Implicit Function and Level Set Methods for Computation of Moving Elements During Microwave Heating

This paper proposed a method based on transformation optics, implicit function, and level set methods to solve the challenge of multi-physics simulation of a microwave heating cavity with two different motion modes. A 3D computation model with a rotating turntable, a lifting support rod, and a sample is proposed as a detailed demonstration. Based on the theory of transformation optics, the rotating turntable is surrounded by two circles with a time-varying, inhomogeneous and anisotropy medium, and the electric field in the moving region is rotated by controlling the two mediums. The implicit function and level set methods compute the lifting motion by setting the properties of the lifting region as a function of space and time. The correctness of the proposed method is verified by comparing the proposed method’s results with the discrete position’s results, and then its accuracy is further verified by experiment. Subsequently, compared with the implicit function and level set methods only, the proposed method is more accurate. Finally, the effects of lifting motion, rotating motion and lifting motion (i.e., spiral motion) on microwave heating uniformity and heating efficiency were analyzed, respectively.

Aiming at the intercoupling of multiple physics and the time-varying characteristics of boundary conditions in the microwave heating process, how to optimize the temperature uniformity of materials with a cooperative-mode stirrer is focused in this paper. First, the formation of standing waves can be effectively avoided by introducing the mode stirrer, thereby improving the heating efficiency of the material. Description of pattern stirrer motion processes using implicit functions and level set methods. Second, in order to optimize the temperature uniformity of the material, the stirrer is made intelligent, and the electromagnetic field distribution can be optimized by using different stirrer positions and directions, and the temperature uniformity is improved through intelligent coordination of stirrers in different positions. Finally, the finite element method is used to perform numerical simulation calculations on integer and continuous variables. The results show that the proposed method can improve the temperature uniformity of the conventional microwave heating model by 28.2%–81.44% and 23.2%∼63.91% at each level and lead hammer section respectively, and can improve the heating efficiency by 14.8%∼36.4%. According to its performance when heating different shapes and different materials, the proposed method is efficient and feasible.

The level set method is a mathematical and computational, technique for tracking a moving interface over time. It can naturally handle topological changes such as merging or breaking interfaces. Intrinsic geometric properties of the interface, such as curvature and normal direction, are easily determined from the level set function p. There are many applications of the level set method, including kinetic crystal growth, epitaxial growth of thin films, image restoration, vortex dominated flows, and so forth. Most applications described in the growing literature on the applications of level sets advance the level set equation with explicit time integration. Hence, small CFL-respecting time steps are needed to maintain stability. In this thesis, an implicit level set method is introduced and applied to wildland firespread models, removing vulnerability to instability.

For the desorption of methane, thermal stimulation is an alternative to develop coalbed methane (CBM) when it is difficult to reduce the formation pressure. Microwave heating is a promising thermal method to increase the gas recovery of CBM especially for the CBM reservoir with high heterogeneity and low water content. The current study aims to establish a fully coupled numerical model to understand the enhanced gas recovery (EGR) mechanism of CBM under microwave heating. In the study, the CBM reservoir model was developed first. Then a mathematical model considering electromagnetic excitation, heat transfer, mass transfer, Langmuir adsorption, and fluid flow was built. Moreover, some important parameters were set as temperature-dependent to achieve the coupling effects among the multiphysics. Based on the above two models, a fully coupled electromagnetic-thermal-hydraulic-mechanical model was solved by the finite element, so that the distributions of electric field, reservoir temperature, methane concentration were able to be investigated. Finally, a sensitivity analysis including water content, microwave power and microwave heating mode was done based on the heating efficiency and EGR. Under microwave heating, the electric field distributes near the microwave heater with the maximum electric intensity as 1.07×103 V/m. The high electric intensity and low thermal conductivity easily enables microwaves to generate the required temperature region within CBM reservoir, so that 200 W power was applied to continuous heat the formation. Under 1 day, the maximum temperature of CBM reservoir increased to 81 °C, enabling the desorption of methane. Moreover, heating efficiency is controlled by the dielectric properties as well as electric field intensity of the CBM reservoir, although the existence of water content increases the dielectric constant within the CBM reservoir. In addition, by setting the temperature-dependent properties, microwave heating shows the ability to induce the pore volume changes by generating thermal stress, so that the porosity and permeability of CBM reservoir near the heater increase from 0.15 to 0.24 and from 0.36 mD to 1.47 mD, respectively. Based on the above positive effects of microwave heating, the CBM recovery could be significantly enhanced. Finally, in order to transfer the heat deeper into the reservoir, the feasibility of stepwise microwave heating mode has been successfully proven based on the temperature distribution within the CBM reservoir. In the study, microwave has showed great potential in enhancing the CBM recovery resulting from its high heating efficiency and pore induction effect. The results presented in this paper can provide comprehensive guidance for the optimization of microwave heating parameters.

