Measurement of Wall Deformation and Flow Limitation In a Mechanical Trachea

1995 ◽  
Vol 117 (1) ◽  
pp. 146-152 ◽  
Author(s):  
C. Walsh ◽  
P. A. Sullivan ◽  
J. S. Hansen ◽  
L.-W. Chen
Keyword(s):  
Mechanical Model ◽  
Wave Speed ◽  
Nonlinear Material ◽  
Collapsible Tube ◽  
Wall Model ◽  
Rigid Tube ◽  
Long Wave ◽  
Wall Deformation ◽  
Human Trachea ◽  
Material Constitutive Equation

A mechanical model of the human trachea is investigated experimentally. A modified version of an earlier model, it consists of a square sectioned rigid tube in which part of one wall is removed, and replaced by a prestretched flat latex membrane. Air is drawn from atmosphere through an inlet into the rigid upstream tube; it then flows through the flexible section and finally through a rigid section Into a plenum chamber where suction is applied. As the membrane collapses in response to flow, the transmural pressure and deflection are measured at the mid-point. These values are used in conjunction with a finite deformation membrane wall theory to determine the elastic constant in a nonlinear material constitutive equation. This equation is used to predict the tube law. Results show that the flow limits at the long wave speed predicted by this law. Thus it behaves as a conventional collapsible tube while having the advantage of a rational wall model.

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

scholarly journals Dynamics of liquid films on vertical fibres in a radial electric field

2014 ◽  
Vol 752 ◽  
pp. 66-89 ◽  
Author(s):  
Zijing Ding ◽  
Jinlong Xie ◽  
Teck Neng Wong ◽  
Rong Liu
Keyword(s):  
Electric Field ◽  
Wave Speed ◽  
Nonlinear Evolution ◽  
Radial Electric Field ◽  
Liquid Films ◽  
Asymptotic Model ◽  
Nonlinear Behaviour ◽  
Wave Instability ◽  
Long Wave ◽  
Evolution Study

AbstractThe long-wave behaviour of perfectly conducting liquid films flowing down a vertical fibre in a radial electric field was investigated by an asymptotic model. The validity of the asymptotic model was verified by the fully linearized problem, which showed that results were in good agreement in the long-wave region. The linear stability analysis indicated that, when the ratio (the radius of the outer cylindrical electrode over the radius of the liquid film) $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\beta <e$, the electric field enhanced the long-wave instability; when $\beta >e$, the electric field impeded the long-wave instability; when $\beta =e$, the electric field did not affect the long-wave instability. The nonlinear evolution study of the asymptotic model compared well with the linear theory when $\beta <e$. However, when $\beta =e$, the nonlinear evolution study showed that the electric field enhanced the instability which may cause the interface to become singular. When $\beta >e$, the nonlinear evolution studies showed that the influence of the electric field on the nonlinear behaviour of the interface was complex. The electric field either enhanced or impeded the interfacial instability. In addition, an interesting phenomenon was observed by the nonlinear evolution study that the electric field may cause an oscillation in the amplitude of permanent waves when $\beta \ge e$. Further study on steady travelling waves was conducted to reveal the influence of electric field on the wave speed. Results showed that the electric field either increased or decreased the wave speed as well as the wave amplitude and flow rate. In some situations, the wave speed may increase/decrease while its amplitude decreased/increased as the strength of the external electric field increased.

On the theory of solitary Rossby waves

1977 ◽  
Vol 82 (4) ◽  
pp. 725-745 ◽  
Author(s):  
L. G. Redekopp
Keyword(s):  
Wave Speed ◽  
Rossby Waves ◽  
Vries Equation ◽  
Finite Amplitude ◽  
Long Wave ◽  
Atmospheric Stratification ◽  
De Vries ◽  
Eddy Structures ◽  
Layer Region ◽  
Wave Limit

