Computation of the Unsteady Transonic Flow in Harmonically Oscillating Turbine Cascades Taking Into Account Viscous Effects

Abstract

This paper presents the numerical results of a code for computing the unsteady transonic viscous flow in a two-dimensional cascade of harmonically oscillating blades. The flow field is calculated by a Navier–Stokes code, the basic features of which are the use of an upwind flux vector splitting scheme for the convective terms (Advection Upstream Splitting Method), an implicit time integration, and the implementation of a mixing length turbulence model. For the present investigations, two experimentally investigated test cases have been selected, in which the blades had performed tuned harmonic bending vibrations. The results obtained by the Navier–Stokes code are compared with experimental data, as well as with the results of an Euler method. The first test case, which is a steam turbine cascade with entirely subsonic flow at nominal operating conditions, is the fourth standard configuration of the “Workshop on Aeroelasticity in Turbomachines.” Here the application of an Euler method already leads to acceptable results for unsteady pressure and damping coefficients and hence this cascade is very appropriate for a first validation of any Navier–Stokes code. The second test case is a highly loaded gas turbine cascade operating in transonic flow at design and off-design conditions. This case is characterized by a normal shock appearing on the rear part of the blades’s suction surface, and is very sensitive to small changes in flow conditions. When comparing experimental and Euler results, differences are observed in the steady and unsteady pressure coefficients. The computation of this test case with the Navier–Stokes method improves to some extent the agreement between the experiment and numerical simulation.

Kinetic mesh-free method for flutter prediction in turbomachines

“…It can be seen that our TKFMG code clearly shows that flutter is present for IBPA = −90 • . Also in the figure we have shown the results of Euler computations by Ji & Liu (1999), Gruber & Cartsens (1998). It can be observed that the trend is captured correctly, that is, regions of positive and negative aerodynamic damping given by computations are in agreement with those observed by experiments.…”

“…In order to validate the method for aeroelastic applications as well as demonstrate the power of the method to deal with multiple oscillating bodies we have computed the unsteady flow for the 4th standard aeroelastic test case (Bolcs & Fransson 1986). Results from the present computations are also compared with other Euler computations (Gruber & Cartsens 1998;Ji & Liu 1999;Mani & Feng 2001). All of them predict the flutter using energy method (Carta 1967).…”

Considerations on the spring analogy

“…This method is applied by Grü ber and Carstens [8] on a cascade in forced vibration. They used structured meshes generated by elliptic grid generation.…”

Investigation of Periodic Boundary Conditions in Multi-Passage Cascade Flows Using Overset Grids

“…The current trends in gas turbine design towards higher flow velocities and slender blades demand an accurate and detailed study of aeroelastic behavior of corn- pressor and turbine blades. The prediction of blade flutter is critical in turbomachinery design and development, and considerable experimental and computational efforts are currently being made to determine flutter boundaries in highly loaded cascades with transonic and supersonic inflow (Ayer and Verdon 1996, Griiber and Carstens 1996, FOrsching 1996, He 1996 It is, therefore, of great interest to develop numerical methods to accurately predict the unsteady aerodynamics of vibrating blades in cascade flows.…”