Characteristics analysis of a flow between two rotating discs in the air supply system to the turbine rotor blade based on adapted similarity criteria


Аuthors

Didenko R. A.1*, Piralishvili S. A.2**, Shahov V. G.3***

1. United Engine Corporation “Saturn”, 163, Lenin av., Rybinsk, Yaroslavl region, 152903, Russia
2. ,
3. Samara National Research University named after Academician S.P. Korolev, Samara, Russia

*e-mail: roman.didenko@npo-saturn.ru
**e-mail: piral@list.ru
***e-mail: shakhov@ssau.ru

Abstract

The article presents the results of theoretical study and computation of the adiabatic flow in

the cooling air feeding system with a pre-swirl. The pre-swirled cooling air is being supplied

through the stationary swirling unit, flows upward along the radius in the rotating cavity,

formed by the walls of the rotating disk and disk-deflector, and leaves the rotating cavity

through the channels in the disk, meant for feeding air to the turbine blade. Based on the nondimensional

form of momentum equations of the flow in rotating cavity, it is demonstrated that

there are two similarity criteria, which can control the turbulent flow in the rotating cavity. Ekman

and Rossby numbers relate to them. From the practical viewpoint, it is more convenient to

use rotational Reynolds number Reϕ instead Ekman number, non-dimensional mass flow rate

Cw instead Rossby number, and turbulent flow parameter λT = Cw/ Reφ0.8 for complex studies.

As t he f low i n t he s ystem i s h ighly p re-swirled, non-dimensional initial swirl ratio β derived

while non-dimensionalizing of the momentum equations is also used in analysis. The main indices of the delivery system efficiency are non-dimensional adiabatic effectiveness Θ, loss coefficient ζ and specific power consumption of the system N. Numerical simulation was performed with commercial Ansys CFX software. To solve the Reynolds Averaged Navies-Stokes (RANS) equations a finite volume coupled algebraic multi-grid solver was used. The scheme of the second order of accuracy was used for computations. The energy equation was solved with regard for the viscous work term. The Buoyancy effect was ignored. As the result of this work, the strategy of the flow analysis was formulated based on the dependences of main indices of the system efficiency on non-dimensional similarity criteria. According to the obtained results there is no effect of Reϕ and Cw on adiabatic effectiveness Θ. With increasing of Reϕ the loss coefficient ζ decreases. Specific power consumption of the system N increases with Cw and decreases with increasing Reϕ and initial swirl ratio β.

Keywords:

Navier-Stokes equations, Rossby number, Reynolds number, Ekman number, flow swirl, generalized turbulent flow parameter

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