| Summary: | 碩士 === 國立中正大學 === 化學工程研究所 === 88 === This thesis is to numerically study the pattern formation of two-dimensional combustion waves. A two-dimensional mathematical model is first constructed, including equations of heat transfer and reaction kinetics as well as the boundary conditions. The finite-difference method along with the alternating-direction implicit scheme is used to solve the above model equations. The combustion of the square reactant sample, where the reaction Ti + C → TiC takes place, is initiating with an external heat source applied to the corner of the reactant sample. The studied parameters are magnitude of external heat source, initial temperature of the reactant sample, porosity, diluent as well as the degree of mixing inhomogenity. The main findings are listed as follows.
When the magnitude of external heat source increases, the reaction time first decreases and then increases such that there exists a minimum of reaction time. The reaction time is inversely proportional to the increase of the initial temperature. The reaction time also rises with the increase of porosity, degree of diluent and mixing inhomogenity as well. In addition, the ignition time decreases as the porosity or the degree of diluent increases. All of the above results are explained by the heat transfer mechanisms.
Next, combustion temperature remains unchanged when the magnitude of external heat source varies. Increase of the initial temperature results in increase of the combustion temperature. However, the extent of temperature raise (Tc/Tc,298K) is not uniform throughout the reactant sample. For the large increase of initial temperature or the large reactant sample, the temperature raise of is larger when the spatial location is nearer the ignition spot.
Next, combustion velocity is respectively varied as all the studied parameters changed. However, the shapes of the combustion wavefronts remain the same. When mixing inhomogenity exists, the wavefront complexity increases as the degree of mixing inhomogenity or the diluent increases. A wavefront dispersion is defined to quantify the wavefront complexity. As expected, the wavefront dispersion is larger when the degree of mixing inhomogenity or the diluent increases. Moreover, because of mixing inhomogenity, the reactant concentration is not uniform such that single hot spot or several hot spots propagate in a local fashion along the combustion wavefront. This result is consistent with the experimental observation [1].
The computed heat transfer components, including conduction, convection, radiation and released reaction heat, are computed to depict the heat transfer involved in the SHS reaction. First, temperature of the reactant powders in a certain location raises by receiving reaction heat of the adjacent reacted powders via heat conduction. As the temperature increases, the heat loss to the environment starts due to heat convection, following by radiation heat loss at a higher temperature. At this stage, temperature is continuously increasing, because the energy gain by conduction is much large than the convection and radiant heat losses. As the energy accumulates to overcome the activation energy, the reaction starts and releases reaction heat such that the temperature rises rapidly. Because of extremely high temperature, the radiant heat loss is very large and suppresses the convective heat loss. In the meanwhile, conduction heat loss transfers energy to the adjacent unreacted reactant powders. The temperature starts to decline due to conduction, convection and radiation. However, this reacted spot receives a moderate energy “reversely” via heat conduction of the energy released by the subsequent reaction. When the cooling takes place from the high temperature, it is found that the magnitude of radiation is much larger than the convection and conduction, and the order of magnitudes of them are O(103), O(102) and O(10), respectively.
Finally, the phenomena of the accelerating of edge velocity and non-uniform wavefronts are explained using the heat transfer mechanism and a geometric relationship.
|
|---|
