Techniques to Assess Acoustic-Structure Interaction in Liquid Rocket Engines

Abstract

Acoustoelasticity is the study of the dynamic interaction between elastic structures and acoustic enclosures. In this dissertation, acoustoelasticity is considered in the context of liquid rocket engine design. The techniques presented here can be used to determine which forcing frequencies are important in acoustoelastic systems. With a knowledge of these frequencies, an analyst can either find ways to attenuate the excitation at these frequencies or alter the system in such a way that the prescribed excitations do result in a resonant condition. The end result is a structural component that is less susceptible to failure.

The research scope is divided into three parts. In the first part, the dynamics of cylindrical shells submerged in liquid hydrogen (LH₂) and liquid oxygen (LOX) are considered. The shells are bounded by rigid outer cylinders. This configuration gives rise to two fluid-filled cavities: an inner cylindrical cavity and an outer annular cavity. Such geometries are common in rocket engine design. The natural frequencies and modes of the fluid-structure system are computed by combining the rigid wall acoustic cavity modes and the <em>in vacuo</em> structural modes into a system of coupled ordinary differential equations. Eigenvalue veering is observed near the intersections of the curves representing natural frequencies of the rigid wall acoustic and the <em>in vacuo</em> structural modes. In the case of a shell submerged in LH₂, system frequencies near these intersections are as much as 30% lower than the corresponding <em>in vacuo</em> structural frequencies. Due to its high density, the frequency reductions in the presence of LOX are even more dramatic. The forced responses of a shell submerged in LH₂ and LOX while subject to a harmonic point excitation are also presented. The responses in the presence of fluid are found to be quite distinct from those of the structure <em>in vacuo</em>.

In the second part, coupled mode theory is used to explore the fundamental features of acoustoelastic systems. The result is the development of relatively simple techniques that allow analysts to make informed decisions concerning the importance of acoustic-structure coupling without resorting to more time consuming and complex methods. In this part, a new nondimensional parameter is derived to quantify the fundamental strength of a particular acoustic-structure interaction irrespective of material and fluid properties or cavity size. It is be shown that, in some cases, reasonable approximations of the coupled acoustic-structure frequencies can be calculated without explicit knowledge of the uncoupled component mode shapes. Monte Carlo simulations are performed to determine the parameter values over which the approximate coupled frequency expressions are accurate. General observations concerning the forced response of acoustoelastic systems are then made by investigating the response of a simplified two mode system.

The third part of this research discusses the implementation of a component mode synthesis (CMS) technique for use with geometrically complex acoustoelastic systems. The feasibility of conceptually similar techniques was first demonstrated over 30 years ago. Since that time there have been remarkable advancements in computational methods. It is therefore reasonable to question the extent to which CMS remains a computationally advantageous approach for acoustoelastic systems of practical interest. This work demonstrates that relative to the most recent release of the popular finite element software package, ANSYS, CMS techniques have a significant computational advantage when the forced response of an acoustoelastic system is of interest. However, recent improvements to the unsymmetric eigensolver available in ANSYS have rendered CMS a less efficient option when calculating system frequencies and modes. The CMS technique is then used to generate new results related to geometrically complex acoustoelastic systems.