Investigation and development of low-fidelity analytical models for forced response, flutter and distortion propagation analysis

Abstract

The study describes a methodology for the analysis and design of turbomachinery components at low-fidelity level. This methodology is part of a broad, object-oriented environment developed at the Rolls-Royce VUTC. The approach described in this thesis is applicable to any axial turbomachinery configuration, however, main emphasis is made on compressors. The purpose of the research is to provide the opportunity to perform forced response, flutter and other unsteady analysis without the need for the expensive CFD runs. This is particularly demanded in the early stages of the aero-engine design process or in any other cases when the detailed information of the engine is not yet available, however, a broad unsteady parametric analysis based on the existing information is needed. The model uses a linearized form of the mass, momentum and energy budgets to relate small changes in the state of the gas at several positions in the machine to known disturbances at inlet or outlet, or to known changes in the geometry. The chosen approach allows usage of an arbitrary gas model without the assumption of constant gas properties. It also provides a straightforward way to obtain a steady-state solution in a minimal amount of iterations and to evaluate the exact values of the characteristic slopes. The unsteady solution methodology represents an extended and improved Semi-Actuator Disc model. The major improvements are the real geometry application, ability to handle rotating bladerows, loss models implementation and the cascade impedance model. As the solver is linearized, the harmonic perturbations are assumed to have small amplitude compared to the steady-state data and relatively long wavelength, compared to the blade measurements. Thus contributions of several perturbation sources may be superimposed within the model. The model has a block-wise structure, where every block represents a blade or an empty duct. Non-reflecting boundary conditions are applied to the blocks boundary interfaces together with a thought-through method for the angular frequency scattering. This allows assembling a multi-bladerow domain with both rotating and stationary bladerows for the unsteady analysis. A great deal of effort has been made to connect the system to a modern and general representation of the engine geometry. This data is then used to set up the domain geometry with minimal assumptions, thus considering the changes in areas, radii and the slope of the annulus. The complex blade profile information is accessible at any moment during the computation, thus allowing using a chosen set of loss and deviation models. The model uses the same geometry database as used for the CFD and FE analysis, however, any geometry data may be overridden on demand. The model has been validated on a variety of data, from the previous publications, for forced response and flutter and from alternative solvers for distorted casings. The agreement between the calculated results and the reference data is very satisfactory, with nearly exact match for a series of idealized cases. The improvements introduced in this approach, such as cascade impedance model and the loss and deviation model package extend and complete several statements made in previous publications regarding the effect of total pressure loss and presence of the passage end reflections. The model is also validated against more complex reference cases, such as 3D CFD simulation of the LP turbine blade flutter, providing a good estimation of the damping curve slope in the low-ND region. Having a tip clearance loss model, the non-uniform casing simulations have been setup for evaluation of the relationship between the unsteady mass flow and pressure ratio perturbations. A thorough literature survey is made on the previous publications of the similar subject. The survey reviews a series of the modular systems for the axial turbomachinery analysis and then continues with the investigation of semi-empirical closures for the total pressure loss and outlet flow deviation modelling. The latter two play an essential role in this research as their implementation provides more realistic results, comparable to the heavy CFD runs. Greater part of the survey is devoted to the previous publications on various approaches for 1D and 2D unsteady turbomachinery modelling. The research completes with a thorough discussion of the features implemented and the results achieved, concluding with several future work proposals for the eventual further extension of the model as well as its applicability as a keystone for possible construction of a higher-fidelity solver. The primary programming object-oriented environment chosen for the model implementation is C++ with some parts written in FORTRAN.