The energetics of flow through a rapidly oscillating tube with slowly varying amplitude.
Motivated by the problem of self-excited oscillations in fluid-filled collapsible tubes, we examine the flow structure and energy budget of flow through an elastic-walled tube. Specifically, we consider the case in which a background axial flow is perturbed by prescribed small-amplitude high-frequen...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2011
|
| _version_ | 1797103384471273472 |
|---|---|
| author | Whittaker, R Heil, M Waters, S |
| author_facet | Whittaker, R Heil, M Waters, S |
| author_sort | Whittaker, R |
| collection | OXFORD |
| description | Motivated by the problem of self-excited oscillations in fluid-filled collapsible tubes, we examine the flow structure and energy budget of flow through an elastic-walled tube. Specifically, we consider the case in which a background axial flow is perturbed by prescribed small-amplitude high-frequency long-wavelength oscillations of the tube wall, with a slowly growing or decaying amplitude. We use a multiple-scale analysis to show that, at leading order, we recover the constant-amplitude equations derived by Whittaker et al. (Whittaker et al. 2010 J. Fluid Mech. 648, 83-121. (doi:10.1017/S0022112009992904)) with the effects of growth or decay entering only at first order. We also quantify the effects on the flow structure and energy budget. Finally, we discuss how our results are needed to understand and predict an instability that can lead to self-excited oscillations in collapsible-tube systems. |
| first_indexed | 2024-03-07T06:19:24Z |
| format | Journal article |
| id | oxford-uuid:f2398acc-9664-44c6-8d5e-64a8fe993f44 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:19:24Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:f2398acc-9664-44c6-8d5e-64a8fe993f442022-03-27T12:01:50ZThe energetics of flow through a rapidly oscillating tube with slowly varying amplitude.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f2398acc-9664-44c6-8d5e-64a8fe993f44EnglishSymplectic Elements at Oxford2011Whittaker, RHeil, MWaters, SMotivated by the problem of self-excited oscillations in fluid-filled collapsible tubes, we examine the flow structure and energy budget of flow through an elastic-walled tube. Specifically, we consider the case in which a background axial flow is perturbed by prescribed small-amplitude high-frequency long-wavelength oscillations of the tube wall, with a slowly growing or decaying amplitude. We use a multiple-scale analysis to show that, at leading order, we recover the constant-amplitude equations derived by Whittaker et al. (Whittaker et al. 2010 J. Fluid Mech. 648, 83-121. (doi:10.1017/S0022112009992904)) with the effects of growth or decay entering only at first order. We also quantify the effects on the flow structure and energy budget. Finally, we discuss how our results are needed to understand and predict an instability that can lead to self-excited oscillations in collapsible-tube systems. |
| spellingShingle | Whittaker, R Heil, M Waters, S The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. |
| title | The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. |
| title_full | The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. |
| title_fullStr | The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. |
| title_full_unstemmed | The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. |
| title_short | The energetics of flow through a rapidly oscillating tube with slowly varying amplitude. |
| title_sort | energetics of flow through a rapidly oscillating tube with slowly varying amplitude |
| work_keys_str_mv | AT whittakerr theenergeticsofflowthrougharapidlyoscillatingtubewithslowlyvaryingamplitude AT heilm theenergeticsofflowthrougharapidlyoscillatingtubewithslowlyvaryingamplitude AT waterss theenergeticsofflowthrougharapidlyoscillatingtubewithslowlyvaryingamplitude AT whittakerr energeticsofflowthrougharapidlyoscillatingtubewithslowlyvaryingamplitude AT heilm energeticsofflowthrougharapidlyoscillatingtubewithslowlyvaryingamplitude AT waterss energeticsofflowthrougharapidlyoscillatingtubewithslowlyvaryingamplitude |