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Computational Radiation Heat Transfer
Two-Phase Downward Flow in Vertical Pipes
Microfluidics
Phonon Transport
The QL Method:
For many problems of practical significance, heat transfer by radiation is an important process that is strongly coupled to convective transport
of heat, particles, and species. Despite this importance, thermal radiation is usually excluded from the engineering simulations because of its high solution cost. This may result in erroneous predictions. Prior attempts by Chui and Raithby (1992,2004), Fiveland and Jessee (1996), and Murthy and Mathur (1999-2001) failed to provide a generally-applicable acceleration scheme for two of the most common computational methods for the Radiative Transfer Equation (RTE): the Finite Volume Method (FVM) and the Discrete Ordinates Method (DOM).
We have developed a new efficient and robust computational method for thermal radiation,
called the QL method, which showed very good performance when applied to a number of 1D and 2D benchmark radiation-only problems. The figure below shows a comparison between the CPU time required by the FVM and QL method to solve a simple 2D problem: isotorpically scattering medium in a square black enclosure with one hot wall. In this figure, the y axis shows the number of work units which is the dimensionless CPU time and the x axis shows the optical thickness which is proportional to the degree of medium's participation in radiation (0 for vacuum). Apparently, in the strongly participating media, the QL method is superior to the FVM which is practically useless because of its high solution cost. There is a small cost penalty in the weakly participating media but the solution cost is very small in this limit.
The real power of the QL method cannot be shown by solving the radiation-only problems. There is a very reasonable expectation that the QL method can be implemented in the general multi-process CFD codes and is able to
substantially reduce the solution cost of thermal radiation.
More information: My thesis and an abridged version of my research seminar
Results of this research will appear in the AIAA Journal of Thermophysics and Heat Transfer and the Journal of Computational Thermal Science . Also they will be presented at the 40th AIAA Thermophysics Conference and the Advances in Computational Heat Transfer (CHT-08) (here).
Second-Order RTE:
The governing equation for thermal radiation is the Radiative Transfer Equation (RTE) which is a first-order
integro-differential equation. Recently, Zhao and Liu (2007) have proposed a second-order form of the RTE,
called SORTE, by rearranging the RTE. They applied the Finite Element Method to solve the SORTE which showed
very good numerical properties: accuracy and smoothness.
Independently, during development of the QL method,
we derived the same second-order RTE and studied its numerical solution with the Finite Volume Method.
Although we observed the same superior numerical properties, we also found out that the iterative solution of
the SORTE is very expensive compared to the solution of the first-order
RTE, especially for weakly participating media. This high cost is partly a result of the elliptic character of SORTE and the large bandwidth of the
discretized equations, and partly due to lack of diagonal dominance.
Results of this research will appear in the Journal of Numerical Heat Transfer B (here).
This research was conducted in the period of 2005 to 2007 under the supervision of Prof. Raithby at the University of Waterloo as a part of my master’s study.
Turbulent gas-liquid flows are widely used in various technological applications such as heat power engineering,
chemical apparatus, food industry, and pharmaceutical industry. A good deal of papers was devoted to the
experimental and numerical modeling of horizontal and upward vertical flows. Downward flows were studied more
scantily while this kind of two-phase flow is the most complicated one, because of the buoyancy effects.
As a result of this complexity, experiment is the only reliable approach to investigate the two-phase downward
flows. Up to now, most of the researchers have experimentally studied this problem in small pipes, with id<50mm.
We are interested in the two-phase air/water downward flow in large pipes (id=600mm) which one of its
applications is the hydraulic air compressors, an abandoned technology used before in Ontario and other parts of
the world. Despite many economical and environmental advantages, the main obstacle preventing this technology
from returning to business is finding an efficient method to mix a large amount of air with water in a downward
vertical pipe. A number of experimental and numerical efforts in the past failed to resolve this problem.
We are planning to run experiment on both small and large-scale test facilities to study the flow patterns
and mixing efficiency. Results will be compared with numerical predictions of an available CFD code.
I am working on this project with Prof. Raithby at the University of Waterloo as a research associate since Sep. 2007.
While studying at the University of Tehran, I developed a 2D finite-volume code using the SIMPLE algorithm to simulate the electroosmotic and pressure-driven flows in microchannels. A number of problems, especially the test case studied by Patankar and Hu (1998), were solved to validate the code. It was one of the first researches on microflows in our school and it was continued by my colleagues to investigate the micromixers and effects of the nonuniform potential distribution on heat and mass transfer.
Heat transfer in dielectrics and semiconductors predominately occurs by phonons, which are quanta of crystal vibration energy. At very small length and time scales, conventional analyses using the Fourier law can yield erroneous results. If phonons are treated as particles, the Boltzmann Transport Equation (BTE) can be used as the governing equation. An analogy between the phonon BTE in the relaxation time approximation and the RTE has long been recognized (Majumdar 1993) which results in the Equation of Phonon Radiative Transfer (EPRT). This similarity has been exploited in developing numerical methods for solving the EPRT by many researchers: Majumdar 1993, Murthy 2002 and 2003, and Yang 2005 just to name a few.
It is interesting to apply the QL method to solve the EPRT in the transient form to investigate its performance in handling the complexities occurring in small scales. This research is underway.
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© 2007 Pedram Hassanzadeh
Last Update: 1/08
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