One-Dimensional Approach to Modeling of Reflected and Transmitted Pressure Pulses in Ducts

Abstract

Numerous aerospace propulsion problems involve propagation of pressure waves and pressure pulses through ducts of variable cross section and their intersections. Pressure waves dissipate when they propagate in moving Newtonian and non-Newtonian fluids and undergo transmission through intersection of ducts and reflection at their walls. Onedimensional numerical approximation of these phenomena will be useful for the multivariant engineering design and optimization as well as for real-time control. While reflection of pressure pulses over closed valves and duct entrances is usually described by uniform boundary conditions and is naturally one-dimensional, reflection and transmission of pressure pulses at intersection of ducts with different cross sections is a multi-dimensional process caused by non-uniform boundary conditions. In the current study, the onedimensional approach is investigated to approximate the multi-dimensional process of reflection and transmission of pressure pulses at intersection of ducts with different cross sections. The approach is facilitated by introduction of local force exerted by solid wall on pressure pulse at intersection of ducts into the conservative form of conservation laws. This source term is incorporated into second-order MacCormack scheme. Finally, it is shown that the non-conservative form of the conservation laws is capable of capturing the wall effect without requiring the addition of the force term. The transmission/reflection predictions from latter approach and using second-order MacCormack scheme exhibit improved agreement with existing analytical solution.