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Wavy Dynamics of Confined and Inclined Falling Liquid Films

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Fluid Mechanics and Fluid Power, Volume 2 (FMFP 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

We present direct numerical simulations of thin viscous films falling in inclined channel of constant relative confinement, η = 2. The two films with the same Kapitza number, Ka = 509.5, flow in a passive and quiescent atmosphere of air, in presence of gravity, with a suitable monochromatic perturbation, applied at the liquid-velocity inlets. The study is made for different values of liquid flow Reynolds number, Re as a control parameter defined in terms of Nusselt flat film solution. Any orientation of films other than vertical leads to symmetry breaking causing the waves to grow differently on both interfaces. Variations of film flow characteristics such as wave amplitude (h), streamwise velocity (u), and minimum occlusion distance (dmin) are examined with Re for both films. The oscillatory behavior of films ranging from progressive periodic to solitary waves with flow reversals is observed for different values of Re. These flow variations are subjected to suppression when the films undergo strong confinement. Suitable scaling law is reported for dmin as a function of Re for two different values of channel inclination.

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Abbreviations

t:

Time [s]

g:

Gravitational acceleration [m/s2]

x, y:

Streamwise and cross-stream coordinates [mm]

u, v:

Streamwise and cross-stream velocities [m/s]

ρ:

Density [kg/m3]

μ:

Dynamic viscosity [Pa s]

ν:

Kinematic viscosity [m2/s]

\(h_{{\text{N}}}\):

Nusselt flat film thickness [mm]

\(u_{{\text{N}}}\):

Nusselt flat film average streamwise velocity [m/s]

Re:

Reynolds number [–]

Ka:

Kapitza number [–]

θ:

Channel inclination [–]

L, H:

Length and width of channel [mm]

η:

Channel confinement ratio [–]

\(\varepsilon\):

Perturbation amplitude at inlet [–]

f:

Perturbation frequency at inlet [Hz]

α:

Scalar volume fraction [–]

\(\overrightarrow {{F_{{\text{s}}} }}\):

Interfacial surface tension force [N]

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Acknowledgements

We sincerely thank National Super Computing Mission-India and Param Shakti for providing the necessary computing resources

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Authors and Affiliations

  1. Department of Mechanical Engineering, IIT Kharagpur, Kharagpur, 721302, India

    Saurabh Dhopeshwar, Ujjwal Chetan, Suman Chakraborty & Rajaram Lakkaraju

  2. Advanced Technology Development Centre, IIT Kharagpur, Kharagpur, 721302, India

    Toshan Lal Sahu

  3. School of Energy Science & Engineering, IIT Kharagpur, Kharagpur, 721302, India

    Prabir Kumar Kar

Authors
  1. Saurabh Dhopeshwar
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  2. Ujjwal Chetan
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  3. Toshan Lal Sahu
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  4. Prabir Kumar Kar
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  5. Suman Chakraborty
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  6. Rajaram Lakkaraju
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Corresponding author

Correspondence to Saurabh Dhopeshwar .

Editor information

Editors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Krishna Mohan Singh

  2. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Sushanta Dutta

  3. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Sudhakar Subudhi

  4. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Nikhil Kumar Singh

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Dhopeshwar, S., Chetan, U., Sahu, T.L., Kar, P.K., Chakraborty, S., Lakkaraju, R. (2024). Wavy Dynamics of Confined and Inclined Falling Liquid Films. In: Singh, K.M., Dutta, S., Subudhi, S., Singh, N.K. (eds) Fluid Mechanics and Fluid Power, Volume 2. FMFP 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-99-5752-1_15

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  • DOI: https://doi.org/10.1007/978-981-99-5752-1_15

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-5751-4

  • Online ISBN: 978-981-99-5752-1

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