APS March Meeting 2024
Monday–Friday, March 4–8, 2024;
Minneapolis & Virtual
Session Z40: DFD XI
11:30 AM–2:30 PM,
Friday, March 8, 2024
Room: 103F
Sponsoring
Unit:
DFD
Chair: Christopher Boyce, Columbia University
Abstract: Z40.00014 : Hydrodynamic characteristics of strong inertial solitary waves on thin film flows
2:06 PM–2:18 PM
Abstract
Presenter:
Saurabh Dhopeshwar
(INDIAN INSTITUTE OF TECHNOLOGY (IIT) Kharagpur)
Authors:
Saurabh Dhopeshwar
(INDIAN INSTITUTE OF TECHNOLOGY (IIT) Kharagpur)
Suman Chakraborty
(INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR)
Rajaram Lakkaraju
(INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR)
We use two-dimensional numerical simulations to investigate the hydrodynamic characteristics of a solitary main hump in falling liquid films over inclined flat surfaces. In this study, a constant monochromatic perturbation is applied to the velocity field at the inlet to enforce the film. The study is made for two control parameters: Reynolds number, Re, and inverse Capillary number, Ca to examine the solitary hump. For all the inverse Capillary numbers under investigation, the wavy film flows reveal the existence of a critical Reynolds number, Rec, such that both the maximum film height, hmax, and discharge, qmax initially increases with Re up to Rec and then decreases. At any Re, these characteristics also show inverse behaviour with Ca such that they decrease with an increase in Ca for Re< Rec and then increase after Rec. This behaviour is attributed to the reduced effective inertia, which is strongly influenced by the surface tension at the interface. Additionally, the asymmetry of the interface shape decreases rapidly for lower Re values, becoming asymptotically constant for Re >> Rec for all Ca values. Suitable analytical expressions for calculating the tail and front length of the solitary wave hump are derived and compared with the numerical results. For films at stronger inertia (Re>Rec), the wave speed varies linearly with hmax independent of Ca. Moreover, the self-similarity of solitary waves in terms of wave speed breaks down for all Ca values. At any Re value, the streamwise velocity profile shows a semi-parabolic nature at both the wave crest and wave tail. However, the region of the front (steeper part) of the wave exhibits a strong non-parabolic nature. These findings provide insights into the intricate interplay of the effect of inertia and surface tension in wavy films, highlighting the importance of the critical Reynolds number, Rec, in determining the film behaviour and characterizing the instability.