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.

Maximising heat transfer efficiency in the cold crucible induction melting process

Induction heating is an efficient method used to melt electrically conductive materials, particularly if melting takes place in a ceramic crucible. This form of melting is particularly good for alloys, as electromagnetic forces set up by the induction coil lead to vigorous stirring of the melt ensuring homogeneity and uniformity in temperature. However, for certain reactive alloys, or where high purity is required, ceramic crucibles cannot be used, but a water-cooled segmented copper crucible is employed instead. Water cooling prevents meltdown or distortion of the metal wall, but much of the energy goes into the coolant. To reduce this loss, the electromagnetic force generated by the coil is used to push the melt away from the walls and so minimise contact with water-cooled surfaces. Even then, heat is lost through the crucible base where contact is inevitable. In a collaborative programme between Greenwich and Birmingham Universities, computer modelling has been used in conjunction with experiments to improve the superheat attainable in the melt for a,number of alloys, especially for y-TiAl intermetallics to cast aeroengine turbine blades. The model solves the discretised form of the turbulent Navier-Stokes, thermal energy conservation and Maxwell equations using a Spectral Collocation technique. The time-varying melt envelope is followed explicitly during the computation using an adaptive mesh. This paper briefly describes the mathematical model used to represent the interaction between the magnetic field, fluid flow, heat transfer and change of phase in the crucible and identifies the proportions of energy used in the melt, lost in the crucible base and in the crucible walls. The role of turbulence is highlighted as important in controlling heat losses and turbulence damping is introduced as a means of improving superheat. Model validation is against experimental results and shows good agreement with measured temperatures and energy losses in the cooling fluid throughout the melting cycle.

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.

A computational model for defect prediction in shape castings based on the interaction of free surface flow, heat transfer, and solidification phenomena

High-integrity castings require sophisticated design and manufacturing procedures to ensure they are essentially macrodefect free. Unfortunately, an important class of such defects—macroporosity, misruns, and pipe shrinkage—are all functions of the interactions of free surface flow, heat transfer, and solidication in complex geometries. Because these defects arise as an interaction of the preceding continuum phenomena, genuinely predictive models of these defects must represent these interactions explicitly. This work describes an attempt to model the formation of macrodefects explicitly as a function of the interacting continuum phenomena in arbitrarily complex three-dimensional geometries. The computational approach exploits a compatible set of finite volume procedures extended to unstructured meshes. The implementation of the model is described together with its testing and a measure of validation. The model demonstrates the potential to predict reliably shrinkage macroporosity, misruns, and pipe shrinkage directly as a result of interactions among free-surface fluid flow, heat transfer, and solidification.

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.

Unstructured staggered mesh methods for fluid flow, heat transfer and phase change

Unstructured grid meshes used in most commercial CFD codes inevitably adopt collocated variable solution schemes. These schemes have several shortcomings, mainly due to the interpolation of the pressure gradient, that lead to slow convergence. In this publication we show how it is possible to use a much more stable staggered mesh arrangement in an unstructured code. Several alternative groupings of variables are investigated in a search for the optimum scheme.

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.

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.

Heat transfer by impinging jets on a moving strip

This paper deals with heat transfer on a moving plate by mean of an impinging jet. Three different turbulence models are used and it turns out that Lam-Bremhorst model is in good agreement with measurements when Re is lower that 5000. In case of moving strip (ratio m=V strip/V jet lower than 1/3), there is almost no effect of m on Nusselt distribution in the stagnation region.

A computational model of coupled heat and moisture transfer with phase change in granular sugar during varying environmental conditions

As part of a comprehensive effort to predict the development of caking in granular materials, a mathematical model is introduced to model simultaneous heat and moisture transfer with phase change in porous media when undergoing temperature oscillations/cycling. The resulting model partial differential equations were solved using finite-volume procedures in the context of the PHYSICA framework and then applied to the analysis of sugar in storage. The influence of temperature on absorption/desorption and diffusion coefficients is coupled into the transport equations. The temperature profile, the depth of penetration of the temperature oscillation into the bulk solid, and the solids moisture content distribution were first calculated, and these proved to be in good agreement with experimental data. Then, the influence of temperature oscillation on absolute humidity, moisture concentration, and moisture migration for different parameters and boundary conditions was examined. As expected, the results show that moisture near boundary regions responds faster than farther away from them with surface temperature changes. The moisture absorption and desorption in materials occurs mainly near boundary regions (where interactions with the environment are more pronounced). Small amounts of solids moisture content, driven by both temperature and vapour concentration gradients, migrate between boundary and center with oscillating temperature.

