there are quantitative differences, such as the length and width of the shear layer and the distribution in the near wake.It is found

Conclusion
The measurements of the velocity field and sound source intensity distribution around a semi-circular cylinder were performed using two sets of standard PIV systems, and the results were compared with those of a circular cylinder.It was found that the magnitude and area of the sound source intensity distribution in the near wake of the semi-circular cylinder were reduced compared with those of the circular cylinder.Such change in the sound source intensity distribution is due to the modification of the time

Figure 1 .
Figure 1.Experimental setup and measuring system.

Figure 2 .
Figure 2. Timing chart of illumination and imaging.

Figure 4 (
Figure 4(a) and Figure 4(b) show the mean velocity distribution around the semi-circular cylinder and the circular cylinder, respectively, which are obtained from the present PIV measurement.Note that the magnitude of the mean velocity is shown by a color contour.The major difference in the mean velocity field appears in the wake

Figure 5 (
Figure 5(a) and Figure 5(b) show the instantaneous sound source intensity distributions downstream of the semi-circular cylinder and the circular cylinder, respectively, which are evaluated from the present experimental data using Equation (2).The sound sources of the semi-circular cylinder are highly concentrated over the semi-circular cylinder and the region nearby, while those of the circular cylinder are found over the circular cylinder as well as in the near-wake region widely.This result suggests that a quantitative difference in the sound source intensity distribution is found in the semicircular cylinder and the circular cylinder.It should be noted that the instantaneous sound source intensity shows both positive and negative values due to the contribution of the signs in the vorticity ω z .
: mean velocities in streamwise and normal direction, respectively U 0 : free stream velocity u, v: instantaneous streamwise and normal velocity, respectively x, y, z: coordinates (see Figure1) next manuscript to SCIRP and we will provide best service for you:Accepting pre-submission inquiries through Email, Facebook, LinkedIn, Twitter, etc.A wide selection of journals (inclusive of 9 subjects, more than 200 journals) Providing 24-hour high-quality service User-friendly online submission system Fair and swift peer-review system Efficient typesetting and proofreading procedure Display of the result of downloads and visits, as well as the number of cited articles Maximum dissemination of your research work Submit your manuscript at: http://papersubmission.scirp.org/Or contact jfcmv@scirp.org