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A method for numerically simulating the hydroelastic behaviour of a passive compliant wall of finite dimensions is presented. Using unsteady potential flow, the perturbation pressures which arise from wall disturbances of arbitrary form are calculated through a specially developed boundary-element method. These pressures may then be coupled to a suitable solution procedure for the wall mechanics to produce an interactive model for the wall/flow system. The method is used to study the two-dimensional disturbances which may occur on a Kramer-type compliant wall of finite length. Finite-difference methods are used to yield wall solutions driven by the fluid pressure after some perturbation from the equilibrium position. Thus, histories of surface deflection and wall energy are obtained. Such a modelling of the physics of the system requires no presupposition of disturbance form.A thorough investigation of divergence instability is carried out. Most of the results presented in this paper concern the response of the compliant wall while (and after) a point pressure pulse, carried in the applied flow, travels over the compliant panel. Above a critical flow speed and once sufficient time has passed, the compliant wall is shown to adopt the particular profile of an unstable mode. After this divergence mode has been established, instability is realized as a slowly travelling downstream wave. These features are in agreement with the findings of experimental studies. The role of wall damping is clarified: damping serves only to reduce the growth rate of the instability, leaving its onset flow speed unchanged. The present predictions provide an improvement upon some of the unrealistic aspects of predictions yielded by travelling-wave and standing-wave treatments of divergence instability.The response of a long compliant panel after a single-point pressure-pulse initiation, applied at its midpoint, is simulated. At flow speeds higher than a critical value, parts of the formerly (at subcritical flow speeds) upstream-travelling wave system change to travel downstream and show amplitude growth. The development of this ‘upstream-incoming’ wave illustrates how divergence instability can occur at locations upstream of the point of initial excitation. Faster flexural waves transmit energy upstream, thereafter these disturbances can evolve into slow downstreamtravelling divergence waves. The spread of the instability to locations both downstream and upstream of the point of initial excitation indicates that divergence is an absolute instability. This behaviour and the effects of wall damping clarified by the present work strongly suggest that divergence is a Class C instability.

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Our aim in this paper is to use a simple theoretical model of the intraspinal cerebrospinal-fluid system to investigate mechanisms proposed for the pathogenesis of syringomyelia. The model is based on an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. According to this model, the leading edge of a pressure pulse tends to steepen and form an elastic jump, as it propagates up the intraspinal cerebrospinal-fluid system. We show that when an elastic jump is incident on a stenosis of the spinal subarachnoid space, it reflects to form a transient, localized region of high pressure within the spinal cord that for a cough-induced pulse is estimated to be 50 to 70 mm Hg or more above the normal level in the spinal subarachnoid space. We propose this as a new mechanism whereby pressure pulses created by coughing or sneezing can generate syrinxes. We also use the same analysis to investigate Williams' suck mechanism. Our results do not support his concept, nor, in cases where the stenosis is severe, the differential-pressure-propagation mechanism recently proposed by Greitz et al. Our analysis does provide some support for the piston mechanism recently proposed by Oldfield et al. and Heiss et al. For instance, it shows clearly how the spinal cord is compressed by the formation of elastic jumps over part of the cardiac cycle. What appears to be absent for this piston mechanism is any means whereby the elastic jumps can be focused (e.g., by reflecting from a stenosis) to form a transient, localized region of high pressure within the spinal cord. Thus it would seem to offer a mechanism for syrinx progression, but not for its formation.

Theoretical studies have shown that compliant walls are able to attenuate the Tollmien–Schlichting waves that lead to conventional two-dimensional boundary-layer transition. This phenomenon was demonstrated in towing-tank tests conducted by Gaster et al. The results of these experiments also featured a different and very dramatic form of boundary-layer breakdown. We contend that this type of breakdown was due to a hydroelastic mode of instability, namely traveling-wave flutter. In this paper we model the two-layer viscoelastic compliant wall of Gaster et al. and its interaction with the boundary-layer flow using the asymptotic theory of Carpenter and Gajjar; en-type calculations are carried out for the traveling-wave flutter. Excellent agreement is found between the stability characteristics of the TWF mode and the measurements of the new form of breakdown found in the experiments; thus a complete understanding of the physical features found in the experiments is now available. Such understanding is essential for progress to be made in the technological development of compliant panels for transition delay.

The most collapsible part of the upper airway in the majority of individuals is the velopharynx which is the segment positioned behind the soft palate. As such it is an important morphological region for consideration in elucidating the pathogenesis of obstructive sleep apnea (OSA). This study compared steady flow properties during inspiration in the pharynges of 9 male subjects with OSA and 9 body-mass index (BMI)-and age-matched control male subjects without OSA. The k-ω SST turbulence model was used to simulate the flow field in subject-specific pharyngeal geometric models reconstructed from anatomical optical coherence tomography (aOCT) data. While analysis of the geometry of reconstructed pharynges revealed narrowing at velopharyngeal level in subjects with OSA, it was not possible to clearly distinguish them from subjects without OSA on the basis of pharyngeal size and shape alone. By contrast, flow simulations demonstrated that pressure fields within the narrowed airway segments were sensitive to small differences in geometry and could lead to significantly different intraluminal pressure characteristics between subjects. The ratio between velopharyngeal and total pharyngeal pressure drops emerged as a relevant flow-based criterion by which subjects with OSA could be differentiated from those without.

A new method for directly determining the eigenmodes of finite flow-structure systems is presented using the classical problem of the interaction of a uniform incompressible flow with a flexible panel, held at both ends, as an exemplar. The method is a hybrid of theoretical analysis and computational modelling. This method is contrasted with Galerkin and travelling-wave methods, which are most often used to study the hydroelasticity of such systems. The new method does not require an a priori approximation of perturbations via a finite sum of modes. Instead, the coupled equations for the wall-flow system are used to derive a single matrix equation for the system that is a second-order differential equation for the panel-displacement variable. This is achieved in this exemplar by applying a combination of boundary-element and finite-element methods to the discretized system. Standard statespace methods are then used to extract the eigenmodes of the system directly. We present the results for the stability of the case of an unsupported flexible plate, elucidating its divergence and flutter characteristics, and the effect of energy dissipation in the structure. We then present the results for the case of a spring-backed flexible plate, showing that its motion is dominated by travelling waves. Finally, we illustrate the versatility of the approach by extracting the stability diagrams and modes for a panel with spatially varying properties and a panel with non-standard boundary conditions. In doing so, we show how spatial inhomogeneity can modify the energy exchanges between flow and structure, thereby introducing a single-mode flutter instability at pre-divergence flow speeds.