Optimal mixing of multiple reacting jets in a gas turbine combustor

Paper presented at the 6th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 30 June - 2 July, 2008.This paper addresses the design optimisation methodology used to optimise a gas turbine combustor exit temperature profile. The methodology uses computational fluid dynamics and mathematical optimisation to optimise the combustor exit temperature profile. The studies from which the results were derived, investigated geometric variations of a complex three-dimensional flow field in a gas turbine combustor. The variation of geometric parameters impacts on mixing effectiveness, of which the combustor exit temperature profile is a function. The combustor in this study is an experimental liquid-fuelled atmospheric combustor with a turbulent diffusion flame. The computational fluid dynamics simulations use the Fluent code with a standard k-ε model. The optimisation is carried out with the Dynamic-Q algorithm, which is specifically designed to handle constrained problems where the objective and constraint functions are expensive to evaluate. All the optimisation cases investigated led to an improved combustor exit temperature profile as compared to the original one.vk201

A strongly interacting dynamic particle swarm optimization method

A novel dynamic interacting particle swarm (DYN-PSO) is proposed. The algorithm can be considered to be the synthesis of two established trajectory methods for unconstrained minimization. In the new method, the minimization of a function is achieved through the dynamic motion of a strongly interacting particle swarm, where each particle in the swarm is simultaneously attracted by all other particles located at positions of lower function value. The force of attraction experienced by a particle at higher function value due to a particle at a lower function value is equal to the difference between the respective function values divided by their stochastically perturbed position difference. The resultant motion of the particles under the influence of the attracting forces is computed by solving the associated equations of motion numerically. An energy dissipation strategy is applied to each particle. The specific chosen force law and the dissipation strategy result in the rapid collapse (convergence) of the swarm to a stationary point. Numerical results show that, in comparison to the standard particle swarm algorithm, the proposed DYN-PSO algorithm is promising

Practical mathematical optimization: basic optimization theory and gradient-based algorithms

This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences. Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and directly applicable. Numerical examples and exercises are included to encourage senior- to graduate-level students to plan, execute, and reflect on numerical investigations. By gaining a deep understanding of the conceptual material presented, students, scientists, and engineers will be able to develop systematic and scientific numerical investigative skills.

Optimization of gas turbine combustor mixing for improved exit temperature profile

In this article, a design optimization technique for mixing in a gas turbine combustor is presented. The technique entails the use of computational fluid dynamics and mathematical optimization to optimize the combustor exit temperature profile. Combustor geometric parameters were used as optimization design variables. This work does not intend to suggest that combustor exit temperature profile is the only performance parameter important for the design of gas turbine combustors. However, it is a key parameter of an optimized combustor that is related to the power output and durability of the turbine. The combustor in this study is an experimental liquid-fuelled atmospheric combustor with a turbulent diffusion flame. The computational fluid dynamics simulations use a standard k-ε model. The optimization is carried out with 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 than with the original one

A study of the feasibility of using mathematical optimisation to minimize the temperature in a smelter pot room

Health hazards arise in large industrial workshops (such as aluminium pot rooms) due to the production of heat by the process equipment inside these workshops, which leads to high temperatures around these pieces of equipment. The heat production is sometimes accompanied by the release of polluting gases and dust particles that are dispersed throughout the workshop. The only large-scale and cost-effective way to ventilate these workshops is through natural ventilation. The effectiveness of the ventilation depends on the architectural shape of the building, the heat source locations and the openings of the windows, louvers and/or roof ventilators through which the air is allowed to enter and exit. This paper describes the investigation into the feasibility of using mathematical optimisation to determine the ideal window slat angles for different prevailing wind conditions. The proposed optimisation methodology employs computational fluid dynamics software (FLUENT), coupled to a computationally economic optimisation algorithm (Dynamic-Q) to determine the optimum slat angles to minimise the maximum temperature. The results of this feasibility study on a large-scale aluminium smelter pot room in Inota, Hungary, show that this is a viable methodology to determine the optimum inlet configuration

Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method. Part 2. Optimisation results

A methodology is proposed for the efficient determination of gradient information, when performing gradient based optimisation of an off-road vehicle’s suspension system. The methodology is applied to a computationally expensive, non-linear vehicle model, that exhibits severe numerical noise. A recreational off-road vehicle is modelled in MSC.ADAMS, and coupled to MATLAB for the execution of the optimisation. The successive approximation method, Dynamic-Q, is used for the optimisation of the spring and damper characteristics. Optimisation is performed for both ride comfort and handling. The determination of the objective function value is performed using computationally expensive numerical simulations. This paper proposes a non-linear pitch-plane model, to be used for the gradient information, when optimising ride comfort. When optimising for handling, a non-linear four wheel model, that includes roll, is used. The gradients of the objective function and constraint functions are obtained through the use of central finite differences, within Dynamic-Q, via numerical simulation using the proposed simplified models. The importance of correctly scaling these simplified models is emphasised. The models are validated against experimental results. The simplified vehicle models exhibit significantly less numerical noise than the full vehicle simulation model, and solve in significantly less computational time

Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method. Part 1. Mathematical modelling

Part 1 of this paper proposed a methodology for the efficient determination of gradient information, when optimising a vehicle’s suspension characteristics for ride comfort and handling. The non-linear full vehicle model, and simplified models for gradient information has been discussed, and validated. In this paper, the simplified models presented in Part 1 are used for gradient information simulations. The convergence histories of the optimisation are compared to those obtained when only the full, computationally expensive, vehicle model is used. For illustration of the proposed gradient-based optimisation methodology, up to four design variables are considered in modelling the suspension characteristics. The proposed methodology is found to be an efficient alternative for the optimisation of the vehicle’s suspension characteristics. The undesirable effects associated with noise in the gradient information is effectively reduced, using the simplified models. Substantial benefits are achieved in terms of computational time needed to reach a solution