Investigation on the mechanism of micro-cracks generated by microwave heating in coal and rock

This paper deals with structural optimization for designing periodic structures in a hole array wavelength filter. The hole array wavelength filter that consists of metallic thin film and dielectric enables to transmit narrow bandwidth light. It is known that transmission spectrum can be changed not only by the periodicity of hole array but also by the shape of holes. For optimizing the hole shape, the level set method is used in this study. In the ordinary level set method, the boundaries are implicitly expressed by the zero level set of a scalar function, called the level set function, within a fixed mesh. Therefore, the material interpolation becomes numerically awkward within the elements across the implicit zero level set because those elements inevitably take on intermediate material properties even if the boundary of zero level set are mathematically clear. As the result, the optimization is likely to yield wrong solution. Here, a new level set optimization method incorporating Arbitrary Lagrangian Eulerian method is proposed to eliminate intermediate values on the interfaces perfectly. As a result, the proposed method can successfully perform the structural optimization of hole shape without intermediate values.

Nonequilibrium heat and mass transfer processes through liquid-vapor interfaces are studied through solutions of the Enskog-Vlasov (EV) equation and the corresponding system of EV26 moment equations. These models fully resolve liquid and vapor bulk regions and the diffuse interface connecting both. With that, evaporation and heat transfer processes can be studied without the need of modeled interface relations. Comparison of numerical results shows qualitative agreement of moment simulations with DSMC solutions of the EV equation, but quantitative differences. Interface resistivities for jump interface conditions are determined from the simulations, which show marked differences to those found from classical kinetic theory, where dimensionless resistivities are constants. In contrast, the EV models give temperature dependent resistivities, some negative off-diagonal resistivities, and indicate non-linear behavior where resistivities depend on mass and heat fluxes through the interface. In summary, the results point to the urgent need for systematic evaluation of resistivities over a wide range of conditions between weak and strong nonequilibrium, close to and far from the critical point.

Numerical analysis of microwave heating cavity: Combining electromagnetic energy, heat transfer and fluid dynamics for a NaY zeolite fixed-bed

Through finite volume method, this study establishes a steady state flow and heat transfer model of a single phase flow flowing vertically upward in annular space. The model sets the inner cylinder of the annular space as a heating body with fixed heat generation rate. Flow and heat transfer boundary layers are set between the flow and the inner cylinder wall, in order to give more accurate description of momentum and heat coupling and transfer processes between the fluid and the solid near the wall. Compared with the constant physical property model, the variable physical property model, in which the fluid density, heat transfer coefficient, and viscosity change along with the temperature, has relatively lower heat transfer capacity and a little bit lower interface shear stress between the fluid and the solid heat transfer surfaces. Through the comparison between Re and Ri of the constant physical property model and the variable physical properties model, it can be concluded that the physical property changes of the fluid have gradually lower impact on flow and heat transfer processes along with the acceleration of the forced circulation of the fluid.

