A COMPARISON OF EXPERIMENTAL AND THEORETICAL RESULTS FOR LABYRINTH GAS SEALS

The basic equations are derived for a two-control-volume model for compressible flow in a labyrinth seal. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation. The circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are compared to experimental test results presented in this report. The results presented are for three teeth-on-rotor and three teeth-on-stator labyrinth seals with different radial clearances. The theory compares well with the cross-coupled stiffness data for both seal types and with the direct damping data for a teeth-on-rotor labyrinth seal. For a teeth-on-stator labyrinth seal, the test results show a decrease in direct damping for an increase in radial seal clearance, while the theory shows the opposite.