D. J. de Kock

Minimizing the effect of automotive pollution in urban geometry using mathematical optimization

Abstract One of the factors that needs to be considered during the layout of new urban geometry (e.g. street direction, spacing and width, building height restrictions) is the effect of the air pollution associated with the automotive transport that would use routes in this urban area. Although the pollution is generated at street level, its effect can be widespread due to interaction of the pollutant dispersion and diffusion with the wind speed and direction. In order to study the effect of a new urban geometry on the pollutant levels and dispersion, a very time-consuming experimental or parametric numerical study would have to be performed. This paper proposes an alternative approach, that of combining mathematical optimization with the techniques of computational fluid dynamics (CFD). In essence, the meteorological information as represented by a wind rose (wind speed and direction), is used to calculate pollutant levels as a function of urban geometry variables: street canyon depth and street canyon width. The pollutant source specified in conjunction with a traffic scenario with CO is used as pollutant. The main aim of the study is to be able to suggest the most beneficial configuration of an idealized urban geometry that minimizes the peak pollutant levels due to assumed traffic distributions. This study uses two mathematical optimization methods. The first method is implemented through a successive maximization–minimization approach, while the second method determines the location of saddle points of the pollutant level, considered as a function of urban geometry and wind rose. Locally, a saddle point gives the best urban geometry for the worst meteorological scenario. The commercial CFD code, STAR-CD, is coupled with a version of the DYNAMIC-Q optimization algorithm of Snyman, first to successively locate maxima and minima in a min–max approach; and then to locate saddle points. It is shown that the saddle-point method is more cost-effective. The methodology presented in this paper can readily be extended to optimize traffic patterns for existing geometry or in the development of geometry modification for pollution control or toxic releases.

Minimisation of heat sink mass using mathematical optimisation

Heat sink designers have to balance a number of conflicting parameters to maximise the performance of a heat sink. This must be achieved within the given constraints of size or volume of the heat sink as well as the mass or material cost of the heat sink. This multi-parameter problem lends itself naturally to optimisation techniques. Traditionally, an experimental approach was used where different heat sink designs were constructed and their performance measured. This approach is both time-consuming and costly. More recently, numerical CFD techniques have been used, but mostly on a trial-and-error basis. This leads to long design cycles and is basically the numerical equivalent of the experimental approach. A better approach is to combine a semi-empirical simulation program with mathematical optimisation techniques. This paper describes the use of mathematical optimisation techniques to minimise heat sink mass or thermal resistance using five design variables. They are heat sink fin height, fin thickness, extrusion length base thickness and number of fins for the heat sink. The simulation uses the Qfin 2.1 code, while the optimisation is carried out by means of the DYNAMIC-e method. This method is specifically designed to handle constrained problems where the objective and/or constraint functions are expensive to evaluate. The paper illustrates how the parameters considered influence the heat sink mass and how mathematical optimisation techniques can be used by the heat sink designer to design compact heat sinks for different types of electronic enclosures.

Optimisation of structured grid spacing parameters for separated flow simulation using mathematical optimisation

Abstract This paper describes the use of computational fluid dynamics (CFD) and mathematical optimisation techniques to minimise the error in predicting the recirculation zone for a separated flow topology. Grid spacing parameters are varied in the optimisation process. The accuracy of separated flow solutions is known to be dependent on the grid resolution and clustering. Although general guidelines have been developed for grid generation of separated flow topologies, the flow solutions using the resulting grids often under-predict features like recirculation zones. This study addresses this aspect by providing an automatic tool for optimising the grid for solution accuracy. This approach has until recently been too expensive, but is becoming more viable with ever-increasing computer power. A two-dimensional sinusoidal hill is used as an example of a separated flow topology. The CFD simulation employs the commercial CFD solver STAR-CD to solve the Reynolds-Averaged Navier–Stokes equations with the RNG k – e turbulence model. CFD solution time is drastically reduced by making use of initial field restarts. The optimisation is carried out by means of Snymans DYNAMIC-Q method, which is specifically designed to handle constrained problems where the objective or constraint functions are expensive to evaluate. Six design variables (grid spacing parameters) are considered in this study. The results indicate that the re-attachment point of the recirculation zone is predicted to within 1% of the specified experimental value in four optimisation iterations and therefore represents a cost-effective way to determine grids based on solution accuracy.

Mathematical maximisation of minimum residence time for two strand continuous caster

Abstract The present paper contains the results of a design optimisation study of a new enlarged tundish at ISCOR, Vanderbijlpark Works, Vanderbijlpark, South Africa. The paper describes the use of computational fluid dynamics (CFD) combined with mathematical optimisation to design the configuration of the new enlarged tundish. Design variables chosen include the position and sizes of baffles and baffle holes and pouring box width, while the design objective is maximisation of the minimum residence time (MRT) at operating level and at a typical transition level. Two different optimisation methods (DYNAMIC-Q and LS-OPT) are used and compared in the study. The combined MRT obtained by DYNAMIC-Q is 0·4, while LS-OPT converges to a value of 0·43, both starting from a combined MRT of 0·21. The study shows how mathematical optimisation techniques can be coupled to a commercial CFD package (FLUENT) to obtain optimum tundish designs with significant improvements. The CFD process is validated using plant data for similar designs.

