Higher order numerical method for aeroelastic problems

Authors

Yu. A. Bykov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky str., Kharkiv, 61046, Ukraine), e-mail: bykow@ipmach.kharkov.ua

Abstract

The accuracy of determining the conditions for the possible onset of uncontrolled oscillations of turbine blades depends on the accuracy and detail of the aerodynamic problem solution. An increased accuracy of the simulation is necessary for complex flows in which shocks waves are present, i.e. in trans- and supersonic flows. The main goal of this paper is to evaluate the influence of the order of numerical scheme approximation on the unsteady characteristics of the blade cascade in the transonic gas flow. This work presents the results of simulating transonic flow in the cascade of oscillating turbine profiles using methods of different accuracy, and a quantitative evaluation of the correspondence of the results to the order of approximation is made. A method for numerical simulation of viscous compressible gas flow through the cascade of oscillating blades is presented. The method is designed to solve the unsteady two-dimensional Reynolds averaged Navier-Stokes equations, which are closed by turbulence modeling equation. For the approximation of the initial equations four different numerical schemes are used: the original Godunov scheme of a first order approximation, the Godunov-Kolgan scheme having a locally second-order approximation, the ENO decomposition of a second order of approximation and the ENO decomposition, which has a locally third order approximation. A cascade of turbine profiles was chosen as a study object, which was examined at the École Polytechnique Fédérale de Lausanne. A detailed analysis of the obtained calculation results was performed. The results were compared with the results of numerical simulation of the second and first order approximation, as well as with experimental data. It is shown that the numerical simulation of complex transonic flows requires the application of methods with increased accuracy. An insufficient order of approximation can sometimes lead to a significant distortion of the results, right up to the sign change in the work of the aerodynamic forces. Along with the application of higher order schemes, it is necessary to use adaptive computational grids, which take into account the flow features and do not introduce additional errors to the region of large gradients of values.

Keywords: computational fluid dynamics; aeroelasticity in turbomachines; unsteady flow; unsteady loads

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Received 20 November 2017

Published 30 March 2018