Stabilising effects of pressure gradient dithering in channels with porous walls

The flow in channels with porous walls admits a similarity solution. For low values of the Reynolds number, there is one solution only, which is symmetric. At a critical value of the Reynolds number, there is a pitchfork bifurcation where two additional similarity solutions appear, both asymmetric....

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Autores principales: Gnavi, Graciela Delia, Ferro, Sergio P.
Publicado: 2003
Materias:
Bifurcation (mathematics)
Binary mixtures
Boundary layers
Diffusion
Navier Stokes equations
Perturbation techniques
Pressure effects
Reynolds number
Wall flow
Berman flows
Porous walls
Pressure gradient dithering
Channel flow
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p93_Gnavi
http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p93_Gnavi
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_03928764_v21_n1_p93_Gnavi
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spelling paper:paper_03928764_v21_n1_p93_Gnavi2023-06-08T15:40:59Z Stabilising effects of pressure gradient dithering in channels with porous walls Gnavi, Graciela Delia Ferro, Sergio P. Bifurcation (mathematics) Binary mixtures Boundary layers Diffusion Navier Stokes equations Perturbation techniques Pressure effects Reynolds number Wall flow Berman flows Porous walls Pressure gradient dithering Channel flow The flow in channels with porous walls admits a similarity solution. For low values of the Reynolds number, there is one solution only, which is symmetric. At a critical value of the Reynolds number, there is a pitchfork bifurcation where two additional similarity solutions appear, both asymmetric. Ferro and Gnavi [Phys. Fluids 12 (2000) 797] in their study of the spatial stability of symmetric solutions extended this type of analysis to include general perturbations, and showed that perturbations of the symmetric solution at the entrance of the channel may grow without bound inside, destabilising the flow if the Reynolds number is high enough. The stability of the asymmetric solutions was also analysed, and it was found that these solutions also lose their spatial stability when the Reynolds number increases. In this paper the influence of a small amplitude perturbation of prescribed frequency (dithering) in the pressure gradient along the channel is evaluated, and it shown that it has a stabilising effect on the symmetric solutions. The results are interesting for their possible application to flow stabilisation in processes such as separation of a binary mixture by gaseous diffusion, and control of boundary layer separation. Fil:Gnavi, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Ferro, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2003 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p93_Gnavi http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p93_Gnavi
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Bifurcation (mathematics)
Binary mixtures
Boundary layers
Diffusion
Navier Stokes equations
Perturbation techniques
Pressure effects
Reynolds number
Wall flow
Berman flows
Porous walls
Pressure gradient dithering
Channel flow
spellingShingle Bifurcation (mathematics)
Binary mixtures
Boundary layers
Diffusion
Navier Stokes equations
Perturbation techniques
Pressure effects
Reynolds number
Wall flow
Berman flows
Porous walls
Pressure gradient dithering
Channel flow
Gnavi, Graciela Delia
Ferro, Sergio P.
Stabilising effects of pressure gradient dithering in channels with porous walls
topic_facet Bifurcation (mathematics)
Binary mixtures
Boundary layers
Diffusion
Navier Stokes equations
Perturbation techniques
Pressure effects
Reynolds number
Wall flow
Berman flows
Porous walls
Pressure gradient dithering
Channel flow
description The flow in channels with porous walls admits a similarity solution. For low values of the Reynolds number, there is one solution only, which is symmetric. At a critical value of the Reynolds number, there is a pitchfork bifurcation where two additional similarity solutions appear, both asymmetric. Ferro and Gnavi [Phys. Fluids 12 (2000) 797] in their study of the spatial stability of symmetric solutions extended this type of analysis to include general perturbations, and showed that perturbations of the symmetric solution at the entrance of the channel may grow without bound inside, destabilising the flow if the Reynolds number is high enough. The stability of the asymmetric solutions was also analysed, and it was found that these solutions also lose their spatial stability when the Reynolds number increases. In this paper the influence of a small amplitude perturbation of prescribed frequency (dithering) in the pressure gradient along the channel is evaluated, and it shown that it has a stabilising effect on the symmetric solutions. The results are interesting for their possible application to flow stabilisation in processes such as separation of a binary mixture by gaseous diffusion, and control of boundary layer separation.
author Gnavi, Graciela Delia
Ferro, Sergio P.
author_facet Gnavi, Graciela Delia
Ferro, Sergio P.
author_sort Gnavi, Graciela Delia
title Stabilising effects of pressure gradient dithering in channels with porous walls
title_short Stabilising effects of pressure gradient dithering in channels with porous walls
title_full Stabilising effects of pressure gradient dithering in channels with porous walls
title_fullStr Stabilising effects of pressure gradient dithering in channels with porous walls
title_full_unstemmed Stabilising effects of pressure gradient dithering in channels with porous walls
title_sort stabilising effects of pressure gradient dithering in channels with porous walls
publishDate 2003
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03928764_v21_n1_p93_Gnavi
http://hdl.handle.net/20.500.12110/paper_03928764_v21_n1_p93_Gnavi
work_keys_str_mv AT gnavigracieladelia stabilisingeffectsofpressuregradientditheringinchannelswithporouswalls
AT ferrosergiop stabilisingeffectsofpressuregradientditheringinchannelswithporouswalls
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