**4. Conclusions**

Minimization of the leakage rate in labyrinth seals is a problem of great importance since it enables improvement of high-power fluid-flow machines efficiency. This paper presented two variants of the method for aerodynamic design of the seal geometry. Variant A can be used when it is impossible to change external dimensions of the seal; it consists in changing the location of the seal teeth. In this variant, the design method anticipates the interference in the geometry of internal elements of the seal. Variant B can be used when there is a possibility to change slightly the height of seal chambers in the fluid-flow machine.

The design method in both variants, A and B, enables improvement of seals in different machines, newly designed as well as already installed but under modernization or repair. This method is based on the observation of thermodynamic and flow phenomena occurring in labyrinth seals, such as the gas flux of a high velocity formation, and the mechanism of kinetic energy dissipation. The above described method allows for determining the resultant geometry unequivocally.

The method in the variant A enables changing the pitch length for the staggered seals to obtain the reduced leakage. For the representative straight through seal geometry the leakage rate reduction ranging from 3.4% to 15.5% had been obtained, when compared with the initial geometry of a constant pitch.

The method in the variant B brings significant reduction of the leakage rate by 15.4% without changing the seal length and with a slight change of the seal height.

Results of calculations presented in this paper confirm the effectiveness of the design method for both variants irrespective of the value of the pressure ratio *pin/pout* in the range from 2 to 2.8. Results presented in the paper show that the use of the improved geometry enables the reduction of leakage of various degrees of wear of the seal, from radial clearance 0.315 to 0.77 mm.

Currently, there is no similar approach to the design of seals in the literature. The method discussed in this article opens up a new perspective on seal design. It is planned to use this design method to other geometries of sealing and to conduct experimental research.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
