Chaotic Natural Convection
Natural convection heat transfer has been shown to exhibit characteristics of chaotic mathematical transitions. Proper Orthogonal Decomposition (POD) is one type of reduced order modeling which has many names and has been used to characterize fluid transitions by prior researchers, but has been applied in a limited way to heat transfer systems. Student researchers are currently performing experimental work that will be compared to CFD models and mathematical predictions of these transitions.
Another student research team has constructing a density flow visualization system known as a Schlieren. This system is used to visualize the flow field for natural convection systems. A photo of a candle (shown at right) was taken with the University of Portland Schlieren system. The team has also posted a few great videos taken with the system.
On the computational side student researchers are working to extend the range of existing CFD models for this area. Early explorations have focused on benchmarking the open source tool OpenFOAM for low driving force natural convection flows.
A computational model has been developed that extends prior work on unsteady natural convection in a tall rectangular cavity with aspect ratio 10. The solution to the weakly compressible Navier-Stokes equation is computed for a range of Rayleigh numbers between 2 · 107 and 2.2 · 108 with Prandtl number 0.71. A detailed spectral analysis has been performed, that shows dynamic system behavior beyond the Hopf bifurcation that was not previously observed. The wider Rayleigh range reveals new dynamic system behavior for the rectangular geometry, specifically a return to a stable oscillatory behavior that was not predicted in prior work.
Proper Orthogonal Decompositions (POD) has been used to analyze the computational results. Five eigenvalue modes were required to capture correctly the basic flow structure. The POD failed to capture subtle aspects of the flow structure at high Rayleigh numbers for the model, indicating that a POD and Galerkin projection for several Rayleigh numbers will be needed to reproduce the complex behavior of the system.
Prior work
Chaotic natural convection behavior has been studied in different geometries in the past, including an annular geometry. This geometry was explored experimentally and computationally using the software tool Comsol. The experimental system included more than 30 thermocouples (individually calibrated) that operate with junctions in stirred temperature bath. Construction of the system required design and manufacture of copper irises and electrical control of three power sources. Post processing and analysis of more than three million lines of temperature data over for more than three years was performed with three programming tools.
The computational fluids model for buoyancy driven flow in an annulus was compared to experimental results. The model required full analysis of radiation view factors in a complex annular system and specification of boundary conditions extracted from the experimental system. In addition, several separate benchmarking CFD studies were performed to calibrate the software.
A reduced order modeling paradigm for the conduction in the wall of the inner annular surface was developed using proper orthogonal decompostion. The reduced order modeling work is part of an effort to develop robust models to understand dynamic systems for the heat transfer community. The complexity of the geometry and boundary conditions for this problem make traditional CFD techniques extremely time consuming. The reduced order modeling techniques are much faster than traditional methods but may be mathematically difficult to implement.
Dillon HE, Emery AF, Mescher A., J.O. Sprenger, S.R. Edwards. 2011. Chaotic Natural Convection in an Annular Cavity from Non-Uniform Vertical Walls Temperatures. Frontiers in Heat and Mass Transfer, Vol 2, Issue 2.
Dillon HE, Emery AF, and Mescher AM. 2011. Chaotic Behavior of Natural Convection in a Tall Rectangular Cavity with Non-Isothermal Walls. International Conference of Numerical Analysis and Applied Mathematics 2011