Abstract
Static test results are presented for smooth annular seals with a length-to-diameter ratio of 0.50, radius R = 51.00 mm, at the nominal radial clearance Cr = 0.2032 mm. Tests were conducted for angular shaft speeds; ω = 2, 4, 6, 8 krpm, axial pressure drops; ΔP = 2.1, 4.13, 6.21, 8.27 bars, and eccentricity ratios ϵ0 = e0/Cr = 0.00, 0.27, 0.53, 0.8 where e0 is the static eccentricity. Three pre-swirl inserts were used to target zero, medium, and high (0., 0.4, and 0.8) pre-swirl ratios for a set of pre-determined operating conditions with ISO VG 2 oil at 46.1°C.
Pitot tubes measured the circumferential velocity at separate upstream and downstream seal locations and were used to calculate pre-swirl ratio, PSR = vinlet/Rω, and outlet-swirl ratio, OSR = voutlet/Rω. For all tested pre-swirl inserts, PSR tended to converge to 0.4∼0.5 as ω increased. PSR and OSR were poorly correlated.
Volumetric leakage rate Q ˙ versus pressure differential ΔP was measured. The measured vector Reynolds number Re, combining the axial and circumferential Reynolds numbers ranged from ∼1000 to ∼3500. Based on Zirkelback and San Andrés 1996 publication, almost all of the flow regime is predicted to lie in the transition regime, with fewer points in the turbulent regime.
Generally, the seals’ static centering properties were obtained by applying a static load Fs and measuring the resulting displacement vector e0. At many low-speed, low-ΔP test conditions, the seal would not remain in the desired centered or near-centered position and had to be forced into place with a centering force Fs. The authors believe that the observed de-centering effects resulted from test operations in the transition flow regime where the friction factor λ does not drop with increasing ΔP and increasing Re. A positive centering Lomakin effect requires that λ drop with increasing axial Reynolds number.
The seals had positive centering effects over a large portion of the predicted transition flow regime, supporting the view that the shift from transition-to-turbulent flow regularly occurred at lower Re values than the Re = 3000 boundary used by Zirkleback and San Andrés.
Transition flow regime on stepped spillways: air–water flow characteristics and step-cavity fluctuations
