Investigation of the Impact of Unsteady Turbulence Effects on the Aeroelastic Analysis of a Low-Pressure Turbine Rotor Blade

Abstract

The impact of the unsteadiness in the considered turbulence quantities on the numerical prediction of the aeroelastic behavior of a low-pressure turbine (LPT) rotor blade is evaluated by means of a numerical study. In this context, one of the main objectives of this work is to compare different nonlinear harmonic balance (HB) approaches—one neglecting and one considering the unsteadiness in the employed turbulence models—with a conventional nonlinear solver of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations in the time domain. In order to avoid unphysical oscillations in the turbulence quantities caused by the Gibbs phenomenon in the chosen HB approach, a filter method based on the Lanczos filter is developed. The developed filter method is applied in the course of the HB simulations considering the unsteadiness in the underlying turbulence model. Furthermore, the impact of its application on the solution of the flow field and on the unsteady surface pressure of the rotor blade, in particular, is discussed in the context of this work.

Prediction of Transient Pressure Fluctuations within a Low-Pressure Turbine Cascade Using a Lanczos-Filtered Harmonic Balance Method

“…The second HB approach resolves the unsteady turbulence components k and ω by the number of harmonics listed in Table 1. As explained in the following and motivated in [8,11], the HB method is then prone to numerical instabilities induced by the unsteady consideration of the turbulence model. Thus, this HB approach requires the application of a Lanczos-type filter method and is therefore in the following abbreviated with HB-σ f .…”

“…However, the consideration of the unsteadiness in the transport equations linked to turbulence modeling is found to be a challenging task due to the destabilizing impact of the Gibbs phenomenon as stressed by [7,8]. Hence, previous studies relying on the HB solution method tend to neglect the transient behavior of turbulence quantities by referring to a so-called frozen eddy viscosity approach [9].…”

“…Hence, previous studies relying on the HB solution method tend to neglect the transient behavior of turbulence quantities by referring to a so-called frozen eddy viscosity approach [9]. The resulting limitations of a solution approach neglecting the transient turbulence behavior are shown by [8]. Furthermore, ref.…”

“…Furthermore, ref. [8] proposes the application of a Lanczos-type filter method to alleviate the undesired impact of the Gibbs phenomenon. The benefit of taking into account the unsteadiness of the underlying turbulence models is demonstrated for the evaluation of a modern low-pressure turbine (LPT) configuration.…”

Minimizing Aliasing in Multiple Frequency Harmonic Balance Computations

“…In addition to filtering, a filtered inverse discrete Fourier transform has also been used to improve the convergence and stability of the harmonic balance method [3,18]. This approach is particularly useful in cases when discontinuities and/or strong gradients lead to slow harmonic convergence (Gibbs phenomenon).…”