This paper introduces an open three-dimensional (3D) flutter test case for steam turbines. The test case is fully described and initial results are presented. The steam turbine last stage blading geometry is taken from a test case originally presented by Durham University. The stage is representative of the aerodynamic characteristics of modern steam turbine blading. To the authors' knowledge, this is the first time that a steam turbine flutter test case is presented based on an open 3D realistic blade geometry. ANSYS CFX and LUFT (Linearized Unsteady Flow solver for Turbomachinery) were both applied to calculate inviscid and RANS steady and unsteady flow solutions. Plots of aerodynamic damping versus inter-blade phase angle and plots of the local work coefficient on the blade for critical cases are presented.

The performance of gas turbine airfoils is continually improved by creating advanced aerodynamic and thermal designs. Optimization methods are used to handle the increasing complexity of such a design. However, optimization is expensive when performed based on 3D CFD calculations. Therefore, an optimization strategy based on simpler, less expensive analysis methods is desirable. Oftentimes, a so-called quasi-3D (Q3D) approach is used, where 2D calculations are carried out on multiple, radially stacked meridional blade sections. This paper investigates the applicability of such an approach for optimization with regard to blade profile loss. Obviously, certain physical effects are neglected using this approach, leading to errors in the predicted blade performance. Still, optimization based on Q3D calculations might be possible if the error is consistent, i.e. not random. For this purpose, a design of experiment (DOE) was carried out to compare and correlate loss predictions from Q3D calculations and high-fidelity 3D CFD calculations for gas turbine blades. It is shown that the total pressure loss coefficients found with both the Q3D and 3D calculations correlate well (75–90%) to warrant the use of a Q3D method for profile shape optimization. Subsequently, an optimization is performed to demonstrate the applicability of the method.

Forced response in turbomachinery refers to the vibration of a component due to an excitation originating from another component. Obstacles, such as struts and blade rows in the upstream and downstream flow path of a turbomachine engine lead to engine order (EO) excitations. To be able to predict the severity of these excitations, both aerodynamic and structural calculations are performed. There is a risk of critical high cycle fatigue (HCF) failure when the force acts at a resonance frequency. Customarily, forcing calculations exclude detailing features, such as leakage flows. The current investigation uses a two stage subsonic model steam turbine configuration with shrouded rotor blades to demonstrate the influence of neglecting flow through seal cavities for blade forcing predictions. Upstream and down-stream vanes are the excitation sources on the rotor blade. Calculation results are compared for a configuration including and excluding the tip shroud cavity. Computed data is compared to available pressure data from tests in the model turbine. The investigation shows for the first blade passing excitation at design point that the axial and circumferential rotor forcing change by +22%, respectively +4% when including the tip shroud cavity for the investigated configuration. The change in forcing arises from the interaction of the leakage flow with the main stream flow. For highly loaded designs this can be of importance if there is a critical excitation.

Forced response analysis is a critical part in the radial turbine design process. It estimates the vibration mode and level due to aerodynamic excitations and then enables the analysis of high-cycle fatigue (HCF) to determine the life span of the turbine stage. Two key aspects of the forced response analysis are the determination of the aerodynamic forcing and damping which can be calculated from unsteady 3D computational fluid dynamics (CFD) simulations. These simulations are problematic due to the high level of complexity in the simulations (multi-row, full annular, tip gap, etc.) and the consequent high-computational cost. The aim of this paper is to investigate and compare different CFD methods applied to the forced response analysis of a radial turbine. Full annular simulations are performed for the prediction of the excitation force. This method is taken as the baseline and is usually the most time-consuming one. One method of reducing the computational effort is to use Phase-lag periodic boundary conditions. A further reduction can be obtained by using a frequency-based method called nonlinear harmonic. For the prediction of aero-damping, the Phase -lag periodic boundary condition method is also available. Moreover, a frequency-based method called harmonic balance can further accelerate the aero-damping calculation. In this paper, these CFD methods will be applied to the simulations of an open-geometry radial turbine with a vaned volute. A comparison of unsteady results from different methods will be presented. These unsteady results will also be implemented to a tuned forced response analysis in order to directly compare the corresponding maximum blade vibration amplitudes.

In turbomachines, forced response of blades is blade vibrations due to external aerodynamic excitations and it can lead to blade failures which can have fatal or severe economic consequences. The estimation of the level of vibration due to forced response is dependent on the determination of aerodynamic damping. The most critical cases for forced response occur at high reduced frequencies. This paper investigates the determination of aerodynamic damping at high reduced frequencies. The aerodynamic damping was calculated by a linearized Navier-Stokes flow solver with exact 3D non-reflecting boundary conditions. The method was validated using Standard Configuration 8, a two-dimensional flat plate. Good agreement with the reference data at reduced frequency 2.0 was achieved and grid converged solutions with reduced frequency up to 16.0 were obtained. It was concluded that at least 20 cells per wavelength is required. A 3D profile was also investigated: an aeroelastic turbine rig (AETR) which is a subsonic turbine case. In the AETR case, the first bending mode with reduced frequency 2.0 was studied. The 3D acoustic modes were calculated at the far-fields and the propagating amplitude was plotted as a function of circumferential mode index and radial order. This plot identified six acoustic resonance points which included two points corresponding to the first radial modes. The aerodynamic damping as a function of nodal diameter was also calculated and plotted. There were six distinct peaks which occurred in the damping curve and these peaks correspond to the six resonance points. This demonstrates for the first time that acoustic resonances due to higher order radial acoustic modes can affect the aerodynamic damping at high reduced frequencies.