On mathematical modelling and mumerical simulation of transient compressible flow across open boundaries

Abstract

In numerical simulations of turbulent reacting compressible flows, artificial boundaries are needed to obtain a finite computational domain when an unbounded physical domain is given. Artificial boundaries which fluids are free to cross are called open boundaries. When calculating such flows, non-physical reflections at the open boundaries may occur. These reflections can pollute the solution severely, leading to inaccurate results, and the generation of spurious fluctuations may even cause the numerical simulation to diverge. Thus, a proper treatment of the open boundaries in numerical simulations of turbulent reacting compressible flows is required to obtain a reliable solution for realistic conditions.

A local quasi-one-dimensional characteristic-based open-boundary treatment for the Favreaveraged governing equations for time-dependent three-dimensional multi-component turbulent reacting compressible flow is presented. A k-ε model for turbulent compressible flow and Magnussen’s EDC model for turbulent combustion is included in the analysis. The notion of physical boundary conditions is incorporated in the method, and the conservation equations themselves are applied on the boundaries to complement the set of physical boundary conditions.

A two-dimensional finite-difference-based computational fluid dynamics code featuring high-order accurate numerical schemes was developed for the numerical simulations.

Transient numerical simulations of the well-known, one-dimensional shock-tube problem, a two-dimensional pressure-tower problem in a decaying turbulence field, and a two-dimensional turbulent reacting compressible flow problem have been performed. Flow- and combustion-generated pressure waves seem to be well treated by the non-reflecting subsonic open-boundary conditions. Limitations of the present open-boundary treatment are demonstrated and discussed.

The simple and solid physical basis of the method makes it both favourable and relatively easy to implement into existing CFD codes for engineering applications.