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Hierarchical Modeling for Population-Based Heat Exchanger Design

  • Author(s): Geb, David
  • Advisor(s): Catton, Ivan
  • et al.
Abstract

To tackle complex problems, engineers have increasingly looked to natural processes and creatures, as models and metaphors, for inspiration. Darwinian evolution and social group behavior, two instances of optimization mechanisms in nature, have inspired the two main families of nature-inspired intelligent computing algorithms, i.e. evolutionary and swarm algorithms. Although both families of algorithms are generally applied towards search and optimization problems, each has its own distinguishing features. In this dissertation, a genetic algorithm and particle swarm optimizer, instances of each main family of nature-inspired intelligent computing algorithms, are implemented to optimize heat transfer devices such as heat sinks and compact heat exchangers. These optimization methods are ideal for obtaining optimal designs of the constrained, multi-parameter, multi-objective, and multi-model complex optimization problems faced by heat transfer device engineers. However, the primary hurdle facing designers of such heat transfer devices, which has precluded the use of these optimization methods, is the significant computational costs of performing direct numerical simulations (DNS), i.e. with CFD, of the flow and heat transfer in such heterogeneous (and porous), hierarchical devices with conjugate effects included and flow often in the turbulent regime. This makes device simulations very costly and population-based optimization nearly impossible, which has resulted in most designs being based on ad hoc considerations, resulting in constrained performance, and thus accumulating financial losses for those manufacturing and operating the devices, and troubling environmental effects, i.e. excessive carbon emissions and thermal pollution, due to the accompanying energy losses.

Breakthroughs in the past few decades in the modeling of transport phenomena in heterogeneous media with Volume Averaging Theory (VAT) have allowed engineers to fully simulate flow and heat transfer in thermal devices in mere seconds on a modern laptop, in comparison with the many hours it takes to do so with CFD, paving the way to thorough optimization studies of the multi-parameter devices. VAT is a hierarchical modeling method in which the lower-scale governing equations are the Navier-Stokes and thermal energy equations in the fluid and solid phases, and the upper-scale governing equations are the VAT-based mass, momentum, and fluid and solid thermal energy transport equations. The two sets of equations are rigorously connected by mathematical scaling (i.e. averaging) procedures and the result of such a model allows a nonlocal description of transport phenomena in heterogeneous thermal devices, with the morphology directly incorporated into the field equations and conjugate effects fully treated.

The upper-scale VAT-based governing equations in hierarchical and heterogeneous media are complicated and at first formidable, yielding additional integral and differential terms when compared to the transport equations in homogeneous media. Understanding these additional terms led to them being directly related to the local transport coefficients, i.e. heat transfer coefficient and drag coefficient, providing a rigorous yet intuitive method of closure to the complicated integro-differential equations, and yielding simple differential equations that are quickly solved with straight forward numerical methods. Closure of the VAT-based equations can be obtained either theoretically, numerically, or experimentally, and past work has focused on numerical methods (i.e. CFD). In this work novel experimental methods for obtaining closure are explored, developed, and then implemented for several surfaces. With the VAT equations closed, rapid simulations can be performed, and thus the nature-inspired optimization methods can be exploited to guide the design to its optimal configuration.

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