Abstract
Interactions through direct contact between blade-tips and outer casings in modern turbomachines require complex formulations and subsequent expensive computational efforts when the classical finite element method is considered. The construction of reduced-order models through component mode synthesis techniques usually improves the computational efficiency and may be used for fast parameter studies yielding a better knowledge of the phenomena of interest. In this highly nonlinear framework, the present study is dedicated to the investigation of the capabilities of fixed- and free-interface reduction strategies to handle accurately such problems through a realistic 2D model and complements former results involving a direct modal projection with respective strong kinematic restrictions. The equations of motion are solved using an explicit time integration scheme together with the Lagrange multiplier method where friction is accounted for. The presented work discusses the notions of both displacement and motion convergences and the possibility to conduct fast parameter studies with the use of relevant reduction bases. It also shows that kinematic restrictions artificially enhance the detection of modal interactions.
Highlights
In modern turbomachines such as aircraft jet engines, improved energy efficiency is achieved by controlling the clearance between the blade-tips and stationary surrounding casings so that aerodynamic leaks are minimized
In the last section, results obtained for each type of reduced order model are exposed: modal convergence of the reduced order models computed with component mode synthesis is assessed, the detection of interaction motion is presented and convergences in terms of displacement and motion are extensively revealed for each component mode synthesis method
A combination of component mode synthesis methods with a contact algorithm based on the Lagrange multiplier technique has been introduced in this paper
Summary
In modern turbomachines such as aircraft jet engines, improved energy efficiency is achieved by controlling the clearance between the blade-tips and stationary surrounding casings so that aerodynamic leaks are minimized. Due to the complexity and size of such formulations discretized through the usual finite element approach, computational times may be prohibitive It is proposed in the present study to extend the work introduced in [5] by building reduced-order models through two different component mode synthesis techniques and conduct a comparison analysis concerning the detection of specific interacting motions. They are here adapted to 2D planar models of the bladed disk and the casing in an explicit time-stepping procedure based on the finite-difference scheme with Lagrange multipliers in order to account for contact constraints [14, 15] In this context, a convergence study, with respect to the number of component modes within the reduction basis, introduces the notions of displacement convergence and motion convergence. In the last section, results obtained for each type of reduced order model are exposed: modal convergence of the reduced order models computed with component mode synthesis is assessed, the detection of interaction motion is presented and convergences in terms of displacement and motion are extensively revealed for each component mode synthesis method
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