Jan A. Visser

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.

Capturing Sudden Increase in Heat Transfer on the Suction Side of a Turbine Blade Using a Navier–Stokes Solver

The numerical modeling of heat transfer on the suction side of a cooled gas turbine blade is one of the more difficult problems in engineering. The main reason is believed to be the transition from laminar to turbulent flow and the inability of standard Navier-Stokes solvers to predict the transition. This paper proves that sudden changes in heat transfer on the suction side of a turbine blade can indeed also be caused by localized shocks disrupting the boundary layer. In contrast to transition, the position of these shocks and the effect of the shocks on the pressure distribution and heat transfer rate can be predicted to within an acceptable degree of accuracy using standard Navier-Stokes solvers. Two well-documented case studies from the literature are used to prove that the pressure distribution around the profile can be predicted accurately when compared to experimental data. At the same time this method can be used to capture sudden changes in heat transfer rate caused by localized shocks. The conclusion from this study is that localized shock waves close to the suction side surface of a turbine blade can have the same effect on the heat transfer rate to the blade as transition.

Multi-disciplinary design optimization of a combustor

A technique for design optimization of a combustor is presented. This technique entails the use of computational fluid dynamics (CFD) and mathematical optimization to minimize the combustor exit temperature profile. The empirical and semi-empirical correlations commonly used for optimizing combustor exit temperature profile do not guarantee optimum. As an experimental approach is time consuming and costly, use is made of numerical techniques. However, using CFD without mathematical optimization on a trial and error basis does not guarantee optimal solutions. A better approach, which is often viewed as too expensive, is a combination of the two approaches, thus incorporating the influence of the variables automatically. In this study the combustor exit temperature profile is optimized. The optimum (uniform) combustor exit temperature profile mainly depends on the geometric parameters. Combustor parameters have been used as optimization variables. The combustor investigated is an experimental liquid-fuelled atmospheric combustor with a turbulent diffusion flame. The CFD simulations use the Fluent code with a standard k–ϵ model. The optimization is carried out using the Dynamic-Q algorithm, which is specifically designed to handle constrained problems where the objective and constraint functions are expensive to evaluate. The optimization leads to a more uniform combustor exit temperature profile compared with the original.

A different approach to discretization for the numerical simulation of three-dimensional heat conduction in irregularly shaped materials

A different approach to discretization is described with which complicated three-dimensional heat transfer problems can be solved with a finite volume approach on a general curvilinear grid. It represents an improvement on the existing methods in that it can easily be expanded to three-dimensional problems. A concise explanation of the transformation process is given, together with a discussion of the discretization procedure. The method is evaluated by solving two simple test problems and comparing the results with those of existing methods and the analytical solution. In conclusion it is found that this method yields equally or more accurate results than the existing methods, with the additional advantage of being easily expandable to three-dimensional problems.

An Efficient Strategy for the Design Optimization of Combustor Exit Temperature Profile

A technique for design optimization of a combustor is presented in this study. The technique entails the use of Computational Fluid Dynamics (CFD) and mathematical optimization to minimize the combustor exit temperature profile. The empirical and semi-empirical correlations commonly used for optimizing Combustor Exit Temperature profile do not guarantee optimum. As experimental approach is time consuming and costly, use is made of numerical techniques. Using CFD without mathematical optimisation on a trial-and-error basis, however, does not guarantee optimal solutions. A better approach that is viewed as too expensive is a combination of the two approaches, thereby, incorporating the influence of the variables automatically. In this study the combustor exit temperature profile is optimised. The optimum (uniform) combustor exit temperature profile depends on mainly the geometric parameters. The combustor exit temperature profile is affected as soon as flow enters the combustor. However, in gas turbine applications where care has been taken on the influence of upstream flow related conditions, the combustor exit temperature profile is changed by dilution hole pattern and size. In this study dilution hole parameters have been used as optimization variables. The combustor in the study is an experimental liquid fuelled atmospheric combustor with turbulent diffusion flame. The CFD simulations uses the Fluent code with Standard k-e model. The optimisation is carried out with Snyman’s Dynamic-Q algorithm, which is specifically designed to handle constrained problems where the objective or constraint functions are expensive to evaluate. The optimization leads to a more uniform combustor exit temperature profile as compared to the original.Copyright

