Film flows on inclined surfaces are often assumed to be of constant thickness, which ensures that the velocity profile is half-Poiseuille. It is shown here that by shallow water theory, only flows in a portion of Reynolds number-Froude number (Re–Fr) plane can asymptotically attain constant film thickness. In another portion on the plane, the constant thickness solution appears as an unstable fixed point, while in other regions the film thickness seems to asymptote to a positive slope. Our simulations of the Navier-Stokes equations confirm the predictions of shallow water theory at higher Froude numbers, but disagree with them at lower Froude numbers. We show that different regimes of film flow show completely different stability behaviour from that predicted earlier. Supercritical decelerating flows are shown to be always unstable, whereas accelerating flows become unstable below a certain Reynolds number for a given Froude number. Subcritical flows on the other hand are shown to be unstable above a certain Reynolds number. In some range of parameters, two solutions for the base flow exist, and the attached profile is found to be more stable. All flows except those with separation become more stable as they proceed downstream.
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October 2012
Research Article|
October 19 2012
Stability of developing film flow down an inclined surface
Sarath Ramadurgam;
Sarath Ramadurgam
1Department of Physics,
Purdue University
, West Lafayette, Indiana 47907, USA
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R. V. K. Chakravarthy;
R. V. K. Chakravarthy
2Department of Aerospace Engineering,
Indian Institute of Technology Madras
, Chennai 600036, India
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Gaurav Tomar;
Gaurav Tomar
3Department of Mechanical Engineering,
Indian Institute of Science
, Bangalore 560012, India
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Rama Govindarajan
Rama Govindarajan
a)
4TIFR Centre for Interdisciplinary Sciences,
Tata Institute of Fundamental Research
, Hyderabad 500075, India
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a)
On lien from the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India. Electronic mail: rama@tifrh.res.in.
Physics of Fluids 24, 102109 (2012)
Article history
Received:
October 11 2011
Accepted:
September 10 2012
Citation
Sarath Ramadurgam, R. V. K. Chakravarthy, Gaurav Tomar, Rama Govindarajan; Stability of developing film flow down an inclined surface. Physics of Fluids 1 October 2012; 24 (10): 102109. https://doi.org/10.1063/1.4758299
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