**2.2 Setup of experiment**

*Noise and Vibration Control - From Theory to Practice*

perforated plates, when the self-sustained tone occurred.

sustained tone using baffle plates and perforated plates.

**2. Generation mechanism of self-sustained tone**

or lock-on phenomenon in the tube bank [1–11, 21, 22].

**2.1 Self-sustained tone**

production losses, etc.

When a resonance phenomenon occurs at a certain velocity, if the acoustic damping is small, a high level sound continues as flow velocity increases. This phenomenon is called the self-sustained tone [12, 13]. The self-sustained tone might cause the surrounding noise problem, and also cause plant shutdown and, hence,

For a countermeasure of the self-sustained tone, a method of inserting a partition plate called a baffle plate inside the duct is generally used. In this method, the baffle plate inserted inside the duct is assumed to increase the natural frequency of the duct, detune the frequency of the vortex shedding from the tube bank and the acoustic natural frequency of the duct, and suppress the resonance phenomenon [14–16]. However, Ishihara et al. [12] demonstrated that the natural frequency of the duct decreases by inserting the baffle plate, and a decision of an appropriate insertion position of the baffle plate is not easy. Hamakawa et al. [16] have investigated the effect of the baffle plate on the acoustic resonance generation from in-line tube banks with small cavity, and they clarified that although sound pressure level of an acoustic mode perpendicular to the flow (lift mode) is suppressed by a baffle plate, that of an acoustic mode parallel to the flow (drag mode) increases. Ishihara and Takahashi proposed that flexible walls such as rubber boards are set on the duct walls for suppressing the self-sustained tone [17]. They expected that the vibration of the flexible walls damp the lift resonance mode when self-sustained tone is generated. They demonstrated that the suppression effect of the rubber sheet appeared when the tension of it is small and it is located at just the tube bank and downstream of the tube bank. On the other hand, to suppress the self-sustained tones, a method using perforated plates and cavities has been proposed by Ishihara and Nakaoka [13]. A perforated plate has long been used in various noise-control applications, such as vehicle exhaust systems, ducts, hearing protection devices, and acoustic panels, because it is well known that perforated plates have an acoustic damping effect [18–20]. Ishihara and Nakaoka [13] thought that a resonance mode perpendicular to the flow (lift mode) might be suppressed by a damping effect of

In this chapter, we review the generation mechanism of the self-sustained tone clarified experimentally and numerically, and the methods for suppressing a self-

The Karman vortex shedding frequency *f*v is generally proportional to the flow

The relation between frequency and flow velocity in a lock-in phenomenon is represented in **Figure 1**. A high level sound called a self-sustained tone occurs due to a lock-in phenomenon [12, 13]. In a lock-in phenomenon, as shown in **Figure 1**, the frequency slightly rises as the flow velocity increases. Furthermore, the lock-in occurs at a certain flow velocity, and does not occur in accordance with the large acoustic damping of the duct if the flow velocity increases. However, with the small

velocity and the natural frequency of the duct *f*a is constant value determined by the duct size and the sound speed. When the flow velocity increases, the *f*v approaches *f*a. Before the *f*v reaches the *f*a, the vortex shedding frequency suddenly locks on to the natural frequency of the duct. The resultant high level sound occurs at or nearly at the natural frequency of the duct, and this phenomenon is called a lock-in or lock-on. There are many studies on the excitation mechanism of a lock-in

**56**

Ishihara et al. [12, 13] performed the experiments to investigate the selfsustained tone. **Figure 3(a)** and **(b)** represents the setup of the experiment and the tube bank. 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

**Figure 2.** *Acoustic resonance and lock-in phenomenon.*

**Figure 3.**

*Setup of experiment and array geometry of tube bank [24]. (a) Setup of experiment. (b) Array geometry of tube bank.*

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 frequency domain with FFT analyzer. The flow velocity is changed by controlling the rotational speed of the blower using the inverter. A high level sound is generated when the shedding frequency of vortices generated in the tube bank nearly coincides with the acoustic natural frequency of the duct system. A flow velocity measurement hole was provided at a position 125 mm upstream of the tube group, and the flow velocity (*U*) was also measured by using a hot wire anemometer. The gap flow velocity *Vg* is obtained from the continuous equation, defined by the flow velocity *U* and the ratio of the area of the duct outlet to the area of the tube bank clearance which is 234 mm (Duct width)/(234 mm – 19 (number of tubes in the width direction)\*6 mm (tube diameter)) = 1.95*,* and represented by *Vg* = 1.95 *U*. The measurement frequency ranges from 100 to 2000 Hz. The sound pressures signal is measured with the sampling frequency of 10,000 Hz, the number of averages of 1000, and the frequency resolution of 20 Hz.