1.46 - Microwave and Radiofrequency Processing of Plant-Related Food Products

With increasing computer capabilities, numerical modeling of two-phase flows has developed significantly over the last few years. Although there are two main categories, namely 'one' fluid and 'two' fluid methods, the 'one' fluid methods are more commonly used for tracking or capturing the interface between two fluids. Level set (LS), volume-of-fluid (VOF), front tracking, marker-and-cell (MAC) and lattice Boltzmann (LB) methods are all 'one' fluid methods. It is clear that there is no perfect method; each method has advantages and disadvantages which make it more appropriate for one kind of problem than for others. For instance, a LS method will accurately compute the curvature and the normal to the interface, but tends to loss mass which is physically incorrect. On the other hand, a VOF method will conserve mass up to machine precision, but the computation of the curvature and normal to the interface is not as accurate. In order to minimize the disadvantages of these methods, several authors have used two or more methods together to model two-phase flows. This is the case for the CLSVOF (Couple Level Set Volume Of Fluid) method, where LS and VOF are coupled together in order to better capture the interface. In CLSVOF, the level set function is used to compute the interface curvature and normal to the interface, while the volume of fluid function is used to capture the interface. For two-phase flows in microchannels, surface tension forces play an important role in determining the dynamics of bubbles whereas gravitational forces are generally negligible. Also it is very important to consider the interaction between the boundaries and the fluids by prescribing or computing the correct contact angle between them. The commercial CFD code FLUENT allows the use of static constant angles, or the use of User Defined Functions (UDF) to compute the dynamic contact angles. It is inappropriate to use a static contact angle to model cases involving moving contact lines. For such cases a dynamic contact angle scheme should be implemented. In this study, FLUENT was used to model adiabatic and diabatic, time dependent two-phase flows. Since FLUENT already contains a VOF method, a LS method was implemented and coupled with VOF into FLUENT via UDFs. Furthermore, since the LS function, used to compute the surface tension force, ceases to be a signed distance to the interface even after one time step, a re-initialization equation was solved after each time step. This involved using a fifth order WENO (Weighted Essentially Non Oscillatory) scheme to discretize the space derivatives (otherwise oscillations of the interface occurred), and a first order Euler method for the time integration. In another part of the study, a 3D dynamic contact angle model based on volume fraction, interface reconstruction, and experimentally available advancing and receding static contact angles was also developed and implemented into FLUENT via UDFs. Several validations for the developed CLSVOF method and dynamic contact angle model are presented in this thesis, these includes a static bubble, a bubble rising in a stagnant liquid for Morton numbers ranging from 102 to 10-11, droplet deformation due to a vortex flow field, droplets spreading over a wall under the gravity effect and droplets sliding over a wall due to gravity. These validations demonstrated the high accuracy and the stability of our methods for modeling these phenomena. A heat and mass transfer model was also implemented into the commercial CFD code FLUENT for simulating of boiling (and condensation) heat transfer. Several simulations were presented with water and R134a as working fluids. The influence of the contact angle and the wall superheat was also studied.