The evolution of long, finite amplitude Rossby waves in a horizontally sheared zonal current is studied. The wave evolution is described by the Korteweg–de Vries equation or the modified Korteweg-de Vries equation depending on the atmospheric stratification. In either case, the cross-stream modal structure of these waves is given by the long-wave limit of the neutral eigensolutions of the barotropic stability equation. Both non-singular and singular eigensolutions are considered and the appropriate analysis is developed to yield a uniformly valid description of the motion in the critical-layer region where the wave speed matches the flow velocity. The analysis demonstrates that coherent, propagating, eddy structures can exist in stable shear flows and that these eddies have peculiar interaction properties quite distinct from the traditional views of turbulent motion.

scholarly journals The stability of continental shelf waves I. Side band instability and long wave resonance

1977 ◽  
Vol 20 (1) ◽  
pp. 13-30 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Continental Shelf ◽  
Stability Criterion ◽  
Wave Speed ◽  
Side Band ◽  
Long Wave ◽  
Wave Resonance ◽  
Shelf Wave ◽  
Shelf Waves ◽  
The Stability ◽  
Continental Shelf Waves

AbstractContinental shelf waves are examined for side band instability. It is shown that a modulated shelf wave is described by a nonlinear Schrödinger equation, from which the stability criterion is derived. Long shelf waves are stable to side band modulations, but as the wavenumber is increased there are regions of instability (in wavenumber space). A change of stability occurs at each long wave resonance, defined by the condition that the group velocity of the shelf wave equals a long wave speed. Equations describing the long wave resonance are derived.

Flow Regulation Characteristics of Thin-Walled Compliant Tubes: Part I—Theoretical Analysis

1990 ◽  
Vol 112 (3) ◽  
pp. 319-329
Author(s):  
Ifiyenia Kececioglu
Keyword(s):  
Reynolds Number ◽  
Wave Speed ◽  
Active Element ◽  
Flow Regulation ◽  
Collapsible Tube ◽  
Speed Flow ◽  
Thin Walled ◽  
Flow Regulator ◽  
High Reynolds ◽  
Set Up

The objective of this investigation is the study of the flow limitation behavior of thin-walled compliant tubes for the design of a flow regulator employing a collapsible tube as its active element. In this paper, the theoretical basis is set up for the high-Reynolds-number wave-speed flow regulation and the low-Reynolds-number frictional flow regulation behaviors of thin-walled compliant tubes. In Part II of this paper [1], experimental results and design criteria are provided in support of the analytically derived characteristic flow regulation curve for the wave-speed flow regulator.

scholarly journals Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Weiguo Zhang ◽  
Xu Chen ◽  
Zhengming Li ◽  
Haiyan Zhang
Keyword(s):  
Explicit Expression ◽  
Solitary Waves ◽  
Wave Speed ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Orbital Stability ◽  
Long Wave ◽  
Stability And Instability ◽  
Stability Of Solitary Waves

This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. SinceJis not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discriminationd′′(c)and give several sufficient conditions which can be used to judge the orbital stability and instability for the two solitary waves. Furthermore, we analyze the influence of the interaction between two nonlinear terms of the equations on the wave speed interval which makes the solitary waves stable.

FSI Analysis of a Healthy and a Stenotic Human Trachea Under Impedance-Based Boundary Conditions

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
M. Malvè ◽  
A. Pérez del Palomar ◽  
S. Chandra ◽  
J. L. López-Villalobos ◽  
A. Mena ◽  
...  
Keyword(s):  
Solid Material ◽  
Flow Patterns ◽  
Bronchial Tree ◽  
Tracheal Wall ◽  
Computed Tomography Images ◽  
Wall Deformation ◽  
Human Trachea ◽  
Fluid Solid Interaction ◽  
Fractal Network