#### **2.3 Results of experiments**

The sound pressure spectrum at each gap velocity (11.4, 15.7, 19.6, and 21.3 m/s) is shown in **Figure 4**. As shown in **Figure 4**, the self-sustained tone is slightly generated at *Vg* = 19.6 m/s, and is clearly generated at *Vg* = 21.3 m/s. The peak frequency of the self-sustained tone is 740 Hz. The relation between overall sound pressure level and the gap velocity obtained from the experiments is represented in **Figure 5**. Sound pressure level generated by a flow in a duct generally follows the 5–8th power laws [13], and the sound pressure level generated in the duct in this experiment follows the 5th power law. Sound following the 5th power law is the ordinary aerodynamic sound. The sound pressure level rises as the gap velocity increases by following the 5th power law when the self-sustained tone is not generated (when the gap velocity is lower than 20 m/s). However, the sound pressure level is over 100 dB when the self-sustained tone is generated (when the gap velocity is higher than 20 m/s). **Figure 5** represents that when the gap flow velocity is over 22 m/s, the overall sound pressure level remains high and is over 110 dB [15]. The self-excited tone is generated at the gap velocity over 20 m/s, and it indicated that if the Strouhal number *St* is assumed to be 0.22, the vortex shedding frequency *fv* is *f <sup>v</sup>* = *St* ∗ *Vg*⁄*<sup>D</sup>* = 0.22 ∗ 20⁄0.006 = 733 Hz. Meanwhile, the resonance frequency *fa* in the width direction of the duct is *fa* = *<sup>C</sup>*⁄2*<sup>L</sup>* = 340/2/0.234 = 726.5 Hz.

**59**

experiments.

**Figure 5.**

**Figure 4.**

*Spectra of sound pressure level.*

respectively.

fa = \_c

2√

**2.4 Unsteady CFD simulations**

( \_\_l lx) 2 + ( \_\_ m ly)

\_\_\_\_\_\_\_\_\_\_\_

*Relation between overall sound pressure level (200–2000 Hz) and the gap velocity.*

on the gap velocity *Vg*, and ranges from 4600 to 10,800.

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

Taking the combined mode in the longitudinal direction into consideration, the resonance frequency *fa* is obtained from Eq. (1) and equals 736.3 Hz, which is very close to the frequency of excitation at 740 Hz obtained from the

> \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (

= 736.3 Hz (1)

\_\_\_\_\_ 1 0.234) 2 + ( \_\_\_\_ 1 1.42) 2

<sup>2</sup> = \_\_\_ 340 2 √

Here, *lx* and *ly* denote the longitudinal duct length and the duct width,

Mori et al. [24] performed compressible CFD simulations to capture the selfsustained tone and compare the simulation results with the measurements [13]. They confirmed that the self-sustained tone at the acoustic mode in the width direction of the duct occurs, and the sound pressure level does not follow the 5th power law when the gap velocity is high, as in the experiments. Unsteady flow fields in the duct are simulated in the paper. Inflow velocities are *U* = 5.846, 7.026, 8.051, 8.564, 9.590, 10.923, and 13.846 m/s, and correspond to the gap velocities, *Vg* = 11.4, 13.7, 15.7, 16.7, 18.7, 21.3, and 27.0 m/s, respectively. **Figure 6** represents the CFD model that is a three-dimensional computational domain. Reynolds number *ReD* is based

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

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

**Figure 4.** *Spectra of sound pressure level.*

*Noise and Vibration Control - From Theory to Practice*

1000, and the frequency resolution of 20 Hz.

0.22, the vortex shedding frequency *fv* is *f*

*fa* = *<sup>C</sup>*⁄2*<sup>L</sup>* = 340/2/0.234 = 726.5 Hz.

