Stability of a flexible insert in one wall of an inviscid channel flow

Burke, Meagan A.; Lucey, Anthony D.; Howell, Richard; Elliott, N. S. J.

doi:10.1016/j.jfluidstructs.2014.03.012

Cited by 13 publications

(5 citation statements)

References 33 publications

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“…We remark that for their figure 7, Davies & Carpenter (1997a) used a tensioned membrane instead of a spring-backed plate and this resulted in a very flexible channel that is more prone to wall-based instabilities. For the spring-backed flexible plate used in our system, an equivalent critical Reynolds number predicted for the onset of two-dimensional divergence instability for steady inviscid fluid flow in a compliant channel (Burke et al 2014) is Re D ≈ 1.25 × 10 4 , having chosen blood for the fluid and characteristic dimension typical of a small blood vessel. This value falls within the range of Reynolds numbers in figure 15(a).…”

Section: Three-dimensional Disturbances In Pulsatile Plane Poiseuillementioning

confidence: 99%

Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel

Tsigklifis

Lucey

2017

J. Fluid Mech.

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The time-asymptotic linear stability of pulsatile flow in a channel with compliant walls is studied together with the evaluation of modal transient growth within the pulsation period of the basic flow as well as non-modal transient growth. Both one (vertical-displacement) and two (vertical and axial) degrees-of-freedom compliant-wall models are implemented. Two approaches are developed to study the dynamics of the coupled fluid–structure system, the first being a Floquet analysis in which disturbances are decomposed into a product of exponential growth and a sum of harmonics, while the second is a time-stepping technique for the evolution of the fundamental solution (monodromy) matrix. A parametric study of stability in the non-dimensional parameter space, principally defined by Reynolds number ($Re$), Womersley number ($Wo$) and amplitude of the applied pressure modulation ($\unicode[STIX]{x1D6EC}$), is then conducted for compliant walls of fixed geometric and material properties. The flow through a rigid channel is shown to be destabilized by pulsation for low $Wo$, stabilized due to Stokes-layer effects at intermediate $Wo$, while the critical $Re$ approaches the steady Poiseuille-flow result at high $Wo$, and that these effects are made more pronounced by increasing $\unicode[STIX]{x1D6EC}$. Wall flexibility is shown to be stabilizing throughout the $Wo$ range but, for the relatively stiff wall used, is more effective at high $Wo$. Axial displacements are shown to have negligible effect on the results based upon only vertical deformation of the compliant wall. The effect of structural damping in the compliant-wall dynamics is destabilizing, thereby suggesting that the dominant inflectional (Rayleigh) instability is of the Class A (negative-energy) type. It is shown that very high levels of modal transient growth can occur at low $Wo$, and this mechanism could therefore be more important than asymptotic amplification in causing transition to turbulent flow for two-dimensional disturbances. Wall flexibility is shown to ameliorate mildly this phenomenon. As $Wo$ is increased, modal transient growth becomes progressively less important and the non-modal mechanism can cause similar levels of transient growth. We also show that oblique waves having non-zero transverse wavenumbers are stable to higher values of critical $Re$ than their two-dimensional counterparts. Finally, we identify an additional instability branch at high $Re$ that corresponds to wall-based travelling-wave flutter. We show that this is stabilized by the inclusion of structural damping, thereby confirming that it is of the Class B (positive-energy) instability type.

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Section: Three-dimensional Disturbances In Pulsatile Plane Poiseuillementioning

confidence: 99%

Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel

Tsigklifis

Lucey

2017

J. Fluid Mech.

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“…Theoretical work has gradually increased the complexity of the models under consideration, starting with a two-dimensional analogue of the Starling resistor. Both linear stability [21][22][23][24][25][26][27][28][29][30] and direct numerical simulation [31][32][33][34][35][36] have been considered. In a similar way to the lumped parameter models, the two-dimensional models produce interesting phenomenology, but cannot be used quantitatively.…”

