Investigation into the performance of turbulence models for fluid flow and heat transfer phenomena in electronic applications

Computational Fluid Dynamics (CFD) is gradually becoming a powerful and almost essential tool for the design, development and optimization of engineering applications. However the mathematical modelling of the erratic turbulent motion remains the key issue when tackling such flow phenomena. The reliability of CFD analysis depends heavily on the turbulence model employed together with the wall functions implemented. In order to resolve the abrupt changes in the turbulent energy and other parameters situated at near wall regions a particularly fine mesh is necessary which inevitably increases the computer storage and run-time requirements. Turbulence modelling can be considered to be one of the three key elements in CFD. Precise mathematical theories have evolved for the other two key elements, grid generation and algorithm development. The principal objective of turbulence modelling is to enhance computational procedures of efficient accuracy to reproduce the main structures of three dimensional fluid flows. The flow within an electronic system can be characterized as being in a transitional state due to the low velocities and relatively small dimensions encountered. This paper presents simulated CFD results for an investigation into the predictive capability of turbulence models when considering both fluid flow and heat transfer phenomena. Also a new two-layer hybrid kε / kl turbulence model for electronic application areas will be presented which holds the advantages of being cheap in terms of the computational mesh required and is also economical with regards to run-time.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

Investigation into the performance of turbulence models for fluid flow and heat transfer phenomena in electronic applications

Heat is extracted away from an electronic package by convection, conduction, and/or radiation. The amount of heat extracted by forced convection using air is highly dependent on the characteristics of the airflow around the package which includes its velocity and direction. Turbulence in the air is also important and is required to be modeled accurately in thermal design codes that use computational fluid dynamics (CFD). During air cooling the flow can be classified as laminar, transitional, or turbulent. In electronics systems, the flow around the packages is usually in the transition region, which lies between laminar and turbulent flow. This requires a low-Reynolds number numerical model to fully capture the impact of turbulence on the fluid flow calculations. This paper provides comparisons between a number of turbulence models with experimental data. These models included the distance from the nearest wall and the local velocity (LVEL), Wolfshtein, Norris and Reynolds, k-ε, k-ω, shear-stress transport (SST), and kε/kl models. Results show that in terms of the fluid flow calculations most of the models capture the difficult wake recirculation region behind the package reasonably well, although for packages whose heights cause a high degree of recirculation behind the package the SST model appears to struggle. The paper also demonstrates the sensitivity of the models to changes in the mesh density; this study is aimed specifically at thermal design engineers as mesh independent simulations are rarely conducted in an industrial environment.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Heat and mass transfer in two-phase porous materials under intensive microwave heating

Computational results for the intensive microwave heating of porous materials are presented in this work. A multi-phase porous media model has been developed to predict the heating mechanism. Combined finite difference time-domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of both temperature and moisture fields as well as energy penetration as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

Coupled 3-D finite difference time domain and finite volume methods for solving microwave heating in porous media

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of temperature and moisture fields as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

Turbulence modelling and its effects on electronic systems

This paper presents simulated computational fluid dynamics (CFD) results for comparison against experimental data. The performance of four turbulence models has been assessed for electronic application areas considering both fluid flow and heat transfer phenomenon. CFD is vast becoming a powerful and almost essential tool for design, development and optimization in engineering problems. However turbulence models remain to be the key problem issue when tackling such flow phenomena. The reliability of CFD analysis depends heavily on the performance of the turbulence model employed together with the wall functions implemented. To be able to resolve the abrupt changes in the turbulent energy and other parameters near the wall a particularly fine mesh is necessary which unfortunately increases the computer storage capacity requirements. The objective of turbulence modelling is to enhance computational procdures of sufficient acccuracy and generality for engineers to anticipate the Reynolds stresses and the scalar transport terms.

A comprehensive copper stockpile leach model: background and parameter sensitivity

The design and development of a comprehensive computational model of a copper stockpile leach process is summarized. The computational fluid dynamic software framework PHYSICA+ and various phenomena were used to model transport phenomena, mineral reaction kinetics, bacterial effects, and heat, energy and acid balances for the overall leach process. In this paper, the performance of the model is investigated, in particular its sensitvity to particle size and ore permeability. A combination of literature and laboratory sources was used to parameterize the model. The simulation results from the leach model are compared with closely controlled column pilot scale tests. The main performance characteristics (e.g. copper recovery rate) predicted by the model compare reasonably well with the experimental data and clearly reflect the qualitiative behavior of the process in many respects. The model is used to provide a measure of the sensitivity of ore permeability on leach behavior, and simulation results are examined for several different particle size distributions.

Explicit finite volume modeling of aircraft anti-icing and de-icing

In this paper, a runback water and ice prediction model is extended to anti-icing and thermal de-icing situations. The resulting coupled equations that govern thin-film flow, ice accretion, and heat conduction in the multilayered system substrate-ice-water are solved using an explicit finite volume approach. The procedure is implemented in the three-dimensional icing code ICECREMO2, and both structured and unstructured grids can be considered. Numerical results are presented to compare the present code simulations to some data provided by other ice prediction codes and to show the capabilities of the present numerical tool.