Combining CFD and Mathematical Optimization to Optimize Combustor Exit Temperature Profile

A technique for design optimization of a combustor is presented in this study. The technique entails the use of Computational Fluid Dynamics (CFD) and mathematical optimization to minimize the combustor exit temperature profile. The empirical and semi-empirical correlations commonly used for optimizing Combustor Exit Temperature profile do not guarantee optimum. As experimental approach is time consuming and costly, use is made of numerical techniques. Using CFD without mathematical optimization on a trial-and-error basis, however, does not guarantee optimal solutions. A better approach that is viewed as too expensive is a combination of the two approaches, thereby, incorporating the influence of the variables automatically. In this study the combustor exit temperature profile is optimized. The optimum (uniform) combustor exit temperature profile depends on mainly the geometric parameters. The combustor exit temperature profile is affected as soon as flow enters the combustor. However, in gas turbine applications where care has been taken on the influence of upstream flow related conditions, the combustor exit temperature profile is optimized by dilution hole pattern and size. In this study combustor parameters have been used as optimization variables. The combustor in the study is an experimental liquid fuelled atmospheric combustor with turbulent diffusion flame. The CFD simulations uses the Fluent code with Standard k-e model. The optimization is carried out with the Dynamic-Q algorithm, which is specifically designed to handle constrained problems where the objective or constraint functions are expensive to evaluate. The optimization leads to a more uniform combustor exit temperature profile as compared to the original.Copyright

A simplified equation to predict heat transfer in an internal duct of a gas turbine nozzle guide vane

This paper presents a simplified formula that can be used to obtain the detailed heat transfer rate and temperature distribution on the surfaces of square and non-square cooling channels of a nozzle guide vane (NGV). Due to the three-dimensional shape of the internally cooling channels, the heat transfer rate can vary substantially between the different sides of the channels. This detailed heat flux and resulting temperature distribution on the walls are important to improve the design of the airfoil as well as to determine the expected usable life of the NGV. This detail heat transfer data is usually obtained by means of a complex three-dimensional simulation of the NGV configuration. Therefore, for design purposes, the heat transfer data on the channel surfaces is often assumed to be the average heat transfer rate on the channel walls. The average heat transfer rate can be obtained by using a simplified heat transfer equation, based on the average Reynolds number in the channel. The simplified formula presented in this paper can be used to obtain the detailed heat transfer rate and temperature distribution on the surfaces of square and non-square cooling channels of a nozzle guide vane (NGV). The simplified formula is based on results obtained from three-dimensional simulations of the heat transfer in the channels and was compared to simulated and experimental data over a range in flow rates and channel geometries. In general, it can be concluded that the formulation produces fast and accurate results over a wide range of applications. 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

A Simplified Equation to Obtain the Complex Heat Transfer Distribution in an Internal Duct of a Semi-Cooled Turbine Blade

Due to the three-dimensional shape of the internally cooling channels of a modern gas turbine blade, the heat transfer rate varies substantially between the different sides of the channels. This detailed heat flux and resulting temperature distribution on the walls are important to improve the design of the blade as well as to determine the durability of the blade. This detail heat transfer data is usually obtained by means of a complex three-dimensional simulation of the blade configuration. Therefore, for design purposes, the heat transfer data on the channel surfaces is often assumed to be the average heat transfer rate on the channel walls. The average heat transfer rate can be obtained by using a simplified heat transfer equation, based on the average Reynolds number in the channel. This paper presents a simplified formula that can be used to obtain the detailed heat transfer rate in square and non-square cooling channels of a stationary, as well as a rotating turbine blade. The simplified formula is based on results obtained from three-dimensional simulations of the heat transfer in the channels and was compared to simulated and experimental data over a range in flow rates and channel geometries. In general, it can be concluded that the formulation produces fast and accurate results over a wide range of applications.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