Plain axial seals are often used in centrifugal pumps as a means to achieve acceptable sealing against leakage flow without the much higher friction losses that are associated with mechanical seals. Examples of their application are the front seals in shrouded radial and mixed-flow pumps and the inter-stage seals in multi-stage pumps. Knowledge about the relation between leakage flow rate and pressure drop over the seal is vital, not only for estimating the volumetric losses, but also for calculating the axial thrust and shaft power of a pump.
Investigations up till now have mainly concentrated on the frictional pressure drop in the seal (e.g. Yamada , Weber ), and hardly on the expansion losses at the exit of the seal. These exit losses are commonly modelled by a kinetic loss coefficient equal to or close to 1, but recent measurements by Storteig  have shown that exit loss coefficients can have values well above 1.
This paper presents an analytical method to compute the exit loss coefficient of a plain axial seal. It is derived from energy and momentum balances and assumes power-law profiles for the velocity distribution in the seal. The power-law coefficients are computed using CFD and are found to only depend on the Reynolds numbers based on axial flow, Reax, and Couette flow in circumferential direction, ReΩ. The resulting exit loss coefficients are shown to range between 1 and 2, depending on the ratio of Reax and ReΩ. Results of the analytical model are compared with measurements and CFD calculations.
This new analytical model can help improve the prediction of rotor dynamic stability, efficiency and axial thrust of turbomachinery without the need for dedicated CFD calculations in these tight clearances.