Research Interests

High Rayleigh Number Convection and Low Order Models

Convective patterns that arise in thermally driven flows are relevant to applications that range in scale from materials processing to geophysical phenomena. We have performed numerical and analytical investigations of the motion generated by lateral heating in both tall and shallow cavities. For certain parameter regimes, multicellular structures occur that have marked influence on the local heat transfer characteristics. Within unstable regimes, low order, models of these flows are being developed by using proper orthogonal decomposition. Bifurcation diagrams for the low order systems are being studied.

Channel Instabilities in Nuclear Reactors

Nuclear reactors operating under natural circulation conditions are susceptible to certain instabilities. We have carried out investigations of non-linear density waves by means of a novel Langrangian formulation that incorporates the coupling between the reactor core flow and the nuclear heating. Both subcritical and supercritical finite amplitude instabilities are found to occur. In practice, the subcritical domain will be of limited extent. Numerical simulations are in good agreement with predictions based on the nonlinear theory.

Ignition and Combustion

We are conducting analyses of wave induced ignition in combustible mixtures for large activation energies. Although the induction domain has a complex structure, progress has been made for the Newtonian limit in which the isentropic (frozen) sound speed is close to the isothermal speed. Excellent agreement with numerical solutions has been obtained for one-step first-order reactions. Extensions to include the ensuing detonation wave structure, and more complex reaction schemes, are under way.

Optical Fiber Coatings

A variety of thermofluid problems arise in the manufacture and coating of optical fibers. In particular, we are analyzing the required cooling length for draw tower design, and have shown that existing experimental data are well correlated by the predicted cooling law. Studies are also being carried out to determine coating thicknesses and meniscusus shapes for general applicator geometries. At small capillary numbers, non-unique solutions are found to arise even for time-independent states.