Multistage centrifugal pumps and compressors are among the most widely used pieces of rotating machinery in industry. A typical application demands the arrangement of several impellers or wheels mounted on a shaft that spins within a stationary case. Annular seals are the most common sealing devices used in this type of machinery. The annular seal design affects both (i) machinery performance in terms of energy conversion efficiency, and (ii) stability due to the interaction within the rotor and the stator through the fluid flow within the seals. Traditionally, the “bulk-flow” theory due to Hirs (ASME J. Lubrication Technol., pp. 137–146) has been used to estimate annular seals leakage and dynamic coefficients. To predict the flow behavior through the seal, this theory relies on empirical friction factor correlations. While leakage is well predicted, the dynamic coefficients are not. The discrepancy is attributed to the friction factor model. Several experiments have produced seal leakage data indicating that friction factor increases as the seal clearance is increased, contradicting predictions based on Moody’s pipe-friction model. A Computational Fluid Dynamics (CFD) commercial code was used to simulate flat-plate-channel-flow experimental tests of water flowing with deliberately roughened surfaces, showing an increase of friction factor with clearance increase. The higher friction factor characteristics of these deliberately roughened surfaces are governed by their ability to develop a high static pressure in the trailing face of each roughness cavity, while the wall shear stresses on the smooth land play a secondary role. In a certain Reynolds number range, the maximum friction factor observed on a specific roughness pattern size is independent of the actual clearance, which we have referred to as the friction-factor-to-clearance indifference behavior. This phenomenon is found to be related to the roughness cavity size and its length-to-clearance ratio.

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