Instabilities associated with fluid handling and operation in liquid rocket propulsion systems and test facilities usually manifest themselves as structural vibrations or some form of structural damage. While the source of the instability is directly related to the performance of a component such as a turbopump, valve or a flow control element, the associated pressure fluctuations as they propagate through the system have the potential to amplify and resonate with natural modes of the structural elements and components of the system. In this paper, the authors have developed an innovative multi-level approach that involves analysis at the component and systems level. The primary source of the unsteadiness is modeled with a high-fidelity hybrid RANS/LES based CFD methodology that has been previously used to study instabilities in feed systems. This high fidelity approach is used to quantify the instability and understand the physics associated with the instability. System response to the driving instability is determined through a transfer matrix approach wherein the incoming and outgoing pressure and velocity fluctuations are related through a transfer (or transmission) matrix. The coefficients of the transfer matrix for each component (i.e. valve, pipe, orifice etc.) are individually derived from the flow physics associated with the component. A demonstration case representing a test loop/test facility comprised of a network of elements is constructed with the transfer matrix approach and the amplification of modes analyzed as the instability propagates through the test loop.
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