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Absolute and convective instability of a relaxational plane liquid jet
KTH, Superseded Departments, Mechanics.ORCID iD: 0000-0003-3737-0091
2003 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 493, 89-119 p.Article in journal (Refereed) Published
Abstract [en]

The stability of a plane relaxational liquid jet has been studied theoretically and experimentally through linear stability analysis and flow visualizations. The relaxational liquid jet is obtained by the outflow of a liquid from a plane channel with an upstream fully developed Poiseuille flow into an ambient stagnant gas. Linear spatial stability calculations show that there are five convectively unstable modes, three sinuous and two dilatational. The spatial stability calculations are compared to experimental results for wavenumber variation and the growth of waves found in the visualizations. These variations have been quantified with a wavelet transform and through a comparison with the spatial stability results the type of mode observed in the visualizations has been determined. For this type of mode the calculated wavenumber variation is in good agreement with the experimental results. Also, in the experiments the breakup of the jet has been observed when the Reynolds number reaches a certain value, and as the Reynolds number increases this breakup moves closer to the channel exit. This upstream movement of the breakup can be explained by the linear stability results. Finally the relaxational liquid jet is shown to be absolutely unstable for a certain parameter region. Close to the nozzle both a sinuous mode and a dilatational mode are shown to be absolutely unstable. As the jet profile relaxes to uniform, the sinuous mode is shown to be the only unstable mode. This occurs for Weber numbers We < 1, which is in agreement with the theory for liquid jets with uniform velocity profile. The frequency selection for the observed waves is believed to be related to the region of absolute instability located closest to the channel exit.

Place, publisher, year, edition, pages
2003. Vol. 493, 89-119 p.
Keyword [en]
sheet, waves, flows
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-22929DOI: 10.1017/s0022112003005871ISI: 000186329300004OAI: oai:DiVA.org:kth-22929DiVA: diva2:341627
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Hydrodynamics of plane liquid jets aimed at applications in paper manufacturing
Open this publication in new window or tab >>Hydrodynamics of plane liquid jets aimed at applications in paper manufacturing
1999 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Process industries are in general depending, in one way or the other, on fluid mechanics.Specifically, paper manufacturing, which probably is the dominant processindustry in Sweden, is depending on the flow of cellulose fibres suspended in water.As a part of the process the suspension, consisting of fibres in water, is spread out onor between two moving permeable weaves, i.e. wires. The speed of this is usually 10–30 m/s and the suspension is spread out by a plane jet issuing from a headbox nozzle.It has been show that the conditions in the headbox and jet have a large influence onthe quality of the final paper sheet. Primarily, streaks in the paper sheet are believedto be the result of streamwise streaks in the headbox jet.The thesis is aimed at the flow phenomena which occur in the headbox jet. Theinvestigations have been made with numerical calculations, stability theory and modelexperiments using water, as well as experiments with a real paper machine headboxand fibre suspension. In the thesis an introduction to the hydrodynamics of planeliquid jets is presented together with a description of the paper forming process andthe fluid mechanics of headbox flow.The basic flow and stability of a two-dimensional plane liquid jet has been investigatedby numerical calculations, stability theory and experiments. The calculationsof the laminar basic flow is successfully compared to pitot-tube measurements of thestreamwise velocity profile. By visualisations of the flow it is found that wave disturbanceson the jet has a severe effect on the flow. These waves can be predicted bylinear stability theory, which shows the presence of five convectively unstable modes.These can be divided into three types and by comparison with the experiments thetype of the visible waves is determined. These waves seem to initiate a break-up ofthe jet, which leads to strong streamwise streaks inside the jet.By flow visualisation of headbox flow of an experimental paper machine, togetherwith analysis of the resulting paper structure using the wavelet method the correspondencebetween flow disturbances and paper quality was investigated. It was shownthat the wave instability, which is present on the low Reynolds number water jet, alsocan be found in the real the headbox jet. It is shown that these waves play an importantrole in the dynamics of the headbox jet and also have an influence on the final papersheet.

Place, publisher, year, edition, pages
Stockholm: KTH, 1999. x, 48 p.
Series
Trita-MEK, ISSN 0348-467X ; 99:10
Keyword
liquid jet, transition, break-up, stability, wavelet, free surface, waves, streamwise streaks, fibre suspension, headbox, forming, shadowgraph, hot-film
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-2839 (URN)99-3009113-0 (ISBN)
Public defence
1999-09-24, 00:00
Note
QC 20100825Available from: 2000-01-01 Created: 2000-01-01 Last updated: 2010-08-26Bibliographically approved

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