Numerical calculations of the 3D transonic flow of an ideal gas through turbomachinery blade rows moving relatively one to another with taking into account the blades oscillations is presented. The approach is based on the solution of the coupled aerodynamic-structure problem for the 3D flow through the turbine stage in which fluid and dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a coupled problem, as the blades oscillations and loads, acting on the blades, are a part of solution. An ideal gas flow through the mutually moving stator and rotor blades with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite-volume difference scheme of Godunov-Kolgan and moving hybrid H-H grid. The structure analysis uses the modal approach and 3D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations with the modal coefficients depending on time. The algorithm proposed allows to calculate turbine stages with an arbitrary pitch ratio of stator and rotor blades, taking into account the blade oscillations by action of unsteady loads caused both outer flow nonuniformity and blades motion. There has been performed the calculation for the stage of the turbine with rotor blades of 0.765 m. The numerical results for unsteady aerodynamic forces due to stator-rotor interaction are compared with results obtained with taking into account the blades oscillations.
3D Unsteady Forces of the Transonic Flow Through a Turbine Stage With Vibrating Blades
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Rza˛dkowski, R, & Gnesin, V. "3D Unsteady Forces of the Transonic Flow Through a Turbine Stage With Vibrating Blades." Proceedings of the ASME Turbo Expo 2002: Power for Land, Sea, and Air. Volume 4: Turbo Expo 2002, Parts A and B. Amsterdam, The Netherlands. June 3–6, 2002. pp. 765-774. ASME. https://doi.org/10.1115/GT2002-30311
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