1 Copyright © 2012 by ASME
Proceedings of the 14
th
International Design Engineering Technical Conference
DAC38
August 12-15, 2012, Chicago, Illinois, USA
DETC2012-71448
NOVEL TOPOLOGICAL APPROACH TO DESIGNING FLOW CHANNELS
Bradley Camburn
Camburn@utexas.edu
Kristin Wood
Wood@mail.utexas.edu
The University of Texas at Austin
Austin, Texas, USA
Richard Crawford
RHC@mail.utexas.edu
ABSTRACT
Many natural systems that transport heat, energy or fluid
from a distributed volume to a single flow channel exhibit an
analogous appearance to trees. Examples include bronchial
tubes, watersheds, lightening, and blood vessels. Commonly for
natural and designed systems with this type of flow, the flow
volume consists primarily of high resistance regimes with a
smaller portion of interdigitated low resistance regions (flow
channels). Perhaps, the most relevant design problem is cooling
of a microchip. Since microchip performance is optimal at
lower temperatures, bulk heat flow resistance for heat exiting
the system should be minimized; therefore, it is critical to
cleverly align the channel to maximize flow. Heat conduction
from a microchip is typically simplified into heat conduction
from a homogenously heat-generating plate. This simplified
problem is used as a standard model with which engineering
designers can compare the performance of various cooling
configurations. Due to the apparent tree-fractal characteristics
of empirically emerging systems (i.e. in nature), several authors
have examined analogous, simplified fractal configurations.
These fractal configurations appear to be the best solution in
current publication. We present a novel topological analysis that
provides insight into performance at a schematic level. This
analysis leads to the development of a new configuration, leaf-
like, which outperforms the current state-of-the-art.
Performance is compared among the configurations with two
parallels analyses: an extensive series of finite element models,
covering a broad combinatory array of material properties and
heating conditions; and topological analysis of path length, or
the average distance heat, energy or fluid, must travel through
the substrate and channel media before exiting through the
point flow channel. There is a strong correlative mapping
between the two analyses. Finite element modeling is employed
because it provides a fundamental mechanics approach to
assessment of heat transfer behavior, while the path length
analysis provides an intuitive and computationally affordable
means to predict performance. Novel contributions of this work
include a configuration for conductive cooling in a plate for
VTP flow, superior to the state-of-the-art, and a topological
analysis of VTP flow that provides a generalized metric of bulk
flow resistance and a schematic level conceptualization of the
mechanics of VTP flow. Future advancements of our research
could include enhancing the algorithm to automatically parse
geometry into channel segments from an image or other
external representation and eventually to even generate a
suitable channel from arbitrary substrate geometry.
INTRODUCTION
A common feature among arteries, lightening, bronchial
airways, leaves, and watersheds is truncated tree-like fractal
organization. This commonality may be due to the fact that
these systems solve a similar type of problem- the transference
of energy or matter from a distributed arrangement (area or
volume) to a single point (sink) [1].
The motivation of this paper is to examine whether the
tree-like fractal found so frequently in nature is in fact optimal
for volume-to-point flow. For the volume-to-point flow problem
the amount of flow channel is constrained. Therefore, it is
important to optimally arrange the available channel.
The approach of this paper is an in-depth look at theoretical
analysis and experiments about one type of volume-to-point
flow. This paper will focus on evaluating the problem of
conduction from a heat generating plate to a sink point-
analogous to cooling a microchip. In the past, tree like fractal
channel geometry has been proposed for this type of cooling
[4]. In order to evaluate this proposal, the performance of
various geometries is compared via literature review and
analyses.
NOMENCLATURE
Fractal, conduction, path length, finite element, volume to
point flow, topology.