Sound reflection at the open end of axisymmetric ducts issuing a subsonic mean flow: A numerical study

This paper investigates the reflection of sound waves as they propagate toward the open end of ducts issuing a cold subsonic mean flow in a stagnant fluid. The investigations are conducted by using a relatively new one-step numerical technique known as the lattice Boltzmann method. The results obtained in terms of end correction, l  , and magnitude of the pressure reflection coefficient, |R||R|, for an unflanged pipe model are in very good agreement with theoretical predictions and experimental data for the range of Mach numbers M≤0.15M≤0.15 and Helmholtz numbers ka≤1.5ka≤1.5. Simulations carried out for a similar pipe terminated by circular horns of different curvature radii show that |R||R| is independent of the horn geometry for Strouhal numbers Sr0<4,Sr0=ka/M. For situations in which M>0M>0, the amplification of the reflection coefficient magnitude, that is |R|>1|R|>1, is normally ∼20∼20 percent higher than that observed for an unflanged pipe issuing an equal Mach number flow. Furthermore, the amplification maxima is found to occur always at Sr0=π/2Sr0=π/2, regardless of whether the pipe is unflanged or terminated by different circular horns. Conversely, the results for the end correction are strongly dependent on the horn curvature. For the low Strouhal number limit, the dimensionless end correction measured at the junction between the horn and the pipe with radius a   becomes l/a=0.31l/a=0.31 for a horn whose curvature radius is 2a2a, and l/a=0.62l/a=0.62 for a horn with curvature radius equal to 4a4a.