**2.3 Results of experiments**

**Figure 3.**

*tube bank.*

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 frequency domain with FFT analyzer. The flow velocity is changed by controlling the rotational speed of the blower using the inverter. A high level sound is generated when the shedding frequency of vortices generated in the tube bank nearly coincides with the acoustic natural frequency of the duct system. A flow velocity measurement hole was provided at a position 125 mm upstream of the tube group, and the flow velocity (*U*) was also measured by using a hot wire anemometer. The gap flow velocity *Vg* is obtained from the continuous equation, defined by the flow velocity *U* and the ratio of the area of the duct outlet to the area of the tube bank clearance which is 234 mm (Duct width)/(234 mm – 19 (number of tubes in the width direction)\*6 mm (tube diameter)) = 1.95*,* and represented by *Vg* = 1.95 *U*. The measurement frequency ranges from 100 to 2000 Hz. The sound pressures signal is measured with the sampling frequency of 10,000 Hz, the number of averages of

*Setup of experiment and array geometry of tube bank [24]. (a) Setup of experiment. (b) Array geometry of* 

The sound pressure spectrum at each gap velocity (11.4, 15.7, 19.6, and 21.3 m/s) is shown in **Figure 4**. As shown in **Figure 4**, the self-sustained tone is slightly generated at *Vg* = 19.6 m/s, and is clearly generated at *Vg* = 21.3 m/s. The peak frequency of the self-sustained tone is 740 Hz. The relation between overall sound pressure level and the gap velocity obtained from the experiments is represented in **Figure 5**. Sound pressure level generated by a flow in a duct generally follows the 5–8th power laws [13], and the sound pressure level generated in the duct in this experiment follows the 5th power law. Sound following the 5th power law is the ordinary aerodynamic sound. The sound pressure level rises as the gap velocity increases by following the 5th power law when the self-sustained tone is not generated (when the gap velocity is lower than 20 m/s). However, the sound pressure level is over 100 dB when the self-sustained tone is generated (when the gap velocity is higher than 20 m/s). **Figure 5** represents that when the gap flow velocity is over 22 m/s, the overall sound pressure level remains high and is over 110 dB [15]. The self-excited tone is generated at the gap velocity over 20 m/s, and it indicated that if the Strouhal number *St* is assumed to be

Hz. Meanwhile, the resonance frequency *fa* in the width direction of the duct is

*<sup>v</sup>* = *St* ∗ *Vg*⁄*<sup>D</sup>* = 0.22 ∗ 20⁄0.006 = 733

**58**

**Figure 5.** *Relation between overall sound pressure level (200–2000 Hz) and the gap velocity.*

Taking the combined mode in the longitudinal direction into consideration, the resonance frequency *fa* is obtained from Eq. (1) and equals 736.3 Hz, which is very close to the frequency of excitation at 740 Hz obtained from the experiments.

## experiments.

$$\mathbf{f\_a} = \frac{\mathbf{c}}{2} \sqrt{\left(\frac{1}{\mathbf{l\_x}}\right)^2 + \left(\frac{\mathbf{m}}{\mathbf{l\_y}}\right)^2} = \frac{340}{2} \sqrt{\left(\frac{1}{0.234}\right)^2 + \left(\frac{1}{1.42}\right)^2} = 73\mathbf{\tilde{6}}.3\text{ Hz}\tag{1}$$

Here, *lx* and *ly* denote the longitudinal duct length and the duct width, respectively.

### **2.4 Unsteady CFD simulations**

Mori et al. [24] performed compressible CFD simulations to capture the selfsustained tone and compare the simulation results with the measurements [13]. They confirmed that the self-sustained tone at the acoustic mode in the width direction of the duct occurs, and the sound pressure level does not follow the 5th power law when the gap velocity is high, as in the experiments. Unsteady flow fields in the duct are simulated in the paper. Inflow velocities are *U* = 5.846, 7.026, 8.051, 8.564, 9.590, 10.923, and 13.846 m/s, and correspond to the gap velocities, *Vg* = 11.4, 13.7, 15.7, 16.7, 18.7, 21.3, and 27.0 m/s, respectively. **Figure 6** represents the CFD model that is a three-dimensional computational domain. Reynolds number *ReD* is based on the gap velocity *Vg*, and ranges from 4600 to 10,800.

**Figure 6.** *CFD model [24].*

Unsteady flow fields are calculated using the commercial CFD code ANSYS Fluent version 17.0. An implicit pressure-based coupled solver with second-order numerical accuracy in both space and time and compressible LES (Dynamic Smagorinsky model) calculation features have been applied. The interaction between the flow and acoustic fields need to be solved when the resonance or selfsustained tone is generated, a high level sound is generated, and the monitor point is near the noise source region. Therefore, the acoustic pressure is directly extracted from the unsteady compressible CFD simulations [25].

