NDLI: Flow and oscillations in collapsible tubes: Physiological applications and low-dimensional models

Content Provider	Springer Nature Link
Author	PEDLEY, T J
Copyright Year	2015
Abstract	The motivation for this subject comes from physiology: Air-flow in the lungs, where flow limitation during forced expiration is a consequence of large-airway collapse, and wheezing, which is a manifestation of self-excited mechanical oscillations; Blood flow in veins, such as those of giraffes, in which the return of blood to the heart from the head must be accompanied by partial venous collapse, and in arteries, which exhibit self-excited oscillations (Korotkov sounds) when compressed by a blood-pressure cuff. Laboratory experiments are frequently conducted in a Starling resistor, a finite length of flexible tube, mounted between two rigid tubes and contained in a pressurised chamber. Steady conditions upstream and downstream give rise not only to steady flows, but also to a rich variety of self-excited oscillations, which theoreticians have been seeking to understand for at least five decades. Some of the observations have been reproduced in full Navier–Stokes computations for a two-dimensional model, but these do not provide physical understanding. We seek a self-consistent mathematical model for the oscillations. We concentrate first on 1D models, in which the key dependent variables are the cross-sectional area A and the cross-sectionally averaged velocity u and pressure p, all taken to be functions of longitudinal coordinate x and time t. The governing equations are those of conservation of mass and momentum and a tube law representing the elastic properties of the vessel. In the momentum equation, the viscous resistance term is conventionally modelled either as a linear function of fluid velocity, accurate at low Reynolds number, or with an ad hoc representation of the energy loss at flow separation. Even with such crude approximations, the predictions of 1D models agree quite well both with observations in the giraffe and with some of the 2D computations and 3D experiments. For a more rational model, we examine a 2D model problem, in which part of one wall of a parallel sided channel is replaced by a membrane under tension. One approach, for large Reynolds-number flow, and a long membrane, is to consider small deflections of the membrane and use interactive boundary-layer theory. This leads to interesting predictions, such as the impossibility of simultaneously prescribing the flow rate and the upstream pressure, but not to oscillations, except in cases where wall inertia is important (flutter). Another approach is to assume a parabolic velocity profile everywhere, leading to a rational choice for the inertia and viscous terms in the 1D momentum equation. If, further, the undisturbed membrane is taken to be flat, by a suitable choice of external pressure distribution, the system leads to an oscillatory instability even without wall inertia. Whether these oscillations have the same physics as those computed numerically at lower Reynolds number remains to be seen.
Starting Page	891
Ending Page	909
Page Count	19
File Format	PDF
ISSN	02562499
Journal	Sadhana
Volume Number	40
Issue Number	3
e-ISSN	09737677
Language	English
Publisher	Springer India
Publisher Date	2015-05-28
Publisher Place	New Delhi
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Collapsible tubes flow-structure interactions 1D models 2D models. Engineering
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Modelling Flow and Oscillations in Collapsible Tubes

Fluid-Structure Interaction in Internal Physiological Flows

Flow in Collapsible Tubes: A Brief Review

Chaotic Oscillations in a Simple Collapsible-Tube Model

Implementation and Validation of a 1D Fluid Model for Collapsible Channels

Analysis of Flow in a Two-Dimensional Collapsible Channel Using Universal “Tube” Law

Fluid Dynamics Modelling Flow and Oscillations in Collapsible Tubes 1

Numerical Analysis for Stability and Self-Excited Oscillation in Collapsible Tube Flow

Self-excited oscillations in three-dimensional collapsible tubes: simulating their onset and large-amplitude oscillations

Flow and oscillations in collapsible tubes: Physiological applications and low-dimensional models

Similar Documents

Modelling Flow and Oscillations in Collapsible Tubes

Fluid-Structure Interaction in Internal Physiological Flows

Flow in Collapsible Tubes: A Brief Review

Chaotic Oscillations in a Simple Collapsible-Tube Model

Implementation and Validation of a 1D Fluid Model for Collapsible Channels

Analysis of Flow in a Two-Dimensional Collapsible Channel Using Universal “Tube” Law

Fluid Dynamics Modelling Flow and Oscillations in Collapsible Tubes 1

Numerical Analysis for Stability and Self-Excited Oscillation in Collapsible Tube Flow

Self-excited oscillations in three-dimensional collapsible tubes: simulating their onset and large-amplitude oscillations

Flow and oscillations in collapsible tubes: Physiological applications and low-dimensional models