In this paper a globally stabilizing boundary feedback control law for an arbitrarily fine discretization of a nonlinear PDE model of a chemical tubular reactor is presented. The objective is to stabilize an unstable steady–state of the system using boundary control of temperature and concentration on the inlet side of the reactor. We discretize the original nonlinear PDE model in space using f...

The aim of this study is to experimentally investigate the effect of the coiled wire insertions on dynamic instabilities and to compare the results with the smooth tube for forced convection boiling. The experiments were conducted in a circular tube, and water was used as the working fluid. Two different pitch ratios (H/D = 2.77 and 5.55) of coiled wire with circular cross-sections were utilise...

Two numerical procedures in the Direct Simulation Monte Carlo method, applying particle flux conservation at inflow/outflow pressure boundaries, are developed to treat the two most important boundary conditions encountered in micromechanical and vacuum devices involving internal gaseous flows. The first one is for both specified pressures at inlet and exit; while the second one is for specified...

We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫ BR |∇v|dx + Per({v > 0}), 1 < p < ∞, over the set {v ∈ H 0 (BR)| v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.

We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...

Forced convective condensation in vertical channel is investigated numerically. The condensation boundary layers that occur due to temperature difference between the walls and saturation temperature of steam is simulated by the volume of fluid (VOF) method. The effect of variations in the hydraulic diameter, steam velocity, Re number and temperature difference between the wall and saturation te...

A method for generating three-dimensional, time-dependent turbulent inflow data for simulations of complex spatially developing boundary layers is described. The approach is to extract instantaneous planes of velocity data from an auxiliary simulation of a zero pressure gradient boundary layer. The auxiliary simulation is also spatially developing, but generates its own inflow conditions throug...

In this note we develop and analyze a system of equations describing a molten linear polymer being extruded in a capillary rheometer which is operating under the controlled condition that the mean velocity at the capillary inlet is maintained at a constant value. Slipping of the melt at the pipe wall is permitted and an evolution equation for the boundary slip parameter is postulated. The combi...

The mixing-plane method for calculating the three-dimensional flow through multistage turbomachinery is used to perform flutter analysis on a single stage transonic compressor. The turbomachine considered is composed of an inlet guide vane (IGV) and a compressor blade (NASA Rotor 67). The mixing-plane boundary condition enables steady and unsteady computation of the flow through multiple blade ...