Section: Because Variations In Fluid Densitymentioning

confidence: 99%

An experimental investigation to model wheezing in lungs

2021

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A quarter of the world's population experience wheezing. These sounds have been used for diagnosis since the time of the Ebers Papyrus ( ca 1500 BC). We know that wheezing is a result of the oscillations of the airways that make up the lung. However, the physical mechanisms for the onset of wheezing remain poorly understood, and we do not have a quantitative model to predict when wheezing occurs. We address these issues in this paper. We model the airways of the lungs by a modified Starling resistor in which airflow is driven through thin, stretched elastic tubes. By completing systematic experiments, we find a generalized ‘tube law’ that describes how the cross-sectional area of the tubes change in response to the transmural pressure difference across them. We find the necessary conditions for the onset of oscillations that represent wheezing and propose a flutter-like instability model for it about a heavily deformed state of the tube. Our findings allow for a predictive tool for wheezing in lungs, which could lead to better diagnosis and treatment of lung diseases.

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“…Conversely, SD is a class A instability, observed in the experiments of Gad-El-Hak, Blackwelder & Riley (1984), taking the form of a stationary or very slowly propagating mode (Carpenter & Garrad 1986); the mechanism of instability is not clearly understood, but non-zero wall damping is essential for destabilisation in an infinitely long system (Carpenter & Garrad 1986), although the story is more complicated when the compliant panel is of finite length (Lucey & Carpenter 1992, 1993; Peake 2004; Burke et al. 2014). In this study we consider the limit of large wall damping to elucidate the mechanism of SD in a long compliant channel.…”

Section: Introductionmentioning

confidence: 99%

“…TWF is a class B instability, observed in the experiments of Gaster (1988), which takes the form of a travelling wave propagating with wavespeed close to that of the unloaded elastic wall (Carpenter & Garrad 1986); the mechanism of instability is similar to that of wind generating water waves, sustained by viscous effects within narrow viscous layers across the flow (Benjamin 1959;Carpenter & Gajjar 1990). Conversely, SD is a class A instability, observed in the experiments of Gad-El-Hak, Blackwelder & Riley (1984), taking the form of a stationary or very slowly propagating mode (Carpenter & Garrad 1986); the mechanism of instability is not clearly understood, but non-zero wall damping is essential for destabilisation in an infinitely long system (Carpenter & Garrad 1986), although the story is more complicated when the compliant panel is of finite length (Lucey & Carpenter 1992Peake 2004;Burke et al 2014). In this study we consider the limit of large wall damping to elucidate the mechanism of SD in a long compliant channel.…”

Section: Introductionmentioning

confidence: 99%

Flow-induced surface instabilities in a flexible-walled channel with a heavy wall

2023

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We consider the stability of laminar high-Reynolds-number flow through a planar channel formed by a rigid wall and a heavy compliant wall under longitudinal tension with motion resisted by structural damping. Numerical simulations indicate that the baseline state (with Poiseuille flow and a flat wall) exhibits two unstable normal modes: the Tollmien–Schlichting (TS) mode and a surface-based mode which manifests as one of two flow-induced surface instabilities (FISI), known as travelling wave flutter (TWF) and static divergence (SD), respectively. In the absence of wall damping the system is unstable to TWF, where the neutrally stable wavelength becomes shorter as the wall mass increases. With wall damping, TWF is restricted to long wavelengths through interaction with the most unstable centre mode, while for wall damping greater than a critical value the system exhibits an SD mode with a two branch neutral stability curve; the critical conditions along the upper and lower branches are constructed in the limit of large wall damping. We compute the Reynolds–Orr and activation energy descriptions of these neutrally stable FISI by continuing the linear stability analysis to the following order in perturbation amplitude. We find that both FISI are primarily driven by the working of normal stress on the flexible wall, lower-branch SD has negative activation energy, while upper-branch SD approaches zero activation energy in the limit of large wall damping. Finally, we elucidate interaction between TS and TWF modes for large wall mass, resulting in stable islands within unstable regions of parameter space.

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Stability of a flexible insert in one wall of an inviscid channel flow

Cited by 13 publications

References 33 publications

Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel

Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel

An experimental investigation to model wheezing in lungs

Flow-induced surface instabilities in a flexible-walled channel with a heavy wall

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