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 two dimensional unstructured staggered mesh method with special treatment of tangential velocity

A two dimensional staggered unstructured discretisation scheme for the solution of fluid flow problems has been developed. This scheme stores and solves the velocity vector resolutes normal and parallel to each cell face and other scalar variables (pressure, temperature) are stored at cell centres. The coupled momentum; continuity and energy equations are solved, using the well known pressure correction algorithm SIMPLE. The method is tested for accuracy and convergence behaviour against standard cell-centre solutions in a number of benchmark problems: The Lid-Driven Cavity, Natural Convection in a Cavity and the Melting of Gallium in a rectangular domain.

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.

Numerical modelling for electromagnetic processing of materials

Electromagnetic processing of materials (EPM) is one of the most widely practiced and fast growing applications of magnetic and electric forces to fluid flow. EPM is encountered in both industrial processes and laboratory investigations. Applications range in scale from nano-particle manipulation to tonnes of liquid metal treated in the presence of various configurations of magnetic fields. Some of these processes are specifically designed and made possible by the use of the electromagnetic force, like the magnetic levitation of liquid droplets, whilst others involve electric currents essential for electrothermal or electrochemical reasons, for instance, in electrolytic metal production and in induction melting. An insight for the range of established and novel EPM applications can be found in the review presented by Asai [1] in the EPM-2003 conference proceedings.

Modelling and optimization of a pneumatic microfeeder system

This paper presents modelling and design optimization of a microfeeder which, as part of a microassembly system, is used for contactless object delivery. The microfeeder consists of an array of microactuators which are controlled by electrostatic actuation and used for maneuvering outcoming air jet for object hovering and delibery. The airflow behaviour in the microactuator is analysed by means of fluid mechanics and Computational Fluid Dynamics (CFD) simulation from three aspects, theoretical analysis, initial design assessment, and design modifications. The focus is put on the basic types of the microfeeder structure and the effects of structural details to the systematic performance. The structural pattern of the microactuator for forming airflow nozzle is identified and two design plans are proposed as basic structure patterns of pneumatic microactuators. The optimized design numerically shows the ability of delivering objects. This paper analyses the flow distribution pattern in microactuators and points out a way for effective design of pneumatic microfeeder systems. The optimization strategy provided by the present paper has close relevance to the design and manufacture of pneumatic microfeeder systems.

Fundamentals of steady state, non-Newtonian rimming flow

Rimming flow on the inner surface of a horizontal rotating cylinder is investigated. Using a scale analysis, a theoretical description is obtained for steady-state non-Newtonian flow. Simple lubrication theory is applied since the Reynolds number is small and the liquid film is thin. Since the Deborah number is very small the flow is viscometric. The shear-thinning number, which characterizes the shear-thinning effect, may be small or large. A general constitutive law for this kind of flow requires only a single function relating shear stress and shear rate that corresponds to a generalized Newtonian liquid. For this case the run-off condition for rimming flow is derived. Provided the run-off condition is satisfied, the existence of a continuous steady-state solution is proved. The rheological models, which show Newtonian behavior at low shear rates with transition to power-law shear thinning at moderate shear rates, are considered. Numerical results are carried out for the Carreau and Ellis models, which exhibit Newtonian behavior near the free surface and power-law behavior near the wall of the rotating cylinder.

Comparison between fluid simulations and experiments in inductively coupled argon/chlorine plasmas

Comparisons of 2D fluid simulations with experimental measurements of Ar/Cl-2 plasmas in a low-pressure inductively coupled reactor are reported. Simulations show that the wall recombination coefficient of Cl atom (gamma) is a crucial parameter of the model and that neutral densities are very sensitive to its variations. The best agreement between model and experiment is obtained for gamma = 0.02, which is much lower than the value predicted for stainless steel walls (gamma = 0.6). This is consistent with reactor wall contaminations classically observed in such discharges. The electron density, negative ion fraction and Cl atom density have been investigated under various conditions of chlorine and argon concentrations, gas pressure and applied rf input power. The plasma electronegativity decreases with rf power and increases with chlorine concentration. At high pressure, the power absorption and distribution of charged particles become more localized below the quartz window. Although the experimental trends are well reproduced by the simulations, the calculated charged particle densities are systematically overestimated by a factor of 3-5. The reasons for this discrepancy are discussed in the paper.

Example of Data Telemetry for Biomedical Applications: An In Vivo Experiment

This letter describes a data telemetry biomedical experiment. An implant, consisting of a biometric data sensor, electronics, an antenna, and a biocompatible capsule, is described. All the elements were co-designed in order to maximize the transmission distance. The device was implanted in a pig for an in vivo experiment of temperature monitoring.

Structure of turbulent flow over arrays of cubical roughness

The structure of turbulent flow over large roughness consisting of regular arrays of cubical obstacles is investigated numerically under constant pressure gradient conditions. Results are analysed in terms of first- and second-order statistics, by visualization of instantaneous flow fields and by conditional averaging. The accuracy of the simulations is established by detailed comparisons of first- and second-order statistics with wind-tunnel measurements. Coherent structures in the log region are investigated. Structure angles are computed from two-point correlations, and quadrant analysis is performed to determine the relative importance of Q2 and Q4 events (ejections and sweeps) as a function of height above the roughness. Flow visualization shows the existence of low-momentum regions (LMRs) as well as vortical structures throughout the log layer. Filtering techniques are used to reveal instantaneous examples of the association of the vortices with the LMRs, and linear stochastic estimation and conditional averaging are employed to deduce their statistical properties. The conditional averaging results reveal the presence of LMRs and regions of Q2 and Q4 events that appear to be associated with hairpin-like vortices, but a quantitative correspondence between the sizes of the vortices and those of the LMRs is difficult to establish; a simple estimate of the ratio of the vortex width to the LMR width gives a value that is several times larger than the corresponding ratio over smooth walls. The shape and inclination of the vortices and their spatial organization are compared to recent findings over smooth walls. Characteristic length scales are shown to scale linearly with height in the log region. Whilst there are striking qualitative similarities with smooth walls, there are also important differences in detail regarding: (i) structure angles and sizes and their dependence on distance from the rough surface; (ii) the flow structure close to the roughness; (iii) the roles of inflows into and outflows from cavities within the roughness; (iv) larger vortices on the rough wall compared to the smooth wall; (v) the effect of the different generation mechanism at the wall in setting the scales of structures.