**3. Application of the Method of Aerodynamic Design for the Staggered Seal of the Geometry Similar to the Element of the Front Sealing in Turbine 13CK60**

The staggered seal consisting of eight teeth located alternately on the shaft and on the body of the sealing (Figure 2) was analyzed. The initial geometry is the staggered seal segment of the external diameter *D* = 139.9 mm, length *LS* = 28.5 mm, height *H* = 4 mm, equal pitch *LP* = 4 mm, the tooth thickness *B* = 0.5 mm, and the clearance height *RC* = 0.315 mm (Figure 2). The paper presents preliminary research. CFD calculations were performed for perfect air. Distribution of local maxima of non-dimensional kinetic energy dependent on the non-dimensional segment length, obtained from the CFD simulation, is shown in Figure 8.

**Figure 8.** Local maxima of the non-dimensional gas kinetic energy emax(i) in the staggered seal with the approximating line *e*(*x*) for boundary conditions *pin/pout* = 2, *Tin* = 300 K, *pout* = 10<sup>5</sup> Pa.

Within the area of the first and last clearances, one local maximum of the kinetic energy was obtained (Figure 8). In other clearances two local maxima of the kinetic energy *emax*(*i*) were obtained. As a result of the design method, variable lengths of the seal pitches *LP*(*i*) were obtained. The first seal pitch is 2.04-mm long and the last one is 6.58-mm long (Figure 9).

**Figure 9.** Resultant distribution of the staggered seal pitch lengths; discontinuous line marks the constant length of the pitch of the initial geometry.

The application of the design method results in the reduction of the leakage rate. To present results, a relative leakage change for the new geometry had been defined, which was in turn compared with the initial geometry comprising eight teeth, which was described by the following formula

$$
\delta \dot{m}(t, 8) = \frac{\dot{m}\_{LP\text{const}}(8) - \dot{m}\_{LPdm}(t)}{\dot{m}\_{LP\text{const}}(8)} \times 100\% \tag{17}
$$

The relative leakage change between the geometry of the seal with equal pitch and the improved one with the same number of teeth t was described by the relation

$$
\delta \dot{m}(t) = \frac{\dot{m}\_{LPconst}(t) - \dot{m}\_{LPdm}(t)}{\dot{m}\_{LPconst}(t)} \times 100\% \tag{18}
$$

Further part of the paper presents results obtained with the use of the design method without changing external dimensions according to the variant A and results of the variant B with a slight change of the seal height.
