The numerical simulation of noncharring thermal degradation and its application to the prediction of compartment fire development

In this paper we present some work concerned with the development and testing of a simple solid fuel combustion model incorporated within a Computational Fluid Dynamics (CFD) framework. The model is intended for use in engineering applications of fire field modeling and represents an extension of this technique to situations involving the combustion of solid fuels. The CFD model is coupled with a simple thermal pyrolysis model for combustible solid noncharring fuels, a six-flux radiation model and an eddy-dissipation model for gaseous combustion. The model is then used to simulate a series of small-scale room fire experiments in which the target solid fuel is polymethylmethacrylate. The numerical predictions produced by this coupled model are found to be in very good agreement with experimental data. Furthermore, numerical predictions of the relationship between the air entrained into the fire compartment and the ventilation factor produce a characteristic linear correlation with constant of proportionality 0.38 kg/sm5/12. The simulation results also suggest that the model is capable of predicting the onset of "flashover" type behavior within the fire compartment.

The numerical simulation of enclosure fires using a Cfd fire field model coupled with a pyrolysis based solid fuel combustion submodel—a first approximation

In this paper, we present some early work concerned with the development of a simple solid fuel combustion model incorporated within a Computational Fluid Dynamics (CFD) framework. The model is intended for use in engineering applications of fire field modeling and represents an extension of this technique to situations involving the combustion of solid cellulosic fuels. A simple solid fuel combustion model consisting of a thermal pyrolysis model, a six flux radiation model and an eddy-dissipation model for gaseous combustion have been developed and implemented within the CFD code CFDS-FLOW3D. The model is briefly described and demonstrated through two applications involving fire spread in a compartment with a plywood lined ceiling. The two scenarios considered involve a fire in an open and closed compartment. The model is shown to be able to qualitatively predict behaviors similar to "flashover"—in the case of the open room—and "backdraft"— in the case of the initially closed room.

Numerical simulation of the mass loss process in pyrolizing char materials

We present here a decoupling technique to tackle the entanglement of the nonlinear boundary condition and the movement of the char/virgin front for a thermal pyrolysis model for charring materials. Standard numerical techniques to solve moving front problems — often referred to as Stefan problems — encounter difficulties when dealing with nonlinear boundaries. While special integral methods have been developed to solve this problem, they suffer from several limitations which the technique described here overcomes. The newly developed technique is compared with the exact analytical solutions for some simple ideal situations which demonstrate that the numerical method is capable of producing accurate numerical solutions. The pyrolysis model is also used to simulate the mass loss process from a white pine sample exposed to a constant radiative flux in a nitrogen atmosphere. Comparison with experimental results demonstrates that the predictions of mass loss rates and temperature profile within the solid material are in good agreement with the experiment.

The numerical simulation of the noncharring pyrolysis process and fire development within a compartment

A pyrolysis model for noncharring solid fuels is presented in this paper. Model predictions are compared with experimental data for the mass loss rates of polymethylmethacrylate (PMMA) and very good agreement is achieved. Using a three-dimensional CFD environment, the pyrolysis model is then coupled with a gas-phase combustion model and a thermal radiation model to simulate fire development within a small compartment. The numerical predictions produced by this coupled model are found to be in very good agreement with experimental data. Furthermore, numerical predictions of the relationship between the air entrained into the fire compartment and the ventilation factor produce a characteristic post-flashover linear correlation with constant of proportionality 0.38 kg/sm5=2. The simulation results also suggest that the model is capable of predicting the onset of "flashover" and "post-flashover" type behaviour within the fire compartment.

The numerical simulation of fire spread within a compartment using an integrated gas and solid phase combustion model

An integrated fire spread model is presented in this study including several sub-models representing different phenomena of gaseous and solid combustion. The integrated model comprises of the following sub-models: a gaseous combustion model, a thermal radiation model that includes the effects of soot, and a pyrolysis model for charring combustible solids. The interaction of the gaseous and solid phases are linked together through the boundary conditions of the governing equations for the flow domain and the solid region respectively. The integrated model is used to simulate a fire spread experiment conducted in a half-scale test compartment. Good qualitative and reasonable quantitative agreement is achieved between the experiment and numerical predictions.

