Bound states in the continuum in open acoustic resonators

We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct–cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich–Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

The Effect of an Upstream Compressor on a Non-Axisymmetric S-Duct

This paper considers the effect of an upstream compressor stage on a compressor inter-spool duct. The duct geometry must be fixed early in the engine design process, well before the design of the upstream stages. It is therefore important that the designer has a good physical insight into how engine representative inlet conditions affect the limits of the duct design space. An experimental and computational investigation of two strutted inter-spool S-ducts was undertaken. Both were tested with and without an upstream stage present. The first duct is of a conventional axisymmetric design with a radius change to length ratio ΔR/L = 0.50. This duct is characteristic of the most extreme ducts considered in modern engine design. The second duct is of a non-axisymmetric design and is 20% shorter, ΔR/L = 0.625. This is well beyond the design limit of axi-symmetric strutted ducts. The paper shows that the presence of the upstream stage increases the duct loss by 54%. The rise in loss occurs on the hub wall and is the result of the incoming stator wakes pooling onto the hub wall, forming a row of contra-rotating streamwise vortex pairs adjacent to the hub wall. These vortices pump boundary layer fluid into the free stream, thus raising the mixing loss. In the non-axisymmetric duct an extra mechanism was observed. The streamwise vortex pairs act to ‘re-energise’ the boundary layer. This reduces strut secondary losses caused by the endwall contouring. The net result is that on the non-axisymmetric duct the presence of an upstream stage only increases the duct loss by 28%. Comparing the two ducts, it is shown that with engine representative inlet conditions, the conventional symmetric duct and 20% shorter non-axisymmetric duct have identical performance. This shows that low loss ducts can be designed which are significantly more extreme than current design limits.

A Three-Dimensional Axisymmetric Calculation Procedure for Turbulent Flows in a Radial Vaneless Diffuser

An analytical model is proposed to calculate the three-dimensional axisymmetric turbulent flowfield in a radial vaneless diffuser. The model assumes that the radial and tangential boundary layer profiles can be approximated by power-law profiles. Then, using the integrated radial and tangential momentum and continuity equations for the boundary layer and corresponding inviscid equations for the core flow, there result six ordinary differential equations in six unknowns which can easily be solved using a Runge-Kutta technique. A model is also proposed for fully developed flow. The results using this technique have been compared with the results from a three-dimensional viscous, axisymmetric duct code and with experimental data and good quantitative agreement was obtained.