The Small Signal Response of Fluid Transmission Lines,Including Developed Mean Flow Effects.

摘要

Mathematical models of fluid transmission lines of arbitrary cross section were developed to describe the propagation of small signals through developed mean flow. The mean flow may be either laminar or turbulent and the fluid, either compressible or incompressible. Expressions for both the frequency and time domain dynamic responses are derived. A characteristic radius is defined for any line of arbitrary cross section, which essentially defines an equivalent circular line having the same dynamic response. The characteristic radius used in dynamic analysis is roughly analogous to the hydraulic radius used in steady flow analysis. In developing the models, the frequency response of annular transmission lines was solved and compared to existing solutions for circular and rectangular lines. Next, the frequency and time domain solutions applicable to arbitrary lines carrying laminar mean flow were obtained in terms of equivalent circular lines. Finally, the concept of a characteristic radius was extended to arbitrary fluid lines carrying turbulent mean flow. The results are shown to be relatively very easy to apply, yet comparable in accuracy to existing, very complex models. The new models should be of significant value to the practicing engineer in fluid systems design and analysis. (Author)