Reliability analysis of flip chip designs via computer simulation

A flip chip component is a silicon chip mounted to a substrate with the active area facing the substrate. This paper presents the results of an investigation into the relationship between a number of important material properties and geometric parameters on the thermal-mechanical fatigue reliability of a standard flip chip design and a flip chip design with the use of microvias. Computer modeling has been used to analyze the mechanical conditions of flip chips under cyclic thermal loading where the Coffin-Manson empirical relationship has been used to predict the life time of the solder interconnects. The material properties and geometry parameters that have been investigated are the Young's modulus, the coefficient of thermal expansion (CTE) of the underfill, the out-of-plane CTE (CTEz) of the substrate, the thickness of the substrate, and the standoff height. When these parameters vary, the predicted life-times are calculated and some of the features of the results are explained. By comparing the predicted lifetimes of the two designs and the strain conditions under thermal loading, the local CTE mismatch has been found to be one of most important factors in defining the reliability of flip chips with microvias.

Low Reynolds number turbulence models for accurate thermal simulations of electronic components

The electronics industry and the problems associated with the cooling of microelectronic equipment are developing rapidly. Thermal engineers now find it necessary to consider the complex area of equipment cooling at some level. This continually growing industry also faces heightened pressure from consumers to provide electronic product miniaturization, which in itself increases the demand for accurate thermal management predictions to assure product reliability. Computational fluid dynamics (CFD) is considered a powerful and almost essential tool for the design, development and optimization of engineering applications. CFD is now widely used within the electronics packaging design community to thermally characterize the performance of both the electronic component and system environment. This paper discusses CFD results for a large variety of investigated turbulence models. Comparison against experimental data illustrates the predictive accuracy of currently used models and highlights the growing demand for greater mathematical modelling accuracy with regards to thermal characterization. Also a newly formulated low Reynolds number (i.e. transitional) turbulence model is proposed with emphasis on hybrid techniques.

Numerical simulation of incompressible flow problems using an unstructured staggered mesh method

A number of two dimensional staggered unstructured discretisation schemes for the solution of fluid flow and heat transfer problems have been developed. All schemes store and solve velocity vector components at cell faces with scalar variables solved at cell centres. The velocity is resolved into face-normal and face-parallel components and the various schemes investigated differ in the treatment of the parallel component. Steady-state and time-dependent fluid flow and thermal energy equations are solved with the well known pressure correction scheme, SIMPLE, employed to couple continuity and momentum. The numerical methods developed are tested on well known benchmark cases: the Lid-Driven Cavity, Natural Convection in a Cavity and Melting of Gallium in a rectangular domain. The results obtained are shown to be comparable to benchmark, but with accuracy dependent on scheme selection.

Thermal-mechanical modelling of power electronic module packaging

In this paper the reliability of the isolation substrate and chip mountdown solder interconnect of power modules under thermal-mechanical loading has been analysed using a numerical modelling approach. The damage indicators such as the peel stress and the accumulated plastic work density in solder interconnect are calculated for a range of geometrical design parameters, and the effects of these parameters on the reliability are studied by using a combination of the finite element analysis (FEA) method and optimisation techniques. The sensitivities of the reliability of the isolation substrate and solder interconnect to the changes of the design parameters are obtained and optimal designs are studied using response surface approximation and gradient optimization method

Study of the thermal stress in a Pb-free half-bump solder joint under current stressing

The thermal stress in a Sn3.5Ag1Cu half-bump solder joint under a 3.82×108 A/m2 current stressing was analyzed using a coupled-field simulation. Substantial thermal stress accumulated around the Al-to-solder interface, especially in the Ni+(Ni,Cu)3Sn4 layer, where a maximal stress of 138 MPa was identified. The stress gradient in the Ni layer was about 1.67×1013 Pa/m, resulting in a stress migration force of 1.82×10-16 N, which is comparable to the electromigration force, 2.82×10-16 N. Dissolution of the Ni+(Ni,Cu)3Sn4 layer, void formation with cracks at the anode side, and extrusions at the cathode side were observed

