A model for the prediction of the leakage vortex circulation was developed, based on the assumption that the leakage jet flow enters as a whole the vortex core, increasing its radius and its moment of momentum in the direction of the vortex axis. Using the assumption that the leakage vortex has a solid body rotation, an expression was derived for the vortex circulation, which demonstrates that this circulation is proportional to the square root of the corresponding tip clearance height. This theoretical result is supported by the available experimental data for both compressors and turbines. A simple model was developed, which demonstrates the ability of the proposed theory to calculate the leakage vortex circulation, provided that the vortex trace is known.
A method for predicting the tip clearance effects in the flow field inside and downstream the blade passage, compatible with a meridional flow calculation procedure, has been developed by the authors. The method uses incompressible considerations and accounts for the calculation of the circumferentially mean deficit radial profiles of the various flow quantities. In the calculation procedure the tip clearance flow effects are considered as a modification to the basic flow, existing in the absence of tip clearance. The complete calculation procedure was used in order to calculate the leakage vortex circulation and the induced velocity field in various axial flow cases, with satisfactory results.