Self-sustained oscillations in a closed side branch system

Self-sustained oscillations of the flow in a closed side branch system due to a coupling of vortex shedding with acoustical resonances are considered. The configuration consists of two closed side branches of same length placed opposite to each other along a main pipe. This is called a cross-junction. Numerical simulations, based on the Euler equations for two-dimensional inviscid and compressible flows, are performed. As the radiation into the main pipe is negligible at the resonance frequency, this acoustically closed system is a good test-case of such Euler numerical calculations. The numerical results are compared to acoustical measurements and flow visualization obtained in a previous study. Depending on the flow conditions, the predicted pulsation amplitudes are about 30–40% higher than the measured amplitudes. This is partially due to the absence of visco-thermal dissipation in the numerical model but also to the effect of wall vibrations in experiments. A simple analytical model is proposed for the prediction of the pulsation amplitudes. This model is based on Nelsonʹs representation of the shear layer as a row of discrete vortices convected at constant velocity from the upstream edge towards the downstream edge. When the downstream edge is sharp, this results in a spurious interaction between the singularity of the vortices and of the edge flow. This artefact is partially compensated by suppressing the singularity of the acoustical flow at the edge, or when a junction with rounded edges, as found in engineering practice, is considered. In spite of its crudeness, the analytical model provides a fair prediction (within 30%) which makes it useful for engineering applications.