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Significant impact on the stage efficiency have leakage of the working fluid through the seal gaps and discharge openings. The dependence of the leakage (and associated losses) of the stage bounding surfaces parameters can dramatically affect the distribution of the optimal parameters along the radii and, hence, the spatial structure of the flow therein. The latter, in turn, is determined by the shape and twist law of guide vane and impeller.

Development of algorithms for the axial turbine stages crowns twist laws optimization demanded the establishment of appropriate in the terms of computer time methods for calculating the quantities of leaks and losses on them, allowing the joint implementation of the procedure for calculating the spatial parameters of the flow in the stage.

The leakage calculation is necessary to conduct together with a spatial calculation step, as the results of which the parameters in the calculation sections are determined, including the meridian boundaries of the flow path. The flow capacity depends on the clearance (or leakages) values, in connection with which main stream flow calculation is made with the mass flow amplification at fixed the initial parameters and counter-pressure on the mean radius, or clarifying counter-pressure at fixed initial parameters and mass flow. The need for multiple stage spatial parameters calculation (in the optimization problem the number of direct spatial calculations increases many times) demanded a less time-consuming, but well reflecting the true picture of the flow,

methods of spatial stage calculation in the gaps described above (Fig. 2.3).

When calculating stage in view of leakage the continuity equation is convenient to take as [8]:

where μ – the mass transfer coefficient, which allows to take into account changes in the amount of fluid passing through the crowns, and at the same time to solve a system of ordinary differential equations in sections in front of and behind the impeller like with a constant flow rate.

The leakage mass transfer coefficients [13] is defined as follows:

In the case of wet steam flow with loss of moisture, crown overall mass transfer coefficient is given by

where ψ_{m,i} flow coefficient, is usually determined in function of the degree of humidity and pressure ratio [8].