A generalized non-reflecting inlet boundary condition for steady and forced compressible flows with injection of vortical and acoustic waves

Abstract

This paper describes a new boundary condition for subsonic inlets in compressible flow solvers. The method uses characteristic analysis based on wave decomposition and the paper discusses how to specify the amplitude of incoming waves to inject simultaneously three-dimensional turbulence and one-dimensional acoustic waves while still being non-reflecting for outgoing acoustic waves. The non-reflecting property is ensured by using developments proposed by Polifke et al. [1, 2]. They are combined with a novel formulation to inject turbulence and acoustic waves simultaneously at an inlet. The paper discusses the compromise which must be sought by the boundary condition formulation between conflicting objectives: respecting target unsteady inlet velocities (for turbulence and acoustics), avoiding a drift of the mean inlet velocities and ensuring non-reflecting performances for waves reaching the inlet from the computational domain. This well-known limit of classical formulations is improved by the new approach which ensures that the mean inlet velocities do not drift, that the unsteady components of velocity (turbulence and acoustics) are correctly introduced into the domain and that the inlet remains non-reflecting. These properties are crucial for forced unsteady flows but the same formulation is also useful for unforced cases where it allows to reach convergence faster. The method is presented by focusing on the expression of the ingoing waves and comparing it with the classical NSCBC approach [3]. Four tests are then described: (1) the injection of acoustic waves through a non reflecting inlet, (2) the compressible flow establishment in a nozzle, (3) the simultaneous injection of turbulence and ingoing acoustic waves into a duct terminated by a reflecting outlet and (4) a turbulent, acoustically forced Bunsen-type premixed flame.