Experimental Investigations of Flow Development, Gap Instability and Gap Vortex Street Generation in Eccentric Annular Channels

Abstract

Isothermal flow development, gap instability, and gap vortex street generation in eccentric annular channels have been studied experimentally. A representative paradigm of a flow in a highly eccentric annular channel was examined for a channel having an inner-to-outer diameter ratio d/D = 0.50 and an eccentricity e = 0.8 for a Reynolds number Re = 7300. Observation of the flow development has identified three distinct regions: the entrance region, the fluctuation-growth region and the rapid-mixing region. Weak quasi-periodic velocity fluctuations were first detected in the downstream part of the entrance region, and grew into very strong ones, reaching peak-to-peak amplitudes in the narrow gap that were nearly 60% of the bulk velocity. The dependence on inlet conditions, d/D, e and Re on the development and structure of flows was also investigated. Experimental conditions covered the ranges: 0 ≤ Re ≤ 19000, 0 ≤ e ≤ 0.9 and d/D = 0.25, 0.50 and 0.75. For Re < 7000, the Strouhal number, the normalized mid-gap axial flow velocity and the axial and cross-flow fluctuation intensities at mid-gap were found to increase with increasing Re and to depend strongly on inlet conditions. At higher Re, however, these parameters reached asymptotic values that were only mildly sensitive to inlet conditions. A map was constructed for the various stages of periodic motions vs. e and Re and it was found that, for e < 0.5 or Re < 1100, the flow was unconditionally stable as far as gap instability is concerned. For e ≤ 0.5, transition to turbulence occurred at Re ≈ 6000, whereas, for 0.6 ≤ e ≤ 0.9, the critical Reynolds number for the formation of periodic motions was found to increase with eccentricity from 1100 for e = 0.6 to 3800 for e = 0.9. The use of an empirically derived "mixing layer Strouhal number" permitted a universal description of gap vortex street periodicity in eccentric annular channels. This study has contributed to our understanding of the physical mechanisms that lead to gap instability and the development of a gap vortex street and the dependence of these flow phenomena on the channel geometry and the dynamic conditions of the flow.