*3.2.2 Onset gap velocity of self-sustained tone*

**Figure 16** represents the onset gap velocity of the self-sustained tone. The vertical axis shows the gap velocity of the tube bank when the self-sustained tone is generated and the horizontal axis shows the pattern of the baffle plate positions as shown in this figure. In patterns (−1, 0, and + 1) where the baffle plate is inserted in the entire tube bank, the self-sustained tone was not generated within the range of the flow velocity that the setup of experiment can produce. The self-sustained tone is not generated because vortices are assumed to become very small in patterns (−1, 0, +1) as described later. Furthermore, the onset gap velocity of the selfsustained tone shows a significantly different tendency between the upstream and the downstream positions of the baffle plate.

**Figure 16.** *Gap velocity and pattern of baffle plate positions ([12]).*

The measurement position of the fluctuation velocity in the tube bank by the hot wire anemometer is shown in **Figure 17**. Because the baffle plate is inserted at the center of the tube bank, the hot wire probe is inserted in the neighboring flow channel. Additionally, the fluctuation velocity is measured between each tube row (12 mm interval). Measurement examples (the measurement position is 36 mm) of the fluctuation velocity *Uf* of the flow in the tube bank and SPL are shown in **Figures 18** and **19**. The vertical axis shows the fluctuation velocity of the flow and the horizontal axis shows the frequency. Two peaks (one sharp and the other dull) are represented in **Figures 18** and **19**. The sharp peak is due to the self-sustained tone and the dull peak is due to Karman vortex shedding as represented in **Figure 18**. The Karman vortex occurs in the tube bank, and the Strouhal number is about 0.13–0.19. The peak frequency of Karman vortex shedding is in proportion to the flow velocity and increases as the flow velocity increases. On the other hand, the peak frequency of the self-sustained tone coincides with the natural frequency of the duct, the sharp peak is assumed to correspond to the flow fluctuations related to the generation of the self-sustained tone. To distinguish the sharp peak from other peaks, it is referred to as "Excitation flow fluctuation" in this chapter. However, Karman vortices are generated and the excitation flow fluctuation is not generated if the baffle plate inserted in the entire tube bank suppresses the self-sustained tone.

#### *3.2.3 Suppression mechanism of self-sustained tone by baffle plate*

The sound power which the vortices add to the acoustic field of the duct is given by Eq. (3) from Howe [27]. The parameters are *W*: sound power [W], ρ: gas density [kg/m3 ], ω <sup>→</sup>: vorticity [rad/s], *U* <sup>→</sup> : flow velocity, [m/s], and → φ̇: particle velocity [m/s].

$$w = \rho \not\!\!\slash \vec{a} \times \vec{U} \not\!\rightarrow \!\!\slash \vec{\rho} \!\!dV \tag{3}$$

**67**

the self-sustained tone.

the flow velocity.

**Figure 18.**

*Countermeasure for High Level Sound Generated from Boiler Tube Bank Duct*

the center of the duct, which means that the gradient of the sound pressure or the particle velocity is the maximum in the center of the duct and tube bank. Therefore, the vorticity and particle velocity decrease due to the baffle plate inserted in the duct; as a result, the sound power decreases. This is the suppression mechanism of

*The fluctuation velocity of flow and the sound pressure level at observation point* ③ *without the baffle plate ([26]).*

The distribution of the excitation flow fluctuation in the tube bank when the self-sustained tone is generated is examined. Here, it has been non-dimensionalized as shown in Eq. (4) because the excitation flow fluctuation is a value depending on

*u* = *Uf*/*Vg* (4)

**Figure 20** represents the distribution of the excitation flow fluctuation in the tube bank. The vertical axis shows the baffle plate positions. The circle shows the dimensionless excitation flow fluctuation and its radius indicates the value of the excitation flow fluctuation while the horizontal axis shows the measurement

