On the Thermodynamic Process in the Bulk-Flow Model for the Estimation of the Dynamic Coefficients of Labyrinth Seals

The impact of sealing equipment on the stability of turbomachineries is a crucial topic because the power generation market is continuously requiring high rotational speed and high performance, leading to the clearance reduction in the seals. The accurate characterization of the rotordynamic coefficients generated by the seals is pivotal to mitigate instability issues. In the paper, the authors propose an improvement of the state-of-the-art one-control volume (1CV) bulk-flow model (Childs and Scharrer, 1986, "An Iwatsubo-Based Solution for Labyrinth Seals: Comparison to Experimental Results," ASME J. Eng. Gas Turbines Power, 108(2), pp. 325-331) by considering the energy equation in the steady-state problem. Thus, real gas properties can be evaluated in a more accurate way because the enthalpy variation, expected through the seal cavities, is evaluated in the model. The authors assume that the enthalpy is not a function of the clearance perturbation; therefore, the energy equation is considered only in the steady-state problem. The results of experimental tests of a 14 teeth-on-stator (TOS) labyrinth seal, performed in the high-pressure seal test rig owned by GE Oil&Gas, are presented in the paper. Positive and negative preswirl ratios are used in the experimental tests to investigate the effect of the preswirl on the rotordynamic coefficients. Overall, by considering the energy equation, a better numerical estimation of the rotordynamic coefficients for the tests with the negative preswirl ratio has been obtained (as it results from the comparison with the experiments). Finally, the numerical results are compared with a reference bulk-flow model proposed by Thorat and Childs (2010, "Predicted Rotordynamic Behavior of a Labyrinth Seal as Rotor Surface Speed Approaches Mach 1," ASME J. Eng. Gas Turbines Power, 132(11), p. 112504), highlighting the improvement obtained.