Anthony Lucey

A numerical simulation of the interaction of a compliant wall and inviscid flow

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.

Boundary layer instability over compliant walls: Comparison between theory and experiment

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 essen...

Progress on the Use of Compliant Walls for Laminar-Flow Control

Thispaperreviewsand assessestherecentprogresstoward making theuseofcompliantwallsa practicalmethod of laminar-e ow control. Three main areas are covered. First, the current understanding of the vitally important e ow-induced surface instabilities is assessed. Some new results are included. Then the optimization of multiplepanel compliant walls is considered. New numerical simulation results are included showing that short compliant panels are very effective in suppressing Tollmien ‐Schlichting waves. It is found that for marine applications appropriately designed multiple-panel compliant walls are capable of suppressing Tollmien ‐Schlichting waves to indee nitely high Reynolds numbers. Finally, the feasibility of using compliant walls for laminar-e ow control in aeronautical applications is assessed. It is found that, although there is no reason in principle why compliant walls cannot be used in air, in practice exceptionally delicate walls are required to obtain the necessary match between thee uid and structural inertias. Theresulting lack ofrobustness forsuch walls isdeemed to make them completely impractical for aeronautical applications.

Optimization of Viscoelastic Compliant Walls for Transition Delay

The potential of wall compliance for delaying boundary-layer transition through the attenuation of TollmienSchlichting waves (TSW) has been recognized in many previous theoretical studies. The present paper seeks to determine the best transition-delaying performance possible using compliant walls made from viscoelastic materials for marine applications. The wall may take the form of either a homogeneous slab of material or a thin, stiff upper layer resting on a thick, soft substrate, the latter type holding the most promise in the practical use of compliant walls. To determine the growth rates of the TSW, a highly efficient means of solving the coupled Orr-Sommerfeld/compliant-wall eigenproblem is presented. Using spectral methods, the eigenproblem is cast in a matrix form which can then be solved using an SIMD parallel computer. What prevents the use of very soft compliant walls to suppress TSW completely is the existence of hydroelastic instabilities in the wall/flow system, namely traveling-wave flutter (TWF) and divergence. Efficient methods are also presented for the evaluation of these wall-based instabilities. A thorough investigation of the effects of the wall configuration and its material properties is carried out. Both single- and double-layer walls are optimized over the full range of wall parameters. It is shown that the best performance of single- and double-layer viscoelastic walls, respectively yield 2.5- and 5-fold delays of transition when compared with a rigid wall. These factors have been achieved using the conservative value of n = 1 in the en calculations.

The excitation of waves on a flexible panel in a uniform flow

The wave–bearing behaviour of a finite flexible plate in a uniform flow is studied when a source of continuous oscillatory excitation is present. The method of numerical simulation is employed so that any prescription of response is avoided. A series of numerical experiments is carried out and analysed using methods similar to those applicable to a physical experiment. It is found that the plate can respond at frequencies other than that of the driver; these frequencies may either be present in the start–up procedure or be generated by wave conversions at the panel edges. At early times in the response evolution, two types of behaviour are evident. These may be separately characterized as response to low–frequency excitation and response to high–frequency excitation. The former is dominated by spatially growing waves and the latter by absolute stability. The long–time behaviour of the flexible panel shows disturbance amplitude growth at all locations for flow speeds that approach zero in the limit of an infinitely long flexible plate. For parameters corresponding to a realistic flexible panel, the long–time growth of the deformation is found to be attributable to a combination of low–frequency unstable waves which are capable of convecting wall energy and thus disturbance growth to all parts of the flexible panel; the mechanism for this features repeated wave conversions at the panel ends. This convective mechanism predominates despite the presence of an absolute instability found in the system studied here. In the later stages of the flexible–panel response, the line excitation is largely insignificant. An attempt is made to reconcile the observations of the present numerical experiments with the predictions of hydroelastic boundary–value studies of an infinitely long flexible plate and the rigorous structural–acoustics approach to the problem in which causality is a key element.

Measurement, Reconstruction, and Flow-Field Computation of the Human Pharynx With Application to Sleep Apnea

Repetitive closure of the upper airway characterizes obstructive sleep apnea. It disrupts sleep causing excessive daytime drowsiness and is linked to hypertension and cardiovascular disease. Previous studies simulating the underlying fluid mechanics are based upon geometries, time-averaged over the respiratory cycle, obtained usually via MRI or CT scans. Here, we generate an anatomically correct geometry from data captured in vivo by an endoscopic optical technique. This allows quantitative real-time imaging of the internal cross section with minimal invasiveness. The steady inhalation flow field is computed using a k- shear-stress transport (SST) turbulence model. Simulations reveal flow mechanisms that produce low-pressure regions on the sidewalls of the pharynx and on the soft palate within the pharyngeal section of minimum area. Soft-palate displacement and side-wall deformations further reduce the pressures in these regions, thus creating forces that would tend to narrow the airway. These phenomena suggest a mechanism for airway closure in the lateral direction as clinically observed. Correlations between pressure and airway deformation indicate that quantitative prediction of the low-pressure regions for an individual are possible. The present predictions warrant and can guide clinical investigation to confirm the phenomenology and its quantification, while the overall approach represents an advancement toward patient-specific modeling.

Effect of the velopharynx on intraluminal pressures in reconstructed pharynges derived from individuals with and without sleep apnea

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 nine male subjects with OSA and nine body-mass index (BMI)- and age-matched control male subjects without OSA. The k-ωSST 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.

On the direct determination of the eigenmodes of finite flow-structure systems

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 state-space 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.

Wave Excitation on Flexible Walls in The Presence of a Fluid Flow

Theoretical and computational investigations of wave excitation and evolution in fully-coupled flow-structure systems are discussed. A distinguishing feature of the body of work reviewed is its attempt to shed light on how and where waves come into being in response to some form of applied excitation. Identifying the properties of such waves and their contributions to the overall system behaviour is also a key objective of the studies reviewed. The model problem of waves initiated by line excitation applied to an elastic plate adjacent to a uniform flow (Brazier-Smith & Scott 1984 and Crighton & Oswell 1991) is first described. Thereafter, work that incorporates enhancements to the structural, geometric and fluid-flow models is presented. The results of these studies are related to the findings of the progenitor model problem in order to assess its general applicability in this branch of fluid-structure interaction.

Numerical simulation of pharyngeal airflow applied to obstructive sleep apnea: effect of the nasal cavity in anatomically accurate airway models

Repetitive brief episodes of soft-tissue collapse within the upper airway during sleep characterize obstructive sleep apnea (OSA), an extremely common and disabling disorder. Failure to maintain the patency of the upper airway is caused by the combination of sleep-related loss of compensatory dilator muscle activity and aerodynamic forces promoting closure. The prediction of soft-tissue movement in patient-specific airway 3D mechanical models is emerging as a useful contribution to clinical understanding and decision making. Such modeling requires reliable estimations of the pharyngeal wall pressure forces. While nasal obstruction has been recognized as a risk factor for OSA, the need to include the nasal cavity in upper-airway models for OSA studies requires consideration, as it is most often omitted because of its complex shape. A quantitative analysis of the flow conditions generated by the nasal cavity and the sinuses during inspiration upstream of the pharynx is presented. Results show that adequate velocity boundary conditions and simple artificial extensions of the flow domain can reproduce the essential effects of the nasal cavity on the pharyngeal flow field. Therefore, the overall complexity and computational cost of accurate flow predictions can be reduced.