Dynamics of an axisymmetric electromagnetic ‘crucible’ melting

Different industrial induction melting processes involve free surface and melt-solid interface of the liquid metal subject to dynamic change during the technological operation. Simulation of the liquid metal dynamics requires to solve the non-linear, coupled hydrodynamic-electromagnetic-heat transfer problem accounting for the time development of the liquid metal free boundary with a suitable turbulent viscosity model. The present paper describes a numerical solution method applicable for various axisymmetric induction melting processes, such as, crucible with free top surface, levitation, semi-levitation, cold crucible and similar melting techniques. The presented results in the cases of semi-levitation and crucible with free top surface meltings demonstrate oscillating transient behaviour of the free metal surface indicating the presence of gravity-inertial-electromagnetic waves which are coupled to the internal fluid flow generated by both the rotational and potential parts of the electromagnetic force.

PHYSICA - A software environment for the modelling of multi-physics phenomena

A brief description of a software environment in FORTRAN77 for the modelling of multi-physics phenomena is given. The numerical approach is based on finite volume methods but extended to unstructured meshes (ie. FV-UM). A range of interacting solution procedures for turbulent fluid flow, heat transfer with solidification/melting and elasto-visco-plastic solid mechanics are implemented in the first version of PHYSICA, which will be released in source code form to the academic community in late 1995.

Modelling the fluid dynamics and coupled phenomena in arc weld pools

A 3D model of melt pool created by a moving arc type heat sources has been developed. The model solves the equations of turbulent fluid flow, heat transfer and electromagnetic field to demonstrate the flow behaviour phase-change in the pool. The coupled effects of buoyancy, capillary (Marangoni) and electromagnetic (Lorentz) forces are included within an unstructured finite volume mesh environment. The movement of the welding arc along the workpiece is accomplished via a moving co-ordinator system. Additionally a method enabling movement of the weld pool surface by fluid convection is presented whereby the mesh in the liquid region is allowed to move through a free surface. The surface grid lines move to restore equilibrium at the end of each computational time step and interior grid points then adjust following the solution of a Laplace equation.

Three-phase computations of the continuous casting process

In this paper, the continuous casting process for steel slab production is modelled using a mult-physics approach. For this purpose, a Finite Volume (FV) numerical model was constructed in 3D, with the following characteristics: Time dependent, turbulent fluid flow and heat transfer in the molten steel and flux regions, solidification of the skin layer, under prescribed heat loss boundary conditions, particle tracking simulation of argon bubbles injected with the metal into the mould, full coupling between bubbles and liquid through buoyancy and interfacial forces using a novel gas accumulation technique, and a full transient simulation of flux-metal interface behaviour under the influence of gravity and fluid inertial forces and bubble plume buoyancy. The unstructure mesh FV code PHYSICA developed at Greenwich was used for carry out the simulations with physical process data and properties supplied by IRSID SA.

The development and validation of computational MHD techniques for the modelling of metal production processes

Magnetic fields are used in a number of processes related to the extraction of metals, production of alloys and the shaping of metal components. Computational techniques have an increasingly important role to play in the simulation of such processes, since it is often difficult or very costly to conduct experiments in the high temperature conditions encountered and the complex interaction of fluid flow, heat transfer and magnetic fields means simple analytic models are often far removed from reality. In this paper an overview of the computational activity at the University of Greenwich is given in this area, covering the past ten years. The overview is given from the point of view of the modeller and within the space limitations imposed by the format it covers the numerical methods used, attempts at validation against experiments or analytic procedures; it highlights successes, but also some failures. A broad range of models is covered in the review (and accompanying lecture), used to simulate (a) A-C field applications: induction melting, magnetic confinement and levitation, casting and (b) D-C field applications such as: arc welding and aluminium electroloysis. Most of these processes involve phase change of the metal (melting or solidification), the presence of a dynamic free surface and turbulent flow. These issues affect accuracy and need to be address by the modeller.