Effect of Blade Row Interaction on Rotor Film Cooling

The mechanisms of blade row interaction affecting rotor film cooling are identified to make recommendations for the design of film cooling in the real, unsteady turbine environment. Present design practice makes the simplifying assumption of steady boundary conditions despite intrinsic unsteadiness due to blade row interaction; we argue that if film cooling responds nonlinearly to unsteadiness, the time-averaged performance will then be in error. Nonlinear behavior is confirmed using experimental measurements of flat-plate cylindrical film cooling holes, mainstream unsteadiness causing a reduction in film effectiveness of up to 31% at constant time-averaged boundary condition. Unsteady computations are used to identify the blade row interaction mechanisms in a high-pressure turbine rotor: a “negative jet” associated with the upstream vane wake, and frozen and propagating vane potential field interactions. A quasi-steady model is used to predict unsteady excursions in momentum flux ratio of rotor cooling holes, with fluctuations of at least ±30% observed for all hole locations. Computations with modified upstream vanes are used to vary the relative strength of wake and potential field interactions. In general, both mechanisms contribute to rotor film cooling unsteadiness. It is recommended that the designer should choose a cooling configuration that behaves linearly over the expected unsteady excursions in momentum flux ratio as predicted by a quasi-steady hole model.

Effect of Blade Row Interaction on Rotor Film Cooling

The mechanisms of blade row interaction affecting rotor film cooling are identified in order to make recommendations for the design of film cooling in the real, unsteady turbine environment. Present design practice makes the simplifying assumption of steady boundary conditions, despite intrinsic unsteadiness due to blade row interaction; we argue that if film cooling responds non-linearly to unsteadiness, the time-averaged performance will then be in error. Non-linear behaviour is confirmed using experimental measurements of flat-plate cylindrical film cooling holes, main-stream unsteadiness causing a reduction in film effectiveness of up to 31% at constant time-averaged boundary condition. Unsteady computations are used to identify the blade row interaction mechanisms in a high-pressure turbine rotor: a ‘negative jet’ associated with the upstream vane wake, and frozen and propagating vane potential field interactions. A quasi-steady model is used to predict unsteady excursions in momentum flux ratio of rotor cooling holes, with fluctuations of at least ±30% observed for all hole locations. Computations with modified upstream vanes are used to vary the relative strength of wake and potential field interactions. In general, both mechanisms contribute to rotor film cooling unsteadiness. It is recommended that the designer should choose a cooling configuration which behaves linearly over the expected unsteady excursions in momentum flux ratio as predicted by a quasi-steady hole model.

Application of the Modal Approach for Prediction of Forced Response Amplitudes for Fan Blades

Forced response is the main reason for high cycle fatigue in turbomachinery. Not all resonance points in the operating range can be avoided especially for low order excitation. For highly flexible carbon fiber reinforced polymer (CFRP) fans, an accurate calculation of vibration amplitudes is required. Forced response analyses were performed for blade row interaction and boundary layer ingestion (BLI). The resonance points considered were identified in the Campbell diagram. Forced response amplitudes were calculated using a modal approach and the results are compared to the widely used energy method. For the unsteady simulations, a time-based linearization of the unsteady Reynolds average Navier–Stokes equations were applied. If only the resonant mode was considered, the forced response amplitude from the modal approach was confirmed with the energy method. Thereby, forced response due to BLI showed higher vibration amplitudes than for blade row interaction. The impact of modes which are not in resonant to the total deformation were investigated by using the modal approach, which so far only considers one excitation order. A doubling of vibrational amplitude was shown in the case of blade row interaction for higher rotational speeds. The first and third modeshapes as well as modes with similar natural frequencies were identified as critical cases. The behavior in the vicinity of resonance shows high vibration amplitudes over a larger frequency range. This is also valid for high modes with many nodal diameters, which have a greater risk of critical strain.

Application of the Modal Approach for Prediction of Forced Response Amplitudes for Fan Blades

Forced response is the main reason for high cycle fatigue in turbomachinery. Not all resonance points in the operating range can be avoided especially for low order excitation. For highly flexible CFRP fans an accurate calculation of vibration amplitudes is required. Forced response analyses were performed for blade row interaction and boundary layer ingestion. The resonance points considered were identified in the Campbell diagram. Forced response amplitudes were calculated using a modal approach and results are compared to the widely used energy method. For the unsteady simulations a time-linearised URANS method was applied. If only the resonant mode was considered the forced response amplitude from the modal approach was confirmed with the energy method. Thereby forced response due to BLI showed higher vibration amplitudes than for blade row interaction. The impact of modes which are not in resonant to the total deformation were investigated by using the modal approach, which so far, only considers one excitation order. A doubling of vibrational amplitude was shown in the case of blade row interaction for higher rotational speeds. The first and third mode-shape as well as modes with similar natural frequencies were identified as critical cases. The behaviour in the vicinity of resonance shows high vibration amplitudes over a larger frequency range. This is also valid for high modes with many nodal diameters, which have a greater risk of critical strain.

Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System

This paper presents an efficient approach for stabilizing solution and accelerating convergence of a harmonic balance equation system for an efficient analysis of turbomachinery unsteady flows due to flutter and blade row interaction. The proposed approach combines the Runge–Kutta method with the lower upper symmetric Gauss Seidel (LU-SGS) method and the block Jacobi method. The LU-SGS method, different from its original application as an implicit time marching scheme, is used as an implicit residual smoother with under-relaxation, allowing big Courant–Friedrichs–Lewy (CFL) numbers (in the order of hundreds), leading to significant convergence speedup. The block Jacobi method is introduced to implicitly integrate the time spectral source term of a harmonic balance equation system, in order to reduce the complexity of the direct implicit time integration by the LU-SGS method. The implicit treatment of the time spectral source term thus greatly augments the stability region of a harmonic balance equation system in the case of grid-reduced frequency well above ten. Validation of the harmonic balance flow solver was carried out using linear cascade test data. Flutter analysis of a transonic rotor and blade row interaction analyses for a transonic compressor stage were presented to demonstrate the stabilization and acceleration effect by the combination of the LU-SGS and the block Jacobi methods. The influence of the number of Jacobi iterations on solution stabilization is also investigated, showing that two Jacobi iterations are sufficient for stability purpose, which is much more efficient than existing methods of its kind in the open literature.

Experimental and Numerical Verification of the Core-Flow in a New Low-Pressure Turbine

The flow field in modern axial turbines is non-trivial and highly unsteady due to secondary flow and blade row interaction. In recent years, existing design-tools like two-dimensional flow solvers as well as fully three-dimensional CFD methods have been validated for the assumption of a quasi-steady flow field. Since the inevitable unsteadiness of the flow field has a direct impact on unsteady loss generation and work transfer, existing design methods stand in need of validation for local unsteady effects within the flow field. In order to clearly separate end-wall losses from those generated by blade row interaction within the blade passage, a two-dimensional core-flow is essential for the investigation. Hence, a new 1.5-stage high aspect ratio low pressure turbine has been designed to determine the intensity of core-flow blade row interaction for different axial gaps. First, inlet and outlet conditions of the test rig are evaluated with regard to homogeneity of the flow parameters in their radial and circumferential distributions. Secondly, the measurement data gained from rig tests have been applied as boundary conditions to time-averaged numerical computations. The flow field analysis for two different axial gaps focuses on the verification of the core flow. The authors show that the new turbine has been successfully verified using both test data and the numerical predictions, serving as a precondition for the validation of the numerical model for unsteady effects within the core-flow.

On the Impact of Geometric Variability on Fan Aerodynamic Performance, Unsteady Blade Row Interaction, and Its Mechanical Characteristics

The focus of the present study is to assess and quantify the uncertainty in predicting the steady and unsteady aerodynamic performance as well as the major mechanical characteristics of a contrarotating turbofan, primarily due to geometric variations stemming from the manufacturing process. The basis of this study is the optically scanned blisk of the first rotor, for which geometric variations from blade to blade are considered. In a first step, selected profile sections of the first rotor were evaluated aerodynamically by applying the 2D coupled Euler/boundary-layer solver mises. Statistical properties of the relevant flow quantities were calculated firstly based on the results of the nine manufactured blades. In a second step, the geometric variations were decomposed into their corresponding eigenforms by means of principal component analysis (PCA). These modes were the basis for carrying out Monte Carlo (MC) simulations in order to analyze in detail the blade's aerodynamic response to the prescribed geometric variations. By means of 3D-computational fluid dynamics (CFD) simulations of the entire fan stage for all the nine scanned rotor 1 blade geometries, the variation of the overall stage performance parameters will be quantified. The impact of the instrumentation will be discussed, here partly doubling the standard deviation of the major performance indicators for the instrumented blades and also triggering a premature laminar/turbulent transition of the boundary layer. In terms of the unsteady blade row interaction, the standard deviation of the resulting blade pressure amplitude shall be discussed based on unsteady simulations, taking advantage of a novel harmonic balance approach. It will be shown that the major uncertainty in terms of the predicted blade pressure amplitude is in the aft part of the front rotor and results from upstream shock/blade interaction. Apart from the aerodynamic performance, an analysis of the mechanical properties in terms of Campbell characteristics and eigenfrequencies was carried out for each of the scanned blades of rotor 1, reflecting the frequency scattering of each eigenmode due to geometric variability.