An implicit numerical scheme for gas flow simulation in cascade of vibrating airfoils

Authors

  • Ю. А. Быков A. N. Podgorny Institute for Mechanical Engineering Problems of NAS of Ukraine, Ukraine
  • Виталий Исаевич Гнесин A. N. Podgorny Institute for Mechanical Engineering Problems of NAS of Ukraine, Ukraine

Keywords:

numerical simulation, turbine cascade, aeroelasticity

Abstract

An implicit numerical scheme for unsteady gas-dynamic processes in cascades of vibrating turbine airfoils is presented. The scheme is second-order accurate in time and space and based on modified second-order Godunov’s scheme. Proposed scheme is suitable for upgrading existing explicit unsteady flow solvers. The algorithm is developed for unstructured grids usage and utilizes iterative numerical methods for the implicit procedure. A numerical simulation of flow in cascade of 4th standard configuration turbine airfoils is performed. Movement of the airfoils is defined as bending with given frequency and amplitude, inter-blade phase shift is set to zero. In the simulation different time steps are used on purpose to estimate an influence of step value on result accuracy. Conclusion about optimal values for time step is obtained. Estimation of possibility of application of implicit schemes to similar aeroelastic problems is performed. Conclusions about computational effectiveness of exploited scheme are obtained.

Author Biographies

Ю. А. Быков, A. N. Podgorny Institute for Mechanical Engineering Problems of NAS of Ukraine

PhD

Виталий Исаевич Гнесин, A. N. Podgorny Institute for Mechanical Engineering Problems of NAS of Ukraine

Doctor of Technical Sciences, Professor

References

Brouwer, K., Crowell, A. R., McNamara, J. J. (2015) Rapid Prediction of Unsteady Aeroelastic Loads in Shock-Dominated Flows. Proceeding of 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference: 1-20.

Padmanabhan, M. A., Pasiliao, C. L., Dowell, E. H. (2014) Simulation of Aeroelastic Limit-Cycle Oscillations of Aircraft Wings with Stores. AIAA Journal 52(10): 2291-2299.

Chen, T., Xu, M., Xie, L. (2014) Aeroelastic Modeling Using Geometrically Nonlinear Solid-Shell Elements. AIAA Journal, 52(9): 1980-1993.

Kersken, H., Frey, C., Voigt, C., Ashcroft, G. (2012) Time-Linearized and Time-Accurate 3D RANS Methods for Aeroelastic Analysis in Turbomachinery. ASME Journal of Turbomachinery, 134(5): 051024-051024-8.

Gupta, K. K., Voelker, L. S. (2012) Aeroelastic Simulation of Hypersonic Flight Vehicles. AIAA Journal 50(3): 717-723.

Gnesin, V. I., Bykov, Y. A. (2004) Numerical investigation of aeroelastic characteristics of turbomachine blade cascade at off-design operation mode. Journal of Mechanical Engineering, 7(1): 31-40.

Gendel, S., Gottlieb, O., Degani, D. (2015) Fluid–Structure Interaction of an Elastically Mounted Slender Body at High Incidence. AIAA Journal, 53(5): 1309-1318.

Wilcox, D.C. (1988) Reassessment of the Scale-Determining Equation for Advanced Turbulence Models. AIAA Journal, 26(11): 1299-1310.

Beam, R. M., Warming, R. F. (1978) An Implicit Factored Scheme for the Compressible Navier-Stokes Equations. AIAA Journal, 16(4): 393-402.

Paige, C. C., Saunders, M. A. (1982) LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Transactions on Mathematical Software, March 1982, 8(1): 43-71.

Bolcs, A., Fransson, T. H. (1986) Aeroelasticity in Turbomachines. Comparison of Theoretical and Experimental Cascade Results. Communication du Laboratorie de Thermique Appliquee et de Turbomachines, Lausanne, EPFL, 13. — 230 p.

Downloads

Published

2015-12-31

Issue

Vol. 18 No. 4/1 (2015)

Section

Aero- and hydrodynamics in energy machines

License

Copyright (c) 2015 Виталий Исаевич Гнесин, Ю. А. Быков

Creative Commons License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

All authors agree with the following conditions:

  • The authors reserve the right to claim authorship of their work and transfer to the journal the right of first publication of the work under the license agreement (the agreement).
  • Authors have a right to conclude independently additional agreement on non-exclusive spreading the work in the form in which it was published by the jpurnal (for example, to place the work in institution repository or to publish as a part of a monograph), providing a link to the first publication of the work in this journal.
  • Journal policy allows authors to place the manuscript in the Internet (for example, in the institution repository or on a personal web sites) both before its submission to the editorial board and during its editorial processing, as this ensures the productive scientific discussion and impact positively on the efficiency and dynamics of citation of published work (see The Effect of Open Access).