Numerical computation of gas flow through an exhaust duct: an investigation of the exit boundary conditions

A numerical investigation of the exit plane boundary conditions of an engine exhaust duct is presented. The conventional boundary condition which is used in non-linear analysis is the so-called zero-pressure condition. Various forms of implementation of this condition are used to investigate the relative effects upon the error which arises from numerical approximation oferö pressure condition. The computational domain is then extended downstream of the exit boundary, to model acoustic radiation into a free or half space without the need for any boundary condition at the duct exit plane. The Sommerfeld radiation condition is used to set the boundary conditions at a finite far-field location, making it possible for the computational domain to be set at a finite size. Calculations on the extended domain are used to determine the error in the radiated sound levels which is caused by the fundamental inadequacy of the zero-pressure boundary condition in representing the actual conditions at the exit exit plane. A modification of the conventional zero-pressure exit boundary condition is used, which gives improved results in the non-linear flow regime, without the need to extend the flow domain downstream of the exit boundary. For calculations on the simple duct domain, the flux-split scheme of Radespeil and Kroll is used to reduce spurious modes of the numerical scheme, which are convected to the exit boundary, so that the solution is improved. For the different flow domains considered, examples of small-amplitude single-frequency and multiple-frequency disturbances are presented, followed by higher amplitude multiple-frequency engine source examples. The results for small-amplitude disturbances are compared to those from linearised frequency-domain acoustic analysis. Exit plane velocity profiles and far-field noise spectra corresponding to the computed flows are presented and discussed. Finally, two sets of experimental data, one for a Wankel Rotary Engine and one for a piston engine, are examined against computed data.