Local High-temperature Regions Research Articles

Cavity Effects and Hot Spot Formulation Inmicrowave Heated Ceramic Fibers

AbstractRecently the heating of a thin ceramic cylinder in a single mode applicator was modeled and analyzed assuming a small Biot number and a known uniform electric field through out the sample. The resulting simplified mathematical equations explained the mechanism for the generation and growth of localized regions of high temperature. The results predicted that a hot-spot, once formed, will grow until it consumes the entire sample. Most experimental observations show that the hot-spot stabilizes and moves no further.A new model is proposed which incorporates the effect of the cavity and the nlonuiniform character of the electric field along the axis of the sample. The resulting simplified mathematical equations indicate that these effects stabilize the growth of hot-spots.

Free-radical frontal polymerization: self-propagating thermal reaction waves

Frontal polymerization is a mode of converting monomer into polymer via a localized reaction zone that propagates. Such fronts can exist with free-radical polymerization or epoxy curing. The necessary conditions for the existence of the free-radical frontal polymerization regime are considered. The physicochemical properties of monomers are classified in connection with complications arising in the experiments, including low conversion, convection and bubbles. The density gradient in the reaction zone leading to front decay is the most insidious problem. The analysis of forces that can withstand the Taylor instability allowed us to overcome experimental difficulties and develop approaches to polymerize low-viscosity monomers in the frontal mode. The factors affecting front shape, velocity, conversion, and molecular weight are considered.Historically, frontal polymerization has been performed in neat monomer but we have been able to obtain fronts of very reactive monomers in high-boiling-point solvents including water, DMSO and DMF. Periodic frontal polymerization modes have been observed, including single and multi-point spin modes in which ‘hot spots’(local high-temperature regions) migrate around the front as it propagates. We investigated experimentally the occurrence of the different modes as a function of the initial temperature and the intensity of heat losses and made a qualitative comparison to the results of theoretical analyses based on infinitely narrow reaction zone models.The future directions of research with frontal polymerization are considered, especially with regard to applications to materials synthesis.

Direct simulation vs volume-averaged treatment of adiabatic, premixed flame in a porous medium

For the case of flame thickness being of the order of the pore linear dimension, the flame structure and speed in adiabatic, premixed methane-air combustion in porous media are examined. The local, volume-averaged conservation equations that assume a local thermal equilibrium between the solid and the gas phases (i.e. the single-medium treatment) or allow for a thermal nonequilibrium (i.e. the two-medium treatment) are used along with the direct application of the pointwise conservation equation to a two-dimensional porous medium model (ordered arrangement of discrete or connected square cylinders). The effective properties of the porous medium in the volume-averaged treatments, including the interfacial Nusselt number, are found by applying the local volume-averaging principles. The results show that, although significant variations of the temperature and species concentrations occur over a pore, the flame structure, thickness, speed, and excess temperature (i.e. local gas temperature in excess of the adiabatic temperature) are fairly well predicted by the two-medium model (the single-medium treatment is unable to predict the local excess temperature). However, the volume-averaged treatments are unable to predict the pore-level, local high temperature region in the gas phase (which can be up to 40% above the adiabatic temperature), and the pore-level variation in the flame speed with respect to the flame location in the pore (which can vary by up to 20%). Other shortcomings of the volume-averaged treatments are also revealed through a parametric examination involving the pore-geometry variables, solid to gas conductivity ratio, equivalence ratio, porosity, and flame location within the pore.

Growth and Stabilization of Hot Spots in Microwave Heated Ceramic Fibers

ABSTRACTRecently the heating of a thin ceramic cylinder in a single mode applicator was modeled and analyzed assuming a small Biot number and a known uniform electric field through out the sample. The resulting simplified mathematical equations explained the mechanism for the generation and growth of localized regions of high temperature. The results predicted that a hot-spot, once formed, will grow until it consumes the entire sample. Although this phenomenon is seen in some experiments, others show that the hot-spot stabilizes and moves no further.A new model is proposed which incorporates the dependence of the thermal conductivity and the effective heat transfer coefficient upon temperature, and the nonuniformity of the electric field along the fiber axis. The resulting simplified mathematical equations indicate that these effects may stabilize the growth of hot-spots.

Hot-spot reaction under transient pressure conditions

The initiation of condensed-phase explosives is often caused by hot spots; that is, localized regions of high temperature created by a variety of physical mechanisms, particularly in solid explosives. Once the hot spots are created, further temperature change is governed by (i) self-heating due to chemical reaction, (ii) heat loss by conduction and radiation, and (iii) adiabatic effects due to pressure and specific volume variation. The last effect includes both self-induced pressure change due to thermal expansion against the surroundings, and externally generated pressure change when initiation is attempted by mechanical impact. This paper presents a thermodynamic description of exothermic reaction under conditions of variable pressure and volume. The reaction rate is assumed to be a function of temperature only. The effect of variable pressure enters through its influence on temperature. It is demonstrated that the effects of self-induced pressure change are small. In the case of externally generated pressure change, explosion times can be affected drastically. These results are discussed in terms of initiation by shock waves of finite duration.

Shock-wave initiation of heterogeneous reactive solids

Shock-wave initiation of solid explosives depends on localized regions of high temperature (hot spots) created by heterogeneous deformation in the vicinity of various defects. Current mathematical models of shock initiation tend to fall into two broad categories: (1) thermodynamic-state-dependent reaction-rate models, and (2) the continuum theory of multiphase mixtures. The level of generality possessed by (1) appears to be insufficient for representation of observed initiation phenomena, while that of (2) may exceed necessary requirements based on present measurement capabilities. As a means of bridging the gap between these two models, we present an internal-state-variable theory based on elementary physical principles, relying on specific limiting cases for the determination of functional forms. The appropriate minimum set of internal-state variables are the mass fraction of hot spots μ, their degree of reaction f, and their average creation temperature θ. The overall reaction rate λ̇, then depends on μ, f, and θ in addition to the usual macroscopic thermodynamic variables (current state as well as their history). Two specific forms of this set of equations are applied to time-resolved shock-initiation data on PBX-9404. Numerical solution is achieved by the method of characteristics for rate-dependent chemical reaction. Additional questions such as the effect of thermal equilibrium between phases (solid reactants and gaseous products) on the theoretical results are discussed quantitatively.

The growth and decay of hot spots and the relation between structure and stability

Explosions frequently occur in condensed phase explosives as a consequence of the sudden formation of localized regions of high temperature known as hot spots or temperature spikes. 1 Hot spots may be produced under impact conditions or by irradiation with light, neutrons, and fission fragments or by the arrival of a shock wave at an impedance discontinuity. In spite of their obvious importance hot spots have received little theoretical consideration, probably because the relevant equations are rather intractable. This paper deals with two methods of estimating the critical conditions for explosion to occur. The first method involves an approximate analytical approach and has the advantage of demonstrating the relative importance of the numerous parameters involved. The second method, an exact machine solution of the same problem, gives results in good agreement with those derived from the analytical method. Growth to explosion is shown to depend on the magnitude of a single dimensionless criterion. Finally we consider the dependence of the explosive character of a solid upon its electronic structure.