Side Branch Interaction with Main Line Standing Waves and Related Signal Handling Approaches

Data from a low pressure air test facility are used to quantify the influence of the acoustic field in the main line on side branch resonance behavior. The main line of diameter = 7.6？cm may accumulate acoustic energy broadcast from a resonating branch of diameter = 1.9？cm ( = 0.25). The side branch resonance amplitude is a strong function of branch position along the main line with the normalized pressure rising to 1.2 in the most favorable branch positions with Strouhal number near 0.3. Large time variation of the side branch and main line resonance amplitude is apparent for most branch positions. A moving window is used on the time history to collect an array of power spectral densities (PSDs). Peak amplitude values from the PSD array are represented in a probability density function (PDF) that provides a repeatable characterization of data from the system. 1. Background Small branch lines off larger main delivery lines can exhibit acoustic resonance. Branch lines with a reflective obstruction, such as a valve or instrument, are susceptible to a wavelength standing wave, with a pressure node positioned near where the branch meets the main line, and a pressure antinode positioned at the obstruction. Of course, higher modes are possible with an odd number of quarter wavelengths existing in the branch such that where is the sound speed and the characteristic length, , is the branch length. Vorticity in the fluid near the wall of the main line becomes free at the branch and diverts flow periodically into the downstream branch. This in concert with a side branch resonance near the vortex frequency sustains a standing wave in the branch, Rockwell and Naudascher [1]. The frequency for the vortex formation is predicted using the Strouhal number, , with the branch diameter providing the length scale and set to the flow velocity in the main line. Coupling between the branch acoustic response and the vortex shedding behavior allows for a branch to resonate for values of Strouhal number ranging roughly from 0.2 to 0.6, Ziada and Shine [2]. Strouhal number near 0.4 normally gives the largest amplitude acoustic response in the branch. The position of the branch downstream of a fitting such as a valve, orifice, or elbow has been shown to influence vortex shedding and the associated Strouhal number associated with peak response, Ziada and Shine [2] and Lamoureux and Weaver [3]. More than one vortex can span the branch opening, leading to excitation of fundamental acoustic frequencies in branch lines at higher Strouhal numbers, Ziada [4]. Branches positioned across