Several Strouhal numbers have been measured behind the first row. Typical turbulence spectrum obtained when the hot wire was positioned behind the first row is given in Fig. 5. This multiplicity of Strouhal numbers has been observed by other researchers for staggered tube banks. The Strouhal numbers reported in these references can not be compared with the present results because the tube spacing are considerably different. Direct comparison are, however, possible with the formulas and charts given in References [4]. The formula suggested by Ziada and Oengoren [3] gives St = 0.55, 0.32 and 0.11 which is close to the other observed Strouhal numbers. The charts suggested by Blevins and Bressler [4] gives values of 0.16, 0.15 and 0.22 which is close to the measured values. Thus, the Strouhal numbers in the present arrays are well predicted by the empirical formulas of Ziada and Oengoren [3] and Blevins and Bressler [4].
In Fig. 6, the SPL at the frequencies of the acoustical modes are plotted against the approach velocity. For Duct A (L/d = 3.15), Duct B (L/d = 2.56), Duct C (L/d = 1.97), no resonance emerges for the highest velocity that could be achieved with the present blowers through this array. Very closely spaced arrays tend not to resonate in the conditions of the present tests, possibly due to the suppression of vortex shedding. In the limits, as longitudinal tube spacing diminishes and tubes touch one another, resonance becomes impossible, as a barrier is formed to prevent transverse acoustical waves. Close longitudinal tube spacing in tube bundles sup-presses vortex formation and propagation of acoustical waves. Blevins and Bressler [4] have suggested that resonance is suppressed in the first mode for closely spaced bundles as follows:
Close tube spacing does interfere with classical vortex shedding, but it also interferes with vortex formation and the production of sound. There is little doubt that periodic production of vortices in the separated flow in the near wake of tubes dominates the production of aeroacoustic sound in tube bundles.
The sound pressure fields were measured over the plane and shown in Fig. 7. Measurements were taken at these 7 microphone positions. The measurements of the signals from the microphones are recorded by the fast fourier transform spectrum analyzer, to ensure that only the component due to the resonance is analyzed. From these measurements it can be seen that the acoustical environment around the duct was relatively noisy. There was, however, no clearly developed standing wave pattern observed throughout the range of flow velocities, except at the high flow condition when suddenly an intense acoustical vibratory condition developed. This condition was characterized by a single frequency noise and a clearly defined standing wave.
3.2 Discussion
This investigation has gone some way towards revealing a complex mechanism which cannot be satisfactorily explained by the vortex shedding models. It has also been shown that the frequency of the acoustical vibration bears no simple relationship to the frequency of vortex shedding and the acoustical mechanism behaves in a manner which is consistent with that of a self excited system. At the onset of acoustical instability there will be an acoustical standing wave in the cavity between the tube rows in a direction transverse to the flow. It is reasonable to assume that some interaction between the standing wave and the flow around the tube will occur, thus deflecting the flow as it separates from the tube.
Nearly all techniques in the literature for prediction of acoustical resonance in heat exchanger tube bundles follows a common methodology [4].