*DOI: http://dx.doi.org/10.5772/intechopen.86039*

The particle velocity in the duct is given by the gradient of the sound pressure. Moreover, the phase of the particle velocity to the sound pressure progresses by 90 degrees. The particle velocity is therefore the maximum at the node of the acoustic pressure. In addition, the particle velocity is the largest in the center of the duct width. Karman vortices are strong in the tube bank, and that means the vorticity is large in the tube bank. In addition, the vorticity strongly depends on the fluctuation velocity *Uf* of the flow in the tube bank. Each parameter is controlled by inserting the baffle plate in the center of the duct where these two parameters (the particle velocity and vorticity) are large. As shown **Figure 12(b)**, the sound pressure level is the maximum on the duct wall and the sound pressure level is the minimum in

**Figure 17.** *Measurement positions of fluctuation velocity in duct ([12]).*

*Countermeasure for High Level Sound Generated from Boiler Tube Bank Duct DOI: http://dx.doi.org/10.5772/intechopen.86039*

**Figure 18.**

*Noise and Vibration Control - From Theory to Practice*

The measurement position of the fluctuation velocity in the tube bank by the hot wire anemometer is shown in **Figure 17**. Because the baffle plate is inserted at the center of the tube bank, the hot wire probe is inserted in the neighboring flow channel. Additionally, the fluctuation velocity is measured between each tube row (12 mm interval). Measurement examples (the measurement position is 36 mm) of the fluctuation velocity *Uf* of the flow in the tube bank and SPL are shown in **Figures 18** and **19**. The vertical axis shows the fluctuation velocity of the flow and the horizontal axis shows the frequency. Two peaks (one sharp and the other dull) are represented in **Figures 18** and **19**. The sharp peak is due to the self-sustained tone and the dull peak is due to Karman vortex shedding as represented in **Figure 18**. The Karman vortex occurs in the tube bank, and the Strouhal number is about 0.13–0.19. The peak frequency of Karman vortex shedding is in proportion to the flow velocity and increases as the flow velocity increases. On the other hand, the peak frequency of the self-sustained tone coincides with the natural frequency of the duct, the sharp peak is assumed to correspond to the flow fluctuations related to the generation of the self-sustained tone. To distinguish the sharp peak from other peaks, it is referred to as "Excitation flow fluctuation" in this chapter. However, Karman vortices are generated and the excitation flow fluctuation is not generated if the baffle plate

inserted in the entire tube bank suppresses the self-sustained tone.

The sound power which the vortices add to the acoustic field of the duct is given by Eq. (3) from Howe [27]. The parameters are *W*: sound power [W], ρ: gas density

<sup>→</sup> : flow velocity, [m/s], and

<sup>→</sup> × *U* <sup>→</sup> ) ∙ →

The particle velocity in the duct is given by the gradient of the sound pressure. Moreover, the phase of the particle velocity to the sound pressure progresses by 90 degrees. The particle velocity is therefore the maximum at the node of the acoustic pressure. In addition, the particle velocity is the largest in the center of the duct width. Karman vortices are strong in the tube bank, and that means the vorticity is large in the tube bank. In addition, the vorticity strongly depends on the fluctuation velocity *Uf* of the flow in the tube bank. Each parameter is controlled by inserting the baffle plate in the center of the duct where these two parameters (the particle velocity and vorticity) are large. As shown **Figure 12(b)**, the sound pressure level is the maximum on the duct wall and the sound pressure level is the minimum in

→

φ̇: particle velocity [m/s].

*φ*̇*dV* (3)

*3.2.3 Suppression mechanism of self-sustained tone by baffle plate*

**66**

**Figure 17.**

[kg/m3

], ω

<sup>→</sup>: vorticity [rad/s], *U*

*w* = ρ∫(ω

*Measurement positions of fluctuation velocity in duct ([12]).*

*The fluctuation velocity of flow and the sound pressure level at observation point* ③ *without the baffle plate ([26]).*

the center of the duct, which means that the gradient of the sound pressure or the particle velocity is the maximum in the center of the duct and tube bank. Therefore, the vorticity and particle velocity decrease due to the baffle plate inserted in the duct; as a result, the sound power decreases. This is the suppression mechanism of the self-sustained tone.

