Tilford, Timothy James (2013) Numerical analysis of microwave processing problems using a multidomain solver approach. PhD thesis, University of Greenwich.

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Abstract

This work outlines the process undertaken in the formulation and validation of a numerical model for analysis of practical microwave processing problems. The proposed model adopts a novel multi-domain Eulerian-Lagrangian approach to the problem, defining two discrete numerical domains coupled through a set of data transfer algorithms. One of the numerical domains is defined for analysis of electromagnetic field distribution while the other is used for analysis of the thermophysical aspects of the problem. The thermophysical domain is restricted to the load being processed and is discretised in an Eulerian manner using an unstructured mesh for solution using a finite volume approach. The electromagnetic domain is discretised using a tensor-product rectilinear structured mesh for solution of Maxwell’s equations using a Yee finite difference time domain approach. The thermophysical load is represented within the electromagnetic domain through a mapped Lagrangian complex permittivity distribution rather than being defined explicitly. The two domains are coupled through mapping routines capable of defining the complex permittivity distribution within the electromagnetic domain and transferring the calculated power density distribution into the thermophysical domain. This interdomain coupling allows the meshes in the two domains to be non coincident, enabling the discretisation of the two domains to be completely independent of each other.

This approach to analysis of coupled microwave processing problems is novel and provides a number of significant benefits over conventional single-domain methods. The primary benefit of the approach is that the electromagnetic and thermophysical parts of the analysis can be handled by different solvers using differing meshes. This is a very significant advance as the optimal approach to solving one of the parts be be extremely inefficient or indeed unfeasible for the other. The approach allows electromagnetic fields irradiating complex geometries placed inside a rectilinear microwave ovens to be analyses using a tensor product solver. The solution of the electromagnetic field distribution is typically the most computationally expensive part of a coupled solution of microwave heating. The ability to use a Yee finite difference solver rather than a conformal FDTD or finite element approach provides a very significant reduction in computational expense, enabling more complex analyses to be performed. Solution of thermophysical aspects of the problem are most effectively tackled using an unstructured spatial discretisation in cases with complex geometries. The adoption of an unstructured finite volume approach for the thermophysical part of the analysis provides an analysis capability far beyond that of the finite difference approach typically used in analyses with a finite difference electromagnetic solver.

Further benefits stem from the inherent capability to alter the discretisation of the electromagnetic domain independently of the thermophysical domain, enabling cases with advection and/or rotation of the load within the oven to be considered with relative ease. Analysis of this type of problem is highly complex when using a single domain approach as the mesh needs to be redefined at regular interval during the solution. The capability to refine the discretisation of the electromagnetic domain also improves efficiency in cases where dielectric properties vary significantly during the process as mesh resolution can be varied as the process progresses.

The primary drawback with the adoption of the multidomain approach is that the load is represented in the electromagnetic domain as a mapped Langrian complex permittivity distribution rather than being explicitly defined as part of the domain discretisation. There are therefore issues relating to the smearing of material boundaries which may influence wave scattering across the boundary adversely affecting accuracy of the electric field solution.

In order to study the efficiency and accuracy of the approach a series of tests were conducted to assess the performance of each individual component of the analysis framework to ensure that these had been implemented effectively and to determine the magnitude of any apparent errors. The model was subsequently applied to a simple test case to ensure that the components were coupled in an effective manner. This test and validation process showed that individual components to be accurate and fit for purpose with errors due to data transfer between the two computational domains shown to be small. The results obtained from the validation case agreed relatively closely with experimental data demonstrating the implementation and efficacy of the model.

The model was subsequently validated against two practical microwave processing problems - thawing of food within a domestic microwave oven and polymer curing using a dual-section microwave system.

In the food thawing study, the solution obtained by the numerical model was validated against data obtained during an experimental study. The study was intended to meet the requirements of an industrial partner in research work that eliminated a range of simplifications adopted in alternate studies. The analysis therefore focussed on thawing of a challenging ’real-world’ material, placed in a complex shaped container. The load was placed on the rotating turntable of a domestic microwave oven.

Results obtained from the numerical simulations agree moderately well with experimentally derived data. Primary disparities between experimental data and numerical solutions would appear to stem from inaccuracies in modelling the solid-liquid phase change in a complex multi-component material coupled with the very significant variation in dielectric loss over the melting temperature range.

The microelectronics study focussed on curing of polymer materials in a microelectronics package using a dual-section microwave oven system. The requirement for this study was to predict the optimal process parameters for operation of the system. Numerical assessment of the development of key variables such as temperatures, degree of cure and stresses during the process was critical to this problem. Experimental measurements of these parameters during microwave processing were not feasible. Numerical comparisons of the microwave system with a conventional convection oven process have additionally been carried out. Key results from the study include optimal temperature profiles, final degree of cure distribution and residual stress magnitudes. Numerical data from the analyses are being integrated into an experimental study as part of ongoing work.

An overall assessment of the numerical approach would indicate that it is a viable method of efficiently obtaining solutions to practical microwave processing problems. Further research is required to assess the influence of the smeared dielectric boundary in the finite difference solver on reflection, refraction and focussing effects on the accuracy of the numerical solution.

Item Type:	Thesis (PhD)
Uncontrolled Keywords:	numerical modelling, microwave processing problems,
Subjects:	Q Science > QA Mathematics
Faculty / School / Research Centre / Research Group:	Faculty of Liberal Arts & Sciences
Last Modified:	14 Oct 2016 09:28
URI:	http://gala.gre.ac.uk/id/eprint/11941

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