| Experimental and Modeling Studies on Solitary Wave Dynamics on Vertical and Inclined Film Flows | ||
| Cesar E. Meza Jr., Chemical Engineering, University of Houston, 4800 Calhoun Rd., Houston, TX 77204, Ramesh Raju Mudunuri, University of Houston, Chemical Engineering Dept., Houston, TX 77204 and Vemuri Balakotaiah, Department of Chemical Engineering, University of Houston, 4800 Calhoun Ave., Houston, TX 77204-4004
We present
modeling and experimental study of thin films falling down an inclined plane,
along with new insights to wave behavior. Starting with the 2D Navier-Stokes
equations, we derive a partial differential equation model involving the film
thickness and flow rate, using the integral method. Besides the inclination
angle, the system is governed by two other dimensionless parameters, the
Reynolds number, Re and the Weber number, We. In order to study
the nonlinear dynamics of thin film flows, we simulated pulsing experiments
where the inlet flow rate was periodically excited with two or more
frequencies. We compare the model simulations with experiments of Liu &
Gollub (1994). For commensurate frequencies, the model captures the nonlinear
generation of solitary waves though the interaction of periodic, non-solitary
waves. For incommensurate frequencies, the model predictions are quantitatively
consistent with experiments where the spacing between the weakly interacting solitary
waves is found to be irregular.
Experiments show
that the speed and peak height of solitary waves, correlate linearly. We
analyze the model in a steady traveling coordinate system and present a new
class of solitary wave solutions that exist in the low-frequency limit. For
these waves, the model predicts a slope of Extended Abstract Status: Not Uploaded | ||