Recent experiments by Dr. Ahmed Gamal at Texas A&M measured the effect of blade pitch and blade profile on the leakage coefficients of labyrinth seals and pocket damper seals. An existing seal test rig was modified to include exchangeable blade teeth and turbine flow meter measurements. The seal “journal” was 4” diameter. Inlet pressure to the seal was varied up to 275 psi. The seal exhausted to atmosphere. The same seal was used in all experiments so that the radial clearance was the same in all tests. A 6-bladed labyrinth seal was instrumented for static pressure measurements between the 2nd and 3rd blades, and between the 3rd and 4th blades. This configuration eliminated inlet geometry effects and exit geometry effects. The seal was first fabricated with a straight (rectangular) blade profile. The tests proceeded as follows: 1) Leakage and pressures were measured for at least three different pressure drops across the seal. 2) The seal was then removed and a bevel machined downstream on each blade; then the leakage tests were repeated. 3) The seal was also reversed in the test rig so that the bevel was upstream; then the leakage tests were repeated. 4) The seal was removed and a bevel machined on opposite sides of the blades; then the leakage tests were repeated. The equation below and several other leakage equations in use were used to calculate appropriate discharge coefficients for all the tested cases. Labyrinth seal leakage across one blade (tooth) can be predicted using the St. Venant equation for orifice flow. The “orifice” in this case is the clearance area between the seal blade and the shaft. The St. Venant equation for mass flow is












where Pi is the upstream pressure, Pi+1 is the downstream pressure, Ai is the clearance flow area, and Cd is a discharge coefficient to be experimentally determined. The area Ai = 2πRsCR, where Rs is the shaft radius and CR is the radial clearance.

            Once the discharge coefficient is determined, the equation works well to predict labyrinth seal leakage over a range of discharge pressures. The example below is for a 8” diameter labyrinth seal with flat (square teeth).
















            Over the past 15 years of testing labyrinth seals, the discharge coefficients required to match the measured leakage have varied widely, as shown in the table below for two different values of radial clearance on 4” or 5” diameter seals. The tooth profiles, pressure levels, and pressure ratios have also varied. Two of the tooth profiles are shown to the right of the table below. There were too many variables in the existing data to determine a functional dependence on blade profile, indicating a need for more experiments with controlled variables.
























Results and Conclusions from Dr. Gamal’s Tests

1.      Tests that were carried out to determine the effect of blade thickness showed that doubling the thickness of the blades reduced leakage rates by up to 20% for certain test configurations.

2.      Blade profile results, together with the results of the blade thickness tests, led to the conclusion that while both factors can be used to improve seal leakage performance, they can also work counter to each other in some cases, especially if the clearances are small. Beveling the blades downstream tends to reduce the leakage, but reducing blade thickness at the tip increases the leakage.

3.      Additional tests showed that operating a seal eccentrically (with the shaft offset in the clearance) had the effect of increasing the leakage through the seal. This phenomenon was considerably more pronounced at lower supply pressures. The effect was less pronounced at all pressures for pocket damper seals as compared to standard labyrinth seals.

4.      Gamal’s tests on a three-bladed and a four-bladed seal with the same overall lengths, but with different pitch lengths, showed  that the two seals had almost identical leakage rates, indicating that blade spacing should be considered as important a factor as the number of blades under certain conditions.




1.        Gamal, A. and Vance, J.M., “Labyrinth Seal Leakage Tests: Tooth Profile, Tooth Thickness, And Eccentricity Effects”, Proceedings of GT2007 ASME Turbo Expo 2007: Power for Land, Sea and Air, May 14-17, 2007, Montreal, Canada.

2.        Gamal, A , Ertas, B.H.,. and Vance, J.M., High-Pressure Pocket Damper Seals: Leakage Rates And Cavity Pressures, Proceedings of GT2006, ASME Turbo Expo 2006: Power for Land, Sea and Air, May 8-11, 2006, Barcelona, Spain. Accepted for publication in the ASME Journal of Turbomachinery.