Complex Wave Dynamics on Thin Films
Hsueh-Chia Chang
Bayer Professor of Engineering
Department of Chemical Engineering
University of Notre Dame
Falling-film wave instability is a classical hydrodynamic
instability with a rich spectrum of wave dynamics. A linear
filtering mechanism, well-described by classical linear
Orr-Sommerfeld theory, filters inlet noise into a monochromatic
travelling wave. This travelling wave, however, suffers a modulation
instability and produces localized wave structures (defects) known as
solitary waves. We capture this solitary wave generation mechanism
through two coupled first-order pdes that describe the dynamics of
the local wave texture and film thickness. A blow up solution to this
equation creates wave sinks that coalesce nearby waves into large
solitary waves. We then analyze binary interaction between two
solitary waves by constructing their discrete and essential spectra.
A weighted spectral theory is formulated to produce resonance poles
that determine the rate liquid drains out of a large solitary wave.
Binary interaction is then shown to be driven by two coupled modes--a
translational mode and a kinematic mode due to mass conservation.A
two-dimensional dynamical system then determines the rate by which
two solitary waves attract each other and coalesce. This coalescence
dynamics is integrated into a statistical theory that accurately
predicts the downstream coarsening of wave field in this intriguing
spatio-temporal dynamics.
Chang, H.-C., "Wave Evolution on a Falling Film", Annual Review of
Fluid Mechanics, 26, 103-136 (1994).
Chang, H.-C., Demekhin, E. A. and Kalaidin, E. N.,"Interaction
Dynamics of Solitary Waves on a Falling Flim", J. Fluid Mech., 294,
123-154 (1995)
Chang, H.-C., Demekhin, E. A. and Kalaidin, E. N., "Generation and
Suppression of Radiation by Solitary Pulses", SIAM J. on Applied
Math., 58, 1246 (1998)
Chang, H.-C., Demekhin, E. A. and Kalaidin, E., "Coherent Structures,
Self-Similarity, and Universal Roll Wave Coarsening Dynamics", Phys.
of Fluids, 12, 2268 (2000).
"Complex Wave Dynamics on Thin Films", Chang, H.-C. and Demekhin, E.
A., Elsevier Scientific (2002).
Fast-Igniting Catalytic Converters
Hsueh-Chia Chang
Department of Chemical Engineering
University of Notre Dame, IN 46556
Our current automobile catalytic converter ignites within
one minute but only locally at the downstream end. It requires
another 5 minutes before the heat released at this end can propagate
upstream via solid conduction to lightoff the entire converter to an
elevated, chemically active temperature. During this interval, which
corresponds to 25% of the average American driving time, NOx and
hydrocarbons are released unabated through the exhaust. Using thermal
homogenization theory to analyze the complex reactive thermal
transport in the multi-phase converter monolith. A scalar
convective-diffusion equation with a zero-order reaction term
results. Its blow-up solution is obtained in closed form via
asymptotic expansion. The location of this blow-up phenomenon is
shown to be determined by a single parameter representing the ratio
of the thermal transport time scale to the reactive time scale. It is
shown that if the exhause is preheated to 700K, the ignition location
would be shifted to the leading edge of the converter and the
subsequent lightoff of the entire monolith, being aided by gas-phase
convection, can occur within seconds after the initial ignition. A
new converter (with a pending patent) that promises to alleviate
this important environmental problem is designed and
numerically/experimentally tested.
References:
Leighton, D. T. and Chang, H.-C., "A Theory for Fast-Igniting
Catalytic Converters", AIChE J ,
41, 1898-1915 (1995).
Balakotaiah, V. and Chang, H.-C., "Dispersion of Chemical Solutes in
Chromatographs and
Reactors", Phil. Trans of the Royal Society of London,
A351, 39-75 (1995).
Keith, J. M., Chang, H.-C. and Leighton, D. T., "Designing a
Fast-Iginiting Catalytic
Converter System", AIChE J, 47, 650(2001).
Converted from hcc.txt (plain text).