Aeroacoustics of shear layers in internal flows : closed branches and wall perforations

Abstract

Flow induced pulsations in resonant pipe networks have been observed in many technical applications, such as natural gas transport systems, steam lines of nuclear power plants and re-heat steam lines of boilers. These pulsations, which present a serious threat to the integrity of the systems, have been identifed as self-sustained aeroacoustic oscillations driven by the instability of the flow. The main goal of the proposed research is the prediction of the coupling of acoustic waves with shear layers formed by ow separation in internal ows and the design of remedial measures. We consider here, in particular, the shear layers formed at the opening of closed branches along a pipe and shear layers formed by grazing/bias ow along/through wall perforations. Although there are extensive studies in literature on the pulsations generated by the separating ow along a closed side branch, the configurations with the fl ow entering or leaving the side branch have not been recognized as source of pulsations. In our study, strong flow induced pulsations have been observed experimentally in configurations with a mean ow entering a side branch or flowing out of a side branch. When fl ow induced pulsations occur, wall vibrations can be significant amplitude limiting losses. Therefore, we propose an analytical model for the acoustical energy losses due to wall vibrations induced by an oscillating side branch. The study of the aeroacoustics of complex pipe systems was initiated considering a row of closed side branches placed along a main pipe. Systems with up to 15 shallow side branches produces flow induced pulsations in which the shear layer instability couples with a longitudinal acoustic standing wave along the main pipe. The side branches are not resonant. The whistling observed in such a system is similar to that observed in a main steam line along which a row of safety valves is placed. It is also a model for a corrugated pipe as used in risers for natural gas production. Our experiments and theoretical analysis demonstrate that the aeroacoustic sources are located near the acoustic pressure nodes of the longitudinal acoustic modes. A prediction model for the whistling behavior has been proposed, which is based on the \energy balance between the acoustic sources and the acoustic losses. Experiments carried out on pipe systems with deep closed side branches show that these systems displays strong trapped modes. These systems have been used to test design rules aiming at a reduction of pulsation levels. The most commonly used solution, detuning the side branch length, appears to be inefficient in multiple deep side branch systems. We propose a semi-empirical model for the prediction of the self-sustained oscillations in pipe systems with closed deep side branches with rounded edged T-junctions. It can predict the oscillation amplitude of a system of six deep side branches within 50% and the oscillation frequency within 2%, for the first hydrodynamic mode. It strongly overestimates the amplitude of higher hydrodynamic modes. In car mufflers, liners of the aircraft engine and liners protecting the walls of combustion chambers, perforated walls are used to absorb sound. The sound absorption is due to the interaction of acoustic waves with the shear layers formed by grazing or/and bias fl ow. The sound absorption depends strongly on the shape of the perforations and on the ratio of bias to grazing fl ow velocity. In the low Strouhal number limit, the acoustic resistance (real part of the impedance) of a perforation is observed to be proportional to the steady-state resistance. A high value of the steady-state resistance leads to high pressure losses across the perforation. The design of an efficient acoustic damper requires an optimization between acoustic and fl uid dynamic performances. Both resistance (real part of the impedance) and reactance (imaginary part of the impedance) due to a grazing-bias flow display an oscillating behavior as function of the Strouhal number. In particular, at high Strouhal numbers, positive (sound absorption) and negative (sound production) values of resistance are observed. The geometry of the perforation determines the whistling behavior at high Strouhal numbers. This operating condition should be avoided in technical applications. Analytical models of the steady flow and of the low frequency aeroacoustic behavior of a two-dimensional wall perforation are proposed allowing a quasi-steady prediction for the sound absorption at low Strouhal numbers. They compare favorably with the experiments.