VI-3

Burt S. Tilley

NJIT

In a variety of engineering applications, the transfer of heat is the limiting factor of the functionality of the entire system, such as in electrical generators and cooling arrays. The systems used to transport heat away from the underlying application are prone to hydrodynamic instabilities, with the resulting flow patterns ranging from core-annular flows to films, drops, and slugs. Enhancements in design of these thermal systems are not possible without a better understanding of the underlying physical mechanisms of instability. One configuration of these heat-transfer systems is countercurrent flow, in which water flows under the influence of gravity and the air or water vapor is driven by an adverse pressure gradient. When the adverse pressure gradient is increased sufficiently, large amplitude traveling waves appear on the interface, entrainment of water in the gas occurs. This phenomenon is called flooding, and it is not well understood if the instability of the flow is induced by inlet disturbances to the flow.

Consider two immiscible, incompressible fluids in a vertical channel separated by an interface with large surface tension. The more dense fluid (e. g. water) is flowing down a section of the left channel wall from an inlet at the top to a moving contact line separating the left channel wall, the more dense fluid and the less dense fluid (e. g. air). The less dense fluid is driven by an adverse pressure gradient, such that the shear induced on the denser fluid is in the opposite direction of the flow induced by gravity. From the continuity and Navier-

Stokes equations we systematically derive a single evolution equation that includes the effects of viscosity stratification, density stratification and shear, assuming that the channel thickness is much smaller than the disturbance length scale of the evolution, and the contact-line angle is also small. We further consider the limit where both the kinematic viscosity and density ratios are small, but shear is large, effectively promoting shear effects over the inertial effects in the lighter fluid. Steady-state solutions are found numerically, in which part of the solution is the location of the contact lien in addition to the interfacial shape. Stability is investigated by numerical simulations of the system with oscillatory forcing at the inlet.