Numerical simulation of microwave thawing using a coupled solver approach

Thawing of a frozen food product in a domestic microwave oven is numerically simulated using a coupled solver approach. The approach consists of a dedicated electromagnetic FDTD solver and a closely coupled UFVM multi-physics package. Two overlapping numerical meshes are defined; the food material and container were meshed for heat transfer and phase change solution, whilst the microwave oven cavity and waveguide were meshed for the microwave irradiation. The two solution domains were linked using a cross-mapping routine. This approach allowed the rotation of the food load to be captured. Power densities obtained on the structured FDTD mesh were interpolated onto the UFVM mesh for each timestep/turntable position. The UFVM solver utilised the power density data to advance the temperature and phase distribution solution. The temperature-dependant dielectric and thermo-physical properties of the food load were updated prior to revising the electromagnetic solution. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Two scenarios were investigated: a centric and eccentric placement on the turntable. Developing temperature fields predicted by the numerical solution are validated against experimentally obtained data. Presented results indicate the feasibility of fully coupled simulations of the microwave heating of a frozen product. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical simulation of encapsulant curing within a variable frequency microwave processing system

Curing of encapsulant material in a simplified microelectronics package using an open oven Variable Frequency Microwave (VFM) system is numerically simulated using a coupled solver approach. A numerical framework capable of simulating electromagnetic field distribution within the oven system, plus heat transfer, cure rate, degree of cure and thermally induced stresses within the encapsulant material is presented. The discrete physical processes have been integrated into a fully coupled solution, enabling usefully accurate results to be generated. Numerical results showing the heating and curing of the encapsulant material have been obtained and are presented in this contribution. The requirement to capture inter-process coupling and the variation in dielectric and thermophysical material properties is discussed and illustrated with simulation results.

Computer simulation of crack propagation in power electronics module solder joints

A numerical modelling method for the analysis of solder joint damage and crack propagation has been described in this paper. The method is based on the disturbed state concept. Under cyclic thermal-mechanical loading conditions, the level of damage that occurs in solder joints is assumed to be a simple monotonic scalar function of the accumulated equivalent plastic strain. The increase of damage leads to crack initiation and propagation. By tracking the evolution of the damage level in solder joints, crack propagation path and rate can be simulated using Finite Element Analysis method. The discussions are focused on issues in the implementation of the method. The technique of speeding up the simulation and the mesh dependency issues are analysed. As an example of the application of this method, crack propagation in solder joints of power electronics modules under cyclic thermal-mechanical loading conditions has been analyzed and the predicted cracked area size after 3000 loading cycles is consistent with experimental results.

Computer simulation of aluminium wirebonds with globtop in power electronics modules

In this paper, computer modelling techniques are used to analyse the effects of globtops on the reliability of aluminium wirebonds in power electronics modules under cyclic thermal-mechanical loading conditions. The sensitivity of the wirehond reliability to the changes of the geometric and the material property parameters of wirebond globtop are evaluated and the optimal combination of the Young's modulus and the coefficient of thermal expansion have been predicted.

Numerical simulation of heat transfer in rectangular microchannel

Numerical simulation of heat transfer in a high aspect ratio rectangular microchannel with heat sinks has been conducted, similar to an experimental study. Three channel heights measuring 0.3 mm, 0.6mmand 1mmare considered and the Reynolds number varies from 300 to 2360, based on the hydraulic diameter. Simulation starts with the validation study on the Nusselt number and the Poiseuille number variations along the channel streamwise direction. It is found that the predicted Nusselt number has shown very good agreement with the theoretical estimation, but some discrepancies are noted in the Poiseuille number comparison. This observation however is in consistent with conclusions made by other researchers for the same flow problem. Simulation continues on the evaluation of heat transfer characteristics, namely the friction factor and the thermal resistance. It is found that noticeable scaling effect happens at small channel height of 0.3 mm and the predicted friction factor agrees fairly well with an experimental based correlation. Present simulation further reveals that the thermal resistance is low at small channel height, indicating that the heat transfer performance can be enhanced with the decrease of the channel height.