This paper describes some contributions to Computational Fluid Dynamics (CFD) made by Professor Brian Spalding whilst working at Concentration Heat and Momentum Limited (CHAM) during the period 1993–2004. The discussions focus principally on those areas with which the author had been directly involved with Brian and colleagues at CHAM. Some of the material is now well known in the field, and some not, but familiar material is not submitted as a new or original contribution, but rather to provide examples of Brian’s unique approach to solving practical CFD problems and to explain their origin. The following areas of work are described together with their influence in the field, where this is appropriate: the differential-equation wall-distance calculator; the LVEL model of turbulence; the IMMERSOL model of thermal radiation; virtual mass modelling in Eulerian–Eulerian descriptions of two-phase flow; a space-marching method for hyperbolic and transonic flow; and an automatic convergence-promoting algorithm for SIMPLE-based CFD codes.

Brian Spalding: Some Contributions to Computational Fluid Dynamics During the Period 1993 to 2004

Semiconductors are at the heart of electronic devices such as computers, mobile phones, avionics systems, telecommunication racks, etc. Power dissipation from semiconductor devices is continuing to increase due to the growth in the number of transistors on the silicon chip as predicted by Moore's Law. Thermal management techniques, used to dissipate this power, are becoming more and more challenging to design. Air cooling of electronic components is the preferred method for many designs where the air flow is characterised as being in the laminar-to-turbulent transitional region.

Over the last fifteen years there has been a dramatic take-up of Computational Fluid Dynamics (CFD) technology in the electronics industry to simulate the airflow and temperatures in electronic systems. These codes solve the Reynolds Averaged Navier-Stokes (RANS) equations for momentum and turbulence. RANS models are popular as they are much quicker to solve than time-dependent models such as Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS).

At present the majority of thermal design engineers use the standard k-e model which is a high Reynolds number model. This is because there is limited knowledge on the benefit of using low Reynolds number models in the electronics cooling industry. This Ph.D. investigated and developed low Reynolds number models for use in electronics cooling CFD calculations. Nine turbulence models were implemented and validated in the in-house CFD code PHYSICA. This includes three 
zero-equation, two single equation, and four zonal models. All of these models are described in the public literature except the following two models which were developed in this study:

AUTO_CAP: This zero-equation model automates the existing LVEL_CAP model available within the commercial CFD code FLOTHERM.

ke I kl: This zonal model uses a new approach to blend the k — l model used at the wall with the k-e model used to predict the bulk airflow.

Validation of these turbulence models was undertaken on eight different test cases. This included the detailed experimental work undertaken by Meinders. Results show that the ke I kl model provides the most accurate flow predictions. For prediction of temperature there was no clear favourite. This was probably due to the use of the universal log-law function in this study. A generalised wall function may be more appropriate.

Results from this research have been disseminated through a total of nine peer-reviewed conference and journal publications, evidence of the interest the topic of this investigation generates amongst electronic packaging engineers.

Kulvir Kaur Dhinsa

Papers

Development and application of low Reynolds number turbulence models for air-cooled electronics