The origin of the Cartesian coordinate is placed at the center of the inflow boundary. The cell spacing adjacent to the wall is 0.00025 m. In the wake region near the tube bank, the cell spacing is about 0.002 m. In the far wake region, the cell spacing is stretched to 0.006 m. The domain contains 4,944,100 cells and 5,156,304 nodes. CFD simulation conditions are shown in **Table 1**.

Steady-state simulations were performed using Spalart-Allmaras (S-A) turbulence model and then used as initial conditions of transient LES simulations. The time step size corresponds to the non-dimensional time step based on *fv*, 0.00733. To convert the acoustic pressure time histories obtained from CFD simulations into the frequency spectra, the discrete Fourier transform (DFT) has been applied. The acoustic pressure is extracted from 2500 steps (from t = 0.05 to 0.1 s). The sampling period is 2e-5 s.

Instantaneous snapshots of vorticity fields at *Z* = 0 plane are shown in **Figure 7(a)** and **(b)**, for the cases of *Vg* = 11.4 m/s and *Vg* = 21.3 m/s. A vortex street is formed downstream by vortices shed in the tube bank. At *Vg* = 21.3 m/s, the strength of the vortices is larger than at *Vg* = 11.4 m/s. Instantaneous snapshots of static pressure fields are represented in **Figure 8**. **Figure 8** shows that the value of the static pressure on the upstream side of the tube bank is larger than that on the downstream side, and distinguishing the sound pressure from the static pressure seems to be difficult. Thus, the fluctuation pressure is defined as follows to distinguish easily between the sound pressure and the static pressure [24].

$$dp = p\_s - p\_{mean} \tag{2}$$

**61**

**Figure 8.**

*Static pressure fields. (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

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

Here, *ps* denotes the static pressure which is defined by *ps* = *p* − *p*0, *pmean* denotes the time-averaged pressure, and *p*0 denotes the ambient pressure. Instantaneous snapshots of fluctuation pressure field at Z = 0 plane obtained from the unsteady CFD simulations are represented in **Figure 9**. The value of the fluctuation pressure at *Vg* = 21.3 m/s is much larger than at *Vg* = 11.4 m/s. At *Vg* = 21.3 m/s, the pressure fluctuation clearly represents the resonance mode in the duct width direction. The frequency spectra of SPL are monitored on the wall of the duct near the outflow boundary, and represented in **Figure 10**. The self-sustained tone is generated when the gap velocity *Vg* is 21.3 m/s, and the self-sustained tone is not generated when the gap velocity *Vg* is 11.4 m/s. The peak frequency of the self-sustained tone is about 740 Hz and its high harmonic frequency, 1480 Hz, when the gap velocity *Vg* is 21.3 m/s. This frequency, 740 Hz, is close to the resonance frequency in the duct width direction, 726.5 Hz, and that in the combined mode in the longitudinal direction, 736.3 Hz, as mentioned in Section 2.3. The resonance frequencies obtained from the theory (without the flow) and the CFD simulations or the experiments are slightly different because of the absence or presence of the flow. **Figure 1** shows that the slight increase of the resonance frequency occurs with an increase of the gap flow velocity [24]. The predicted SPL of the dominant tone at 740 Hz reasonably agrees with the measured one. The generation of the higher harmonic at 1480 Hz, which is surrounded by the red circle in **Figure 10**, is also predicted as in the experiments. The predicted SPL of the dominant tone, which is assumed to contribute most to the overall SPL when the

self-sustained tone is generated, reasonably agrees with the measured one.

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

*Vorticity fields. (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

**Figure 7.**


**Table 1.** *CFD simulation conditions.* *Countermeasure for High Level Sound Generated from Boiler Tube Bank Duct DOI: http://dx.doi.org/10.5772/intechopen.86039*

**Figure 7.** *Vorticity fields. (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

*Noise and Vibration Control - From Theory to Practice*

from the unsteady compressible CFD simulations [25].

nodes. CFD simulation conditions are shown in **Table 1**.

the sound pressure and the static pressure [24].

