JFM-14-S-0123.R1_Accepted_Manuscript.pdf (775.82 kB)
Absolute and convective instabilities in counter-current gas-liquid film flows
journal contribution
posted on 2015-08-07, 12:41 authored by Rajagopal Vellingiri, Dmitri TseluikoDmitri Tseluiko, Serafim KalliadasisWe consider a thin liquid film flowing down an inclined plate in the presence of
a counter-current turbulent gas. By making appropriate assumptions, Tseluiko &
Kalliadasis (J. Fluid Mech., vol. 673, 2011, pp. 19–59) developed low-dimensional
non-local models for the liquid problem, namely a long-wave (LW) model and
a weighted integral-boundary-layer (WIBL) model, which incorporate the effect
of the turbulent gas. By utilising these models, along with the Orr–Sommerfeld
problem formulated using the full governing equations for the liquid phase and
associated boundary conditions, we explore the linear stability of the gas–liquid
system. In addition, we devise a generalised methodology to investigate absolute
and convective instabilities in the non-local equations describing the gas–liquid
flow. We observe that at low gas flow rates, the system is convectively unstable
with the localised disturbances being convected downwards. As the gas flow rate is
increased, the instability becomes absolute and localised disturbances spread across
the whole domain. As the gas flow rate is further increased, the system again becomes
convectively unstable with the localised disturbances propagating upwards. We find
that the upper limit of the absolute instability region is close to the ‘flooding’ point
associated with the appearance of large-amplitude standing waves, as obtained in
Tseluiko & Kalliadasis (J. Fluid Mech., vol. 673, 2011, pp. 19–59), and our analysis
can therefore be used to predict the onset of flooding. We also find that an increase
in the angle of inclination of the channel requires an increased gas flow rate for the
onset of absolute instability. We generally find good agreement between the results
obtained using the full equations and the reduced models. Moreover, we find that
the WIBL model generally provides better agreement with the results for the full
equations than the LW model. Such an analysis is important for an understanding of
the ranges of validity of the reduced model equations. In addition, a comparison of
our theoretical predictions with the experiments of Zapke & Kröger (Intl J. Multiphase
Flow, vol. 26, 2000, pp. 1439–1455) shows a fairly good agreement. We supplement
our stability analysis with time-dependent computations of the linearised WIBL model.
To provide some insight into the mechanisms of instability, we perform an energy
budget analysis.
Funding
We acknowledge financial support from EPSRC grant No. EP/K504130/1 and ERC Advanced grant No. 247031. The work of D.T. was partly supported by EPSRC Grant No. EP/J001740/1.
History
School
- Science
Department
- Mathematical Sciences
Published in
Journal of Fluid MechanicsVolume
763Pages
166 - 201Citation
VELLINGIRI, R., TSELUIKO, D. and KALLIADASIS, S., 2015. Absolute and convective instabilities in counter-current gas-liquid film flows. Journal of Fluid Mechanics, 763, pp. 166 - 201.Publisher
© Cambridge University PressVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2014-11-15Publication date
2014-12-11Notes
This is the accepted manuscript of an article subsequently published in the Journal of Fluid Mechanics [© Cambridge University Press]. The definitive version is available at: http://dx.doi.org/10.1017/jfm.2014.667ISSN
0022-1120eISSN
1469-7645Publisher version
Language
- en