1. Introduction
In heat exchangers, such as boilers for commercial use, acoustic resonant noise is occasionally generated in the ducts when gas is flowing laterally with respect to the axis of the tubes. Flow induced vibration and noise in heat exchanger can be found in the review paper [1-4].
The acoustic resonant noise generated from heat exchangers is usually caused by the resonance of acoustic modes inside the boiler and vortex shedding from the tube banks. Many studies have been published on the excitation mechanisms causing acoustic resonance in the tube banks in cross-flow [5-8]. Vortex excitation has been clearly shown to result from the formation of periodic vortices in the space between the tubes [7,8].
It is generally known that vortex shedding frequency varies with the pitch ratio of the tube arrangement. There are many studies on the vortex shedding frequency in the tube banks in cross-flow [6,7,9-12]. Chen [6], Fitz-hugh [9] and Rae & Wharmby [10] have proposed Strouhal number charts for tube banks to estimate the vortex shedding frequency of a heat exchanger at the design stage. And Blevins & Bressler [13,14] have shown that the acoustic resonance of first transverse mode do not occur in the tube banks for small tube pitch ratio. However, the effect of arrangement in the tube banks on acoustic resonance was not clear in detail.
The purpose of the present investigation was to clarify experimentally the effect of arrangement of tube banks on acoustic resonance which occurred in the two-dimensional model similar to an actual boiler plant. And we have examined the effect of tube pitch ratio on acoustic damping and vortex shedding from tube banks.
2. Experimental Apparatus and Procedure
A schematic view of the experimental apparatus used in the present experiment is shown in Figure 1(a). The structure of this apparatus is similar to that of an actual power station heat exchanger. The similarities are described in detail in the paper [15].
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 or 30 mm thick acrylic plate. The test section had a cross-section of 900 × 130 mm. Eight meshes were installed in the transverse direction at the test section inlet to enable a uniform flow without disturbing the sound field. The boundary layer thickness was about 5 mm, the drift in the freestream was
(a)
(b)
Figure 1. Experimental apparatus. (a) Measurement of acoustic resonance; (b) Measurement of acoustic damping and vortex shedding.
less than 2.0%, and the turbulence intensity was less than 1.8% in the freestream velocity. Tube banks were installed in the test section 572 mm downstream from the upstream end plate. A pitot tube was used to measure the freestream velocity, U∞, (oncoming velocity) in the tube banks. The freestream velocity ranged from 2.5 to 15.5 m/s at the test section inlet.
The acoustic damping ratio was measured by using test apparatus without sound absorbing materials as shown in Figure 1(b). The flat speakers and the microphones were set on the side wall at the tube bank part. These speakers had the strong directivity, and the plane wave of sound was generated from its speaker. The resonance curve was measured by the supply of sinusoidal tone from the flat speaker, and the acoustic damping ratio, ζ, was obtained by the half power method. This measurement of acoustic damping ratio was carried out in the condition without the flow. This damping ratio was confirmed to be the almost same as the value with the flow which freestream velocity was less than about 15 m/s.
The tube banks are defined in Figure 2. Figures 2(a) and (b) show the in-line arrangement and staggered arrangement respectively. The tube banks consisted of fifteen rows, with 50 or 49 tubes per row. The tube diameter, D, was 9 mm. The tube pitch ratio for in-line tube banks part in the flow direction, L/D, was ranged from 1.33 to 1.67, and the transverse direction, T/D, was 2.0. The tube pitch ratio for staggered tube banks part in the flow direction, L/D, was 1.44, and the transverse direction, T/D, was 2.0. The tubes were 130 mm in length, and were made of aluminum rods. They were rigidly fixed to both end walls of the test section. The gap velocity was defined as Ug = TU∞/(T-D). Reynolds numbers, based on the gap velocity, Ug, ranged from 2.8 × 103 to 2.0 × 104. The arrangement of tube banks is shown in Table 1 in detail.
The sound pressure level (SPL) of noise was measured using a Bruel & Kjaer 1/2-inch condenser microphone mounted outside the test apparatus as shown in Figure 1. The amplitude and phase delay of the acoustic pressure fluctuations was measured by setting the reference mi-
(a)
(b)
Figure 2. Arrangement of tube banks. (a) In-line arrangement; (b) Staggered arrangement.
Table 1. Specification of tube banks.
crophone at the point X = 790 mm, Y = 75 mm, and placing another fifteen microphones at different locations along the X and Y axes inside the test apparatus.
3. Results and Discussion
3.1. Acoustic Damping
Figure 3 shows the variation of acoustic damping ratio, ζ, plotted against the acoustic mode number, n. As the acoustic mode number increased, the acoustic damping decreased for all tube pitch ratio, L/D. And as the tube pitch ratio in the flow direction decreased, the acoustic damping ratio increased for all acoustic modes. Especially, the acoustic damping ratio for L/D = 1.33 was larger than that for other tube pitch ratio. It is considered that it is difficult to generate the acoustic resonance of low order mode for small tube pitch ratio. This is the similar tendencies with the charts of Blevins & Bressler [13,14]. On the other hand, the acoustic damping ratio of L/D = 1.44 for staggered arrangement agreed well with that of the in-line arrangement of L/D = 1.44.