Unsteady flow fields are calculated using the commercial CFD code ANSYS Fluent version 17.0. An implicit pressure-based coupled solver with second-order numerical accuracy in both space and time and compressible LES (Dynamic Smagorinsky model) calculation features have been applied. The interaction between the flow and acoustic fields need to be solved when the resonance or selfsustained tone is generated, a high level sound is generated, and the monitor point is near the noise source region. Therefore, the acoustic pressure is directly extracted

The origin of the Cartesian coordinate is placed at the center of the inflow boundary. The cell spacing adjacent to the wall is 0.00025 m. In the wake region near the tube bank, the cell spacing is about 0.002 m. In the far wake region, the cell spacing is stretched to 0.006 m. The domain contains 4,944,100 cells and 5,156,304

Steady-state simulations were performed using Spalart-Allmaras (S-A) turbulence model and then used as initial conditions of transient LES simulations. The time step size corresponds to the non-dimensional time step based on *fv*, 0.00733. To convert the acoustic pressure time histories obtained from CFD simulations into the frequency spectra, the discrete Fourier transform (DFT) has been applied. The acoustic pressure is extracted from 2500 steps (from t = 0.05 to 0.1 s). The sampling period is 2e-5 s. Instantaneous snapshots of vorticity fields at *Z* = 0 plane are shown in

**Figure 7(a)** and **(b)**, for the cases of *Vg* = 11.4 m/s and *Vg* = 21.3 m/s. A vortex street is formed downstream by vortices shed in the tube bank. At *Vg* = 21.3 m/s, the strength of the vortices is larger than at *Vg* = 11.4 m/s. Instantaneous snapshots of static pressure fields are represented in **Figure 8**. **Figure 8** shows that the value of the static pressure on the upstream side of the tube bank is larger than that on the downstream side, and distinguishing the sound pressure from the static pressure seems to be difficult. Thus, the fluctuation pressure is defined as follows to distinguish easily between

*dp* = *ps* − *pmean* (2)

**60**

**Table 1.**

**Figure 6.** *CFD model [24].*

*CFD simulation conditions.*

Here, *ps* denotes the static pressure which is defined by *ps* = *p* − *p*0, *pmean* denotes the time-averaged pressure, and *p*0 denotes the ambient pressure. Instantaneous snapshots of fluctuation pressure field at Z = 0 plane obtained from the unsteady CFD simulations are represented in **Figure 9**. The value of the fluctuation pressure at *Vg* = 21.3 m/s is much larger than at *Vg* = 11.4 m/s. At *Vg* = 21.3 m/s, the pressure fluctuation clearly represents the resonance mode in the duct width direction.

The frequency spectra of SPL are monitored on the wall of the duct near the outflow boundary, and represented in **Figure 10**. The self-sustained tone is generated when the gap velocity *Vg* is 21.3 m/s, and the self-sustained tone is not generated when the gap velocity *Vg* is 11.4 m/s. The peak frequency of the self-sustained tone is about 740 Hz and its high harmonic frequency, 1480 Hz, when the gap velocity *Vg* is 21.3 m/s. This frequency, 740 Hz, is close to the resonance frequency in the duct width direction, 726.5 Hz, and that in the combined mode in the longitudinal direction, 736.3 Hz, as mentioned in Section 2.3. The resonance frequencies obtained from the theory (without the flow) and the CFD simulations or the experiments are slightly different because of the absence or presence of the flow. **Figure 1** shows that the slight increase of the resonance frequency occurs with an increase of the gap flow velocity [24]. The predicted SPL of the dominant tone at 740 Hz reasonably agrees with the measured one. The generation of the higher harmonic at 1480 Hz, which is surrounded by the red circle in **Figure 10**, is also predicted as in the experiments. The predicted SPL of the dominant tone, which is assumed to contribute most to the overall SPL when the self-sustained tone is generated, reasonably agrees with the measured one.

