Keywords

1 Introduction

Acoustic resonance may occur in heat exchangers such as gas heaters or boilers which contain tube banks [2, 7, 8, 10]. It is generally known that vortex shedding frequency varies with the pitch ratio of the tube arrangement [3, 9, 11,12,13,14,15]. Chen [2], Fitz-hugh [3], Rae and Wharmby [11] have proposed Strouhal number charts for in-line tube banks to estimate the vortex shedding frequency of a heat exchanger at the design stage. On the other hand, the ducts of heat exchanger of power station were a complicated three-dimensional structure [5, 6]. The proposed Strouhal number may be not effective to predict the acoustic resonance in actual boiler plant due to nonuniformity of incoming velocity at upstream of tube banks. This nonuniformity was caused by the flow separation at upstream of tube banks. Hamakawa et al. [4] have shown the characteristics of acoustic resonance with the flow separation at upstream of tube banks. However, the relation between the flow separation at upstream of tube banks and acoustic resonance was not clear in detail.

The purpose of the present investigation was to clarify the relation between the flow separation at upstream of tube banks and the occurrence of acoustic resonance. We have also discussed the prediction method to estimate the onset velocity of acoustic resonance with flow separation at upstream of tube banks.

2 Experimental Apparatus and Procedure

An schematic view of the experimental apparatus is shown in Fig. 1. The structure of this apparatus is similar to that of a boiler of a power station. The similarities are described in detail in the paper [5, 6]. This apparatus was a subsonic facility with a blower located at its upstream inlet. This was a rectangular duct of 900 mm in width, 150 mm in height, and 1275 mm in length (maximum), and was made of 20 mm thick acrylic plate. Tube banks were installed in the test section. The freestream velocity, U ∞ , ranged from 2.5 to 16.5 m/s at the test section inlet.

Fig. 1
figure 1

Experimental apparatus

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The in-line tube banks consisted of five rows, with 50 tubes per row. The tube diameter, D, was 9 mm. The tube pitch ratio of tube banks part in the flow direction, L/D, was 2.9, and the transverse direction, T/D, was 2.0. The tubes were 130 mm in length. They were rigidly fixed to both end walls of the test section. The flow separation was generated by using the orifice at the upstream of tube banks. The height of passage at the orifice, h/D, were 0, 2.8, 5.7, 8.6, 11.6, 14.4. We have measured the spectra of SPL as parameters of h/D from 0 to 14.4. No flow separation at upstream of tube banks was h/D = 14.4 (h = 130 mm). We calculated the through flow velocity, U h , by using continuity equation and the freestream velocity, U ∞ . The tube gap velocity of tube banks was defined as U g  = TU h /(T − D). This gap velocity correlated the actual gap velocity. Reynolds numbers, based on the gap velocity, U g , ranged from 3.0 × 103 to 1.7 × 104. The time variation of acoustic pressure was measured using a microphone mounted on the side wall as shown in Fig. 1. The amplitude and phase delay of the acoustic pressure fluctuations was measured by setting the reference microphone.

3 Results and Discussion

3.1 Acoustic Resonance with Flow Separation

The time variation of acoustic pressure was measured using a microphone mounted on the side wall as shown in Fig. 1. We calculated the spectrum of acoustic pressure by using Matlab. A single high peak was formed in the spectrum when the acoustic resonance occurred. Figure 2 show the variations of peak frequencies, plotted against the tube gap velocity, U g , for five heights of passage at the orifice, h/D, respectively. The sizes of the symbols show the levels of peak SPLs. When the acoustic resonance of first, second, and third mode occurred at h/D = 8.6, 11.6 and 14.4, the peak SPLs increased respectively. As the gap velocity increased overall, the acoustic mode number and peak SPLs increased. As h/D decreased, St and peak SPLs decreased, and the onset velocity of each mode of acoustic resonance increased.

Fig. 2
figure 2

Variation of peak frequency of SPL against gap velocity

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3.2 Prediction of Onset Velocity of Acoustic Resonance

Hamakawa et al. [4] have shown the spanwise correlation length of vortex shedding from the last row of tube banks. The spanwise scale of vortex shedding from last row of tube banks became the height of flow passage, h, in present experiment. It is considered that the spanwise correlation scale of vortex became small in the tube banks because the oncoming flow of last row of tube banks was disturbed by the interaction between the vortex shedding from tube and the downstream tube. Therefore, we considered that the spanwise scale of vortex shedding from tube banks closed to the height of flow passage, h, in present experiment. In this situation, the sound intensity is proportional to the freestream velocity raised to the sixth power and the spanwise correlation length raised to the second power [1].

Figure 3a shows the variation of peak SPLs of acoustic resonance against height of passage, h. As h/D increased, peak SPLs increased for all acoustic modes. The peak SPLs of acoustic resonance increased due to the increase of excitation force of acoustic resonance which was proportional to spanwise scale of vortex raised to the seconds power. The rate of increase at the first mode was the largest in all acoustic modes.

Fig. 3
figure 3

Variation of peak SPLs and onset velocity of acoustic resonance against height of passage: a peak SPL, b onset velocity

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Figure 3b shows the variation of gap velocity at peak SPLs as a function of height of passage at the orifice, h. As h/D increased, the gap velocity at peak SPLs decreased for all acoustic modes. The onset velocity of acoustic resonance reduced due to the increase of excitation force of acoustic resonance which was proportional to spanwise scale of vortex raised to the seconds power. The dotted lines are the theoretical results calculated by considering the increase of gap velocity kept the peak SPL. The theoretical results agreed well with the experimental results quantitatively. The variation of gap velocity could be predicted by considering the reduction of spanwise scale of vortex and the increase of gap velocity kept the peak SPLs.

4 Conclusions

The relation between the flow separation at upstream of tube banks and the occurrence of acoustic resonance were experimentally investigated in in-line tube banks of tube pitch ratio of 2.9. If the flow separation existed at upstream of tube banks, the acoustic resonance occurred from lower freestream velocity compared with no separation. As height of flow passage decreased, the acoustic resonance occurred at lower freestream velocity. When the acoustic resonance of first, second, and third mode occurred, the peak SPLs increased. As the tube gap velocity increased overall, the acoustic mode number and peak SPLs increased. As height of flow passage decreased, Strouhal number and the peak SPLs decreased, and the onset velocity of each mode of acoustic resonance increased for all acoustic modes. The variation of gap velocity could be predicted by considering the reduction of spanwise scale of vortex and the increase of gap velocity kept the peak SPLs.