On the Modelling of Asymptotic Wavefronts in Long Ducts with Chambers

Abstract

A novel method of determining the possible shapes of pressure wavefronts in ducts after they have travelled sufficient distances to evolve to asymptotic states is introduced. Although it is possible in principle to achieve the same outcome by simulating complete flow histories from the time of the creation of the wavefronts, this can be impracticable. It is especially unsuitable to use such methods when extremely small grid lengths are needed to represent the final outcome adequately. The new method does not simulate the propagation phase at all. Instead, it explores what final end states are possible, but gives no information about the initiating disturbance or the wavefront evolution towards the assessed asymptotic state. Accordingly, the two methods do not overlap, but instead are complementary to each other. A typical case in which the new capability has high potential is described and used to illustrate the purpose and use of the methodology. However, the primary focus is on the presentation and assessment of the method, not on any particular phenomenon. It is shown that the required computational resources are far smaller than those needed for conventional unsteady flow simulations of propagating wavefronts. The potential numerical limitations of the method are highlighted and, with one exception, are shown to be either of no consequence or easily reduced to acceptable levels. Special attention is paid to the one exception because it cannot be proven to be unimportant and, indeed, it would be unsafe to use it in general analyses of wave propagation. However, strong evidence is presented of its acceptability for the study of asymptotic wavefronts.

Keywords

• 1D unsteady flow
• wavefront propagation
• method of characteristics
• micro-pressure waves
• ultra-steep wavefronts
• air chambers