## Abstract

Gas labyrinth seals (LSs) improve turbomachinery operational efficiency and mechanical reliability by reducing secondary leakage. As interlocking labyrinth seals (ILSs) restrict more leakage than conventional see-through LSs, attention is due to their performance. An earlier paper (San Andrés et al. 2019, “Leakage and Cavity Pressures in an Interlocking Labyrinth Gas Seal: Measurements Vs. Predictions,” ASME J. Eng. Gas Turbines Power, 141(10), p. 101007.) details the performance of a particular ILS in an ad hoc test rig via measurements of mass flow (leakage) and cavity pressures while supplied with pressurized air at ambient temperature and operating with a rotor speed to a maximum of 10 krpm (surface speed 79 m/s). The test seal comprises two teeth on the rotor and three teeth on the stator to make a four cavity seal with radial clearance Cr = 0.2 mm. The experimental and numerical leakages for the ILS produce a modified flow factor ($Φ¯$) that is independent of the seal operating conditions, namely, inlet pressure, discharge pressure and rotor speed. The finding leads to an orifice-like loss coefficient cd = 0.36 and an effective clearance (cd × Cr) for the test seal, thus evidencing its effectiveness in reducing leakage. To complement the former research, this paper reports measurements of the leakage and cavity pressures for the same geometry interlocking labyrinth seals configured with two other clearances Cr = 0.3 mm and 0.13 mm. For the ILS with Cr = 0.3 mm, a first configuration is without a swirl brake (baseline), the second is with a swirl brake with 0 deg teeth pitch (axial ribs), and the third configuration is with a swirl brake with teeth angled at 40 deg in the direction of shaft rotation. For tests conducted without shaft rotation and with rotor spinning at 7.5 krpm (surface speed= 59 m/s), the inlet air pressure (Pin) ranges from 0.29 MPa to 0.98 MPa, while the exit pressure (Pout) is set to pressure ratios PR = (Pout/Pin) = 0.3, 0.5, 0.8. As to the ILS with Cr = 0.13 mm, it operates with an upstream swirl brake with axial ribs (0° teeth pitch) and w/o rotor speed. The supply pressure (Pin) varies from 0.59  MPa to 1.4 MPa and PR = 0.3, 0.5. The measurements and bulk-flow model predictions show that the seal mass leakage is proportional to the inlet pressure (Pin), increases as PR decreases and is not affected by either shaft speed or the swirl brake configuration. Seal cavity static pressures drop linearly for all inlet pressures (Pin) and PR = 0.5 and above, except under a choked flow condition at PR = 0.3. Processing of the test data to consolidate the numerous leakage measurements delivers a nearly invariant flow factor $Φ¯$ for each seal clearance and from this follows a unique orifice-like loss coefficient cd = 0.36 for the ILS with Cr = 0.3 mm and cd = 0.33 for the ILS with Cr = 0.13 mm. This finding is remarkable as the test results obtained for the ILS with Cr = 0.2 mm also deliver a similar loss coefficient (cd = 0.36). Finally, predictions of ILS leakage and cavity pressures are within 5% of the measurements for all test conditions. The test data and predictions are of significant value to better the selection and design of gas labyrinth seals in turbomachinery.

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