Design Optimization of Continuous Caster Refractory Components

The paper describes the design optimization of different refractory components used in the continuous casting process. In the first case, an impact pad of a continuous caster tundish is optimized for its turbulence suppression capability, while the inclusion particle trapping of the design is monitored. The impact pad is used in isolation as the only tundish furniture component. In the second case, the Submerged Entry Nozzle (SEN) of the continuous caster mold is optimized for minimum meniscus turbulent kinetic energy (i.e., stable meniscus). In both cases, the design variables are geometrical in nature. The steady-state flow and thermal patterns in the tundish and mold are obtained using the commercial CFD solver FLUENT. In order to perform optimization, the geometries are parameterized and incorporated into a mathematical optimization problem. FLUENT and its pre-processor GAMBIT are linked to a commercial design optimization tool, LS-OPT, to automatically improve the designs using metamodel approximations. The optimization results show a reduction of 12.5% in the turbulence on the slag layer of the tundish, while for the SEN, the results for one design iteration only are shown, due to the high cost of the function evaluations. The final paper will contain additional results. The SEN base and improved designs are validated using water modeling.Copyright

Mathematical Optimization of Electronic Enclosures

The thermal design of electronic enclosures is becoming more important as the demand for smaller, lighter systems with better performance increases. The limiting factor on the lifetime of these systems is the maximum temperature of the electronic components. Nowadays in some systems, the thermal design is the limiting factor for performance increases. A simple yet effective design method that yields optimum designs is therefore required to design these systems. Traditionally, experimental methods were used in the design of electronic enclosures. More recently Computational Fluid Dynamics (CFD) has established itself as a viable alternative to reduce the number of experimentation required, resulting in a reduction in the time scales and cost of the design process. The CFD process is usually applied on a trial and error basis and relies heavily on the insight and experience of the designer to improve designs. Even an experienced designer will only be able to improve the design and does not necessarily guarantee optimum results. A more efficient design method is to combine a mathematical optimizer with CFD. In this study the mathematical optimization method, DYNAMIC-Q, is linked with the commercial CFD package, Icepak to optimize different electronic enclosures. The method is applied to the following design situations commonly found in electronics enclosures. The first case is that of the optimization outlet grille of a telecommunications rack to reduce the electromagnetic interference without exceeding a specified temperature in the rack. The second case involves the optimum placement of electronic components on a printed circuit board to minimize the maximum temperatures of the components. The third case deals with flow through an electronic enclosure cooled by fans placed on the wall of the enclosures. The geometrical arrangement of boards and components on the boards in these enclosures might result in unequal flow distribution between the boards. For this purpose air flow filters of varying free-area ratios are used to make the flow rates between the boards more uniform. The free-area ratios of three filters are determined in order to maximize the total flow rate through system with the added constraint that the flow rates through each of the three filters are within 5% of each other. The last case deals with flow through a simplified notebook where the CPU temperature is minimized by changing the position of two exhaust fans. The study shows that mathematical optimization is a powerful tool that can be combined with CFD to yield optimum designs.Copyright

Constructing a Trade-Off Surface for Extruded Heat Sinks Exposed to Forced Convection

In modern electronic components power densities are being increased continuously while the size and weight decrease. The effective dissipating of the heat produced by these components has now become a major design problem. Ordinary heat sinks often used to dissipate this heat, can in many instances no longer be used. Heat sinks therefore need to be designed and optimized for specific applications. The design of these heat sinks requires a difficult trade-off between conflicting parameters, e.g. mass or material cost, maximum temperature and pressure drop. Since these parameters influence one another, optimum designs require the use of mathematical optimization techniques. In the case of heat sinks, the thermal engineer would typically like to optimize the design simultaneously for three design parameters. The parameters are maximum heat sink temperature, mass and pressure drop. In the formulation of such an optimization problem, where more than one design criterion is important, the engineer currently has to assign the relative importance of each design criteria before starting the optimization. A better approach is to perform a range of optimization problems where the relative importance of the design criteria is varied systematically to obtain a trade-off surface of optimum heat sinks. This surface can then be used to investigate the influence of the different design criteria on each other and to select the optimum heat sink for a specific application. In this study such a trade-off surface is created for an extruded heat sink exposed to forced convection. The constructing of this surface is obtained by combining a semi-empirical simulation program, QFin 3.0 with the DYNAMIC-Q optimization method.Copyright