Turbomachine internal pressure and blade response modelling

Abstract

Blades are critical components of turbomachines, failure of a single blade may result in catastrophic failure of the entire machine. One study found that blade failure was the third largest cause of power generation unit unavailability. Their condition during operation is therefore of interest to monitor. Various intrusive and non-intrusive blade vibration measurement (BVM) techniques have been developed for this purpose. Intrusive techniques such as strain gauge approaches and the frequency modulated grid method require expensive and complex alteration of the actual blades and/or casing. Further, they are prone to failure due to operation in harsh working environments. Therefore the use of intrusive techniques has been predominantly limited to design verification, testing and research. Blade tip timing approaches are currently at the forefront of BVM. The practicality, accuracy and ease of implementation of these approaches have limited their commercial roll out. An alternative nonintrusive source of blade vibration information was found in the internal casing pressure signal (CPS). As the machine operates the blade movement excites the fluid in the casing, producing a measureable response. Unlike BTT approaches which deal with a scarcity of information, CPS based methods must identify blade vibration from a complex signal which contains multiple other sources of information. The issue of how to model the blades response and fluid interaction is the topic of this investigation. An available single stage turbomachine mock setup was modified for internal pressure and direct blade vibration measurements. Pressure measurements were taken in line with a redesigned hub and rotor blade assembly. Strain gauges (SG) were applied to blades in order to capture their response. The blades response was modelled as the combination of a forcing function and a multiple degree of freedom transfer function. Repurposed experimental modal analysis frequency response reconstruction techniques were used to model the blades transfer function. It was found that this technique was able to capture the blades underlying behaviour to a high degree. The forcing function was modelled in the time domain as a series of Gaussian shaped force distributions. It was found that the model was able to capture many important aspects of the forcing behaviour. Both the forcing function and blade transfer function were explored using constrained optimisation techniques. The blade-fluid interaction was modelled as a Fourier series. It was shown that the blade behaviour cannot be extracted from a pressure signal using standard frequency analysis techniques. The viability of an inverse problem solution methodology, for the purpose of blade behaviour extraction, was investigated. This was achieved by solving reduced components of the model with SG measurements and observations from pressure measurements. Further the need to isolate the pressure field about individual blades was motivated and a novel time domain windowing technique provided.