Utilizing microwave irradiation, a fundamentally different method of the energy transfer, to the chemical process units can potentially be advantageous compared to the conventional heating, inter alia due to the selective nature of interaction of the microwaves with the matter. This doctoral dissertation addresses some of the aspects associated with the use of the microwave technology in a polyesterification plant. In this context, application of the microwave irradiation to a model polyestrerification reaction, using different types of the microwave applicators was studied. Influence of the microwave irradiation as an alternative form of heat for two selected separation techniques, which can potentially be used in a downstream recovery section in the polyesterification process (for the water purification and recovery unreacted dihydroxy alcohols), namely pervaporation and adsorption-desorption processes, were studied. The microwave-activated processes were compared with the conventionally heated ones focusing on possible reduction in the production time and energy consumption and increase in product quality. Study related to heating of the individual reagents of the polyesterification process in a multimode microwave oven showed that the heating time is several times shorter than with the conventional heating at the expense of a higher electric energy consumption. The results obtained for a model reaction system of adipic acid and neopentyl glycol under the conventional and microwave heating using the multimode microwave cavity did not show significant differences in terms of conversion and the end-product properties. Optimized (lower) usage of the microwave power during the process and effective scale up possibility compared to the multimode cavity were presented by applying the Internal Transmission Line (INTLI) microwave reactor to the studied reactor system (polyesterification reaction of maleic anhydride, phthalic anhydride and 1,2-propylene glycol). The INTLI allows for irradiation of the liquid phase from the inside of the reactor, thereby enabling better coupling of the microwave energy with the liquid mixture. For the selected process conditions, the total energy consumption of the INTLI reactor was up to a factor two lower. Comparison of desorption kinetics and desorption efficiencies for a model polar and non-polar molecules from 13X molecular sieves for two techniques, the microwave swing regeneration (MSR) and the temperature swing regeneration (TSR) showed that microwaves can help to overcome the heat transfer limitations by direct heating of the adsorbent. Significantly faster desorption processes were enabled under the microwave heating with the enhancement being more pronounced in the event of the polar compound. The MSR process runs faster even when the adsorbent temperature is quite lower than the gas temperature in TSR. It was verified that the microwaves do not affect the adsorption capacity of the molecular sieves after several consecutive adsorption-desorption cycles. Membrane pervaporation for dewatering of water/ethanol mixtures, using a hydrophilic membrane, were conducted under the microwave and conventional heating in a multimode microwave oven and a convection oven, respectively. Observations were made that at the conditions with higher water content in the feed, the water flux through the membrane was higher under the conventional heating. On contrary, with lower water in the feed, the opposite trend was found; the water flux through the membrane was higher under the microwave heating. Enhancement in the permeate flux under microwaves, compared to conventional heating, at higher ethanol concentrations in the feed can be explained on the basis of stronger coupling of microwaves with ethanol than water. Contrary to water, the dielectric loss of ethanol increases with increasing temperature; therefore, microwave dissipation is preponderant in the hot areas and can easily lead to local heating and the spatial temperature gradients.

There is a growing body of literature which reports the use of silicon carbide vessels to shield reaction mixtures during microwave heating. In this paper we use electromagnetic simulations and microwave experiments to show that silicon carbide vessels do not exclude the electric field, and that dielectric heating of reaction mixtures will take place in addition to heat transfer from the silicon carbide. The contribution of dielectric heating and heat transfer depends on the dielectric properties of the mixture, and the temperature at which the reaction is carried out. Solvents which remain microwave absorbent at high temperatures, such as ionic liquids, will heat under the direct influence of the electric field from 30-250 degrees C. Solvents which are less microwave absorbent at higher temperatures will be heated by heat-transfer only at temperatures in excess of 150 degrees C. The results presented in this paper suggest that the influence of the electric field cannot be neglected when interpreting microwave assisted synthesis experiments in silicon carbide vessels.

A fully coupled electromagnetic, heat transfer and multiphase porous media model for microwave heating of coal

Transformer is one of the most important pieces of equipment in power system. The insulation aging and lifespan of transformer are significantly affected by hot spot distributions of internal components inside. In the present paper, the electromagnetic losses of different components and heat transfer process in a three-phase forced oil circulation transformer (400 kVA-15 kV/400 V) are numerically studied with finite element method. The leakage magnetic flux and eddy current loss density for metal components and oil tank are carefully analyzed, and the effect of metal components’ electromagnetic loss on hot spot temperature of different components and oil flow in transformer is also studied. It is found that the surface current of metal components is generated by leakage magnetic flux, and surface current density is large when leakage magnetic flux concentrates. The effect caused by relative magnetic permeability of metal components is remarkable on electromagnetic loss of metal components and oil tank, while the effect caused by relative magnetic permeability of transformer tank is relatively small. Due to the mixing of metal components on oil flow, the heat transfer of core is enhanced, its hot spot temperature is lowered, and the hot spot locations of coil and core also change. These results are meaningful for further understanding of heat transfer process in transformer and important for the optimal design of transformer.