In this work, a fluid-solid interaction (FSI) analysis of a healthy and a stenotic human trachea was studied to evaluate flow patterns, wall stresses, and deformations under physiological and pathological conditions. The two analyzed tracheal geometries, which include the first bifurcation after the carina, were obtained from computed tomography images of healthy and diseased patients, respectively. A finite element-based commercial software code was used to perform the simulations. The tracheal wall was modeled as a fiber reinforced hyperelastic solid material in which the anisotropy due to the orientation of the fibers was introduced. Impedance-based pressure waveforms were computed using a method developed for the cardiovascular system, where the resistance of the respiratory system was calculated taking into account the entire bronchial tree, modeled as binary fractal network. Intratracheal flow patterns and tracheal wall deformation were analyzed under different scenarios. The simulations show the possibility of predicting, with FSI computations, flow and wall behavior for healthy and pathological tracheas. The computational modeling procedure presented herein can be a useful tool capable of evaluating quantities that cannot be assessed in vivo, such as wall stresses, pressure drop, and flow patterns, and to derive parameters that could help clinical decisions and improve surgical outcomes.

Tube Collapse and Valve Closure in Ambulatory Venous Pressure Regulation: Studies with a Mechanical Model

1998 ◽  
Vol 5 (1) ◽  
pp. 42-51 ◽  
Author(s):  
Seshadri Raju ◽  
Austin B. Green ◽  
Ruth K. Fredericks ◽  
Peter N. Neglen ◽  
C. Alexander Hudson ◽  
...  
Keyword(s):  
Mechanical Model ◽  
Regulatory Mechanism ◽  
Venous Pressure ◽  
Valve Closure ◽  
Pressure Regulation ◽  
Collapsible Tube ◽  
Adjustable Valve ◽  
Wide Range ◽  
Wall Property ◽  
Property Changes

Purpose: To determine the role of valve closure and column segmentation in ambulatory venous pressure regulation. Methods: Using a mechanical model consisting of a graduated adjustable valve and a collapsible tube, we studied the differential effects of valve closure and tube collapse on venous pressure regulation. By utilizing materials with differing wall properties for the infravalvular tube, the influence of wall property changes on tube function and pressure regulation was explored. Results: Valve closure, per se, does not cause venous pressure reduction. Collapse of the tube below the valve is the primary pressure regulatory mechanism. The nonlinear volume-pressure relationship that exists in infravalvular tubes confers significant buffering properties to the collapsible tube, which tends to retain a near-constant pressure for a wide range of ejection fractions, residual tube volumes, and valve leaks. Changes in tube wall property affect this buffering action, at both the low and high ends of the physiological venous pressure range. Conclusions: The valve and the infravalvular venous segment should be considered together in venous pressure regulation. Tube collapse of the segment below the valve is the primary pressure regulatory mechanism. An understanding of the hydrodynamic principles involved in pressure regulation derived from this model will provide the basis for construction of more complex models to explore clinical physiology and dysfunction.

scholarly journals Orographically generated nonlinear waves in rotating and non-rotating two-layer flow

2005 ◽  
Vol 462 (2065) ◽  
pp. 3-20 ◽  
Author(s):  
E.R Johnson ◽  
J.G Esler ◽  
O.J Rump ◽  
J Sommeria ◽  
G.G Vilenski
Keyword(s):  
Nonlinear Waves ◽  
Wave Speed ◽  
Nonlinear Problems ◽  
Finite Amplitude ◽  
Critical Flow ◽  
Long Wave ◽  
Experimental Apparatus ◽  
Lee Waves ◽  
Towing Speed ◽  
Layer Flow

This paper reports experimental observations of finite amplitude interfacial waves forced by a surface-mounted obstacle towed through a two-layer fluid both when the fluid is otherwise at rest and when the fluid is otherwise rotating as a solid body. The experimental apparatus is sufficiently wide so that sidewall effects are negligible even in near-critical flow when the towing speed is close to the interfacial long-wave speed and the transverse extent of the forced wavefield is large. The observations are modelled by a simple forced Benjamin–Davis–Acrivos equation and comparison between integrations of both linear and nonlinear problems shows the fundamental nonlinearity of the near-critical flow patterns. In both the experiments and integrations rotation strongly confines the wavefield to extend laterally over distances only of order of the Rossby radius and also introduces finite-amplitude sharply pointed lee waves in supercritical flow.

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