Abstract
This paper presents the experimental and analytical results on the attenuation and wave celerity of small disturbances superimposed on laminar or turbulent mean flow.
It is found that the propagation constants of pneumatic transmission lines with laminar through-flow are nearly equal to those without through-flow. But when the mean flow is turbulent, propagation constants depend on the through-flow, and the following results are obtained at each different frequency range.
(1) At low frequencies, the attenuation factor αt depends strongly on the Reynolds number of mean flow and is approximated by the following relation.
αt=0.28λ/{a(1+M)}
where λ, a, M are a friction factor depending on the Reynolds number, a line radius and a Mach number, respectively.
(2) Over a broad mid-band, the rate of attenuation decreases significantly with increasing frequency. The larger the Reynolds number of through-flow is, the higher the frequency at which the rate of attenuation has a local minimum value becomes.
(3) At high frequencies, the propagation constant can be represented as a function of Stokes number and be approximated by the high frequency model which is modified from the F.T. Brown's transmission line model without through-flow.