The distribution of the excitation flow fluctuation in the tube bank when the self-sustained tone is generated is examined. Here, it has been non-dimensionalized as shown in Eq. (4) because the excitation flow fluctuation is a value depending on the flow velocity.

$$\mathfrak{u} = \mathbf{U}\_f / \mathbf{V}\_{\mathbf{g}} \tag{4}$$

**Figure 20** represents the distribution of the excitation flow fluctuation in the tube bank. The vertical axis shows the baffle plate positions. The circle shows the dimensionless excitation flow fluctuation and its radius indicates the value of the excitation flow fluctuation while the horizontal axis shows the measurement

#### **Figure 19.**

*The fluctuation velocity of flow and the sound pressure level at observation point* ③ *with the baffle plate (Pattern of baffle plate position is "0") ([26]).*

**Figure 20.** *Fluctuation velocity of flow on tube bank and the measurement position ([12]).*

position of the flow fluctuation velocity in the tube bank. As represented in **Figure 20**, the excitation flow fluctuation is not generated in the entire tube bank under the condition where the self-sustained tone is not generated. On the other hand, **Figure 20** represents that it is generated in the entire tube bank under the condition of the self-sustained tone being generated. Therefore, the two parameters particle velocity and the excitation flow fluctuation are controlled by inserting the baffle plate. Ishihara et al. [12] thought that it is the suppression mechanism of the self-sustained tone to decrease the sound power by controlling these two parameters.

**69**

**Figure 21.**

*Setup of experiment [29].*

*Countermeasure for High Level Sound Generated from Boiler Tube Bank Duct*

**4. Countermeasure for self-sustained tone using perforated plate**

In this section, we describe the experiments performed by Ishihara and Nakaoka [13] and Ishihara [28]. They carried out some experiments to examine the suppression effect of the perforated plates and cavities installed, and confirmed the suppression effect. They defined the aperture ratio *ϕ* of the perforated plate and investigated how the change in the value of the aperture ratio *ϕ* of the perforated plate affects the self-sustained tone in the duct. They varied the value of the aperture ratio *ϕ* from 1 to 32%. The setup of the experiment is shown in **Figure 21**. The duct is made of acrylic plates that have a thickness of 1 cm. The tube bank consists of an array of bronze tubes whose diameter is *D* = 6 mm. The array geometry is represented in **Figure 3(b)**, where the spacings *T*/*D* and *L*/*D* are 2.0. In the tube bank, there are 9 rows of tubes in the flow direction and 19 tubes in the width direction, which is perpendicular to the flow, and the length in the flow direction is 102 mm. The sound pressure signal is measured using the microphone set near the duct outlet as shown in **Figure 3(a)**, and converted to

The perforated plate is made of iron, and has a length of 400 mm, a height of 250 mm, and a thickness of 2.3 mm. A hole with a diameter of 3 mm was opened in a staggered arrangement on a plate. As shown in **Figure 22(a)**, perforated plates can be mounted from the slit (shown in green), and the duct has two cavities with a depth of *Lc* = 100, 66 and 33 mm. In this experiment, in order to examine the influence of the aperture ratio of the perforated plate on the self-sustained tone suppressing effect, as shown in **Figure 22(b)**, assuming a hole diameter of 3 mm, Ishihara and Nakaoka [13] made six patterns (1, 2, 4, 8, 16, and 32%) of the perforated plates. Here, the aperture ratio *ϕ* is the ratio of the area of the holes to the total

> *πd*<sup>2</sup> \_\_\_ <sup>4</sup> ) \_\_\_\_\_\_\_ *Sp*

Here, *nh* is the number of the hole, *Sp* = 200 × 420 mm is the total area of the perforated plate, and d is the hole diameter (3 mm). Even at the same aperture ratio, if the hole diameter is different, the influence on self-sustained tone may be different. However, in this study, it is assumed that the hole diameter is constant

(5)

*DOI: http://dx.doi.org/10.5772/intechopen.86039*

frequency domain with FFT analyzer.

area of the perforated plate and is defined by Eq. (5).

*<sup>ϕ</sup>* <sup>=</sup> *nh*(

**4.1 Setup of experiment**