**Figure 8.** *Static pressure fields. (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

**Figure 9.** *Fluctuation pressure fields. (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

**Figure 10.** *Spectra of sound pressure level.*

The relation between overall sound pressure level and the gap velocity obtained by both the simulations and experiments is represented in **Figure 11**. In both the simulations and experiments, when the gap velocity is low and below 20 m/s, the sound pressure level rises as the gap velocity increases by following the 5th power law. However,

**63**

**3.1 Setup of experiment**

**Figure 12.**

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

when the gap velocity is higher than 20 m/s, the self-sustained tone is generated and the sound pressure level is high and over 100 dB not by following the 5th power law. **Figures 10** and **11** represent that the sound pressure levels obtained by the simulations reasonably agree with those obtained by the experiments. **Figure 12** shows the SPLs on the wall of the duct at 740 Hz; these are extracted from the unsteady CFD simulations using DFT. As in the experiments, **Figure 12(b)** shows that when *Vg* = 21.3 m/s (the gap velocity is higher than 20 m/s), the SPL on the duct wall clearly represents the acoustic resonance mode in the duct width direction or the combined mode in the duct width and longitudinal directions. However, when *Vg* = 11.4 m/s (the gap velocity is lower than 20 m/s), the acoustic resonance mode is not clearly represented as shown in **Figure 12(a)**. The fluctuation pressure field shown in **Figure 9(b)** is consistent with the acoustic mode at 740 Hz shown in **Figure 12(b)**, which means that the dominant mode in the self-sustained tone is the acoustic mode in the duct width direction or the combined mode in the duct width and longitudinal directions, and is close to the

As shown in **Figures 10** and **11**, the simulations show a reasonable agreement with

In this section, we describe the experiments performed by Ishihara et al. [12, 26].

They have investigated the appropriate insertion position of the baffle plate for the suppression of the self-sustained tone and the mechanism of suppressing the self-sustained tone by inserting the baffle plate. The setup of the experiment is shown in **Figure 3(a)** and the duct used in this experiment is shown in **Figure 13**. 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 5 rows of tubes in the flow direction and 18 tubes in the width direction, which is perpendicular to the flow, and the length in the flow direction is 60 mm. The sound pressure signal is measured using the microphone set near the duct outlet as shown in **Figure 3(a)**, and converted to frequency domain with FFT analyzer. One tube bank is installed in the duct in the present experiment as shown in **Figure 13**. The baffle plate with a length of 60 mm, thickness of 3 mm, and height of 200 mm is inserted in the center of the tube bank

the experiments in terms of the generation prediction of the self-sustained tone.

**3. Countermeasure for self-sustained tone using baffle plate**

acoustic mode obtained from the Eq. (1) and the experiments.

*SPL on the wall of the duct ([24]). (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

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

**Figure 11.** *Relation between overall sound pressure level (200–2000 Hz) and gap velocity.*

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

**Figure 12.**

*Noise and Vibration Control - From Theory to Practice*

*Fluctuation pressure fields. (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

The relation between overall sound pressure level and the gap velocity obtained by both the simulations and experiments is represented in **Figure 11**. In both the simulations and experiments, when the gap velocity is low and below 20 m/s, the sound pressure level rises as the gap velocity increases by following the 5th power law. However,

*Relation between overall sound pressure level (200–2000 Hz) and gap velocity.*

**62**

**Figure 11.**

**Figure 9.**

**Figure 10.**

*Spectra of sound pressure level.*

*SPL on the wall of the duct ([24]). (a) Vg = 11.4 m/s. (b) Vg = 21.3 m/s.*

when the gap velocity is higher than 20 m/s, the self-sustained tone is generated and the sound pressure level is high and over 100 dB not by following the 5th power law. **Figures 10** and **11** represent that the sound pressure levels obtained by the simulations reasonably agree with those obtained by the experiments. **Figure 12** shows the SPLs on the wall of the duct at 740 Hz; these are extracted from the unsteady CFD simulations using DFT. As in the experiments, **Figure 12(b)** shows that when *Vg* = 21.3 m/s (the gap velocity is higher than 20 m/s), the SPL on the duct wall clearly represents the acoustic resonance mode in the duct width direction or the combined mode in the duct width and longitudinal directions. However, when *Vg* = 11.4 m/s (the gap velocity is lower than 20 m/s), the acoustic resonance mode is not clearly represented as shown in **Figure 12(a)**. The fluctuation pressure field shown in **Figure 9(b)** is consistent with the acoustic mode at 740 Hz shown in **Figure 12(b)**, which means that the dominant mode in the self-sustained tone is the acoustic mode in the duct width direction or the combined mode in the duct width and longitudinal directions, and is close to the acoustic mode obtained from the Eq. (1) and the experiments.

As shown in **Figures 10** and **11**, the simulations show a reasonable agreement with the experiments in terms of the generation prediction of the self-sustained tone.
