The basic equations are derived for compressible flow in a straight-through gas labyrinth seal. The flow is assumed to be completely turbulent in the circumferential direction where the shear stresses in the boundary layers attached to the rotor and stator surfaces are determined by the Blasius correlation in smooth pipes. Zero-th-order and linearized first-order equations are developed for the perturbation flow generated by a small motion of the rotor about a centered position. The zero-th-order pressure distribution is found by satisfying the leakage equation while the zero-th-order circumferential velocity distribution is determined by satisfying the circumferential momentum equation. In this analysis we assume a radially linear circumferential velocity distribution in the core region between the two boundary layers. Several leakage models are discussed and compared. Periodic solution to the first-order equations is obtained describing the time dependent non-axisymmetric gas flow. Integration of the resultant pressure and shear stresses along and around the seal defines the reaction force developed by the seal and the corresponding rotordynamic stiffness and damping coefficients necessary for the lateral stability analysis of the rotor. The results of this analysis are then compared with existing experimental data and previous theoretical results.
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