49 research outputs found
A "poor man's" approach for high-resolution three-dimensional topology optimization of natural convection problems
This paper treats topology optimization of natural convection problems. A
simplified model is suggested to describe the flow of an incompressible fluid
in steady state conditions, similar to Darcy's law for fluid flow in porous
media. The equations for the fluid flow are coupled to the thermal
convection-diffusion equation through the Boussinesq approximation. The coupled
non-linear system of equations is discretized with stabilized finite elements
and solved in a parallel framework that allows for the optimization of high
resolution three-dimensional problems. A density-based topology optimization
approach is used, where a two-material interpolation scheme is applied to both
the permeability and conductivity of the distributed material. Due to the
simplified model, the proposed methodology allows for a significant reduction
of the computational effort required in the optimization. At the same time, it
is significantly more accurate than even simpler models that rely on convection
boundary conditions based on Newton's law of cooling. The methodology discussed
herein is applied to the optimization-based design of three-dimensional heat
sinks. The final designs are formally compared with results of previous work
obtained from solving the full set of Navier-Stokes equations. The results are
compared in terms of performance of the optimized designs and computational
cost. The computational time is shown to be decreased to around 5-20% in terms
of core-hours, allowing for the possibility of generating an optimized design
during the workday on a small computational cluster and overnight on a high-end
desktop
A "poor man's" approach to topology optimization of natural convection problems
Topology optimization of natural convection problems is computationally
expensive, due to the large number of degrees of freedom (DOFs) in the model
and its two-way coupled nature. Herein, a method is presented to reduce the
computational effort by use of a reduced-order model governed by simplified
physics. The proposed method models the fluid flow using a potential flow
model, which introduces an additional fluid property. This material property
currently requires tuning of the model by comparison to numerical Navier-Stokes
based solutions. Topology optimization based on the reduced-order model is
shown to provide qualitatively similar designs, as those obtained using a full
Navier-Stokes based model. The number of DOFs is reduced by 50% in two
dimensions and the computational complexity is evaluated to be approximately
12.5% of the full model. We further compare to optimized designs obtained
utilizing Newton's convection law.Comment: Preprint version. Please refer to final version in Structural
Multidisciplinary Optimization https://doi.org/10.1007/s00158-019-02215-
Topology optimisation of natural convection problems
This paper demonstrates the application of the density-based topology
optimisation approach for the design of heat sinks and micropumps based on
natural convection effects. The problems are modelled under the assumptions of
steady-state laminar flow using the incompressible Navier-Stokes equations
coupled to the convection-diffusion equation through the Boussinesq
approximation. In order to facilitate topology optimisation, the Brinkman
approach is taken to penalise velocities inside the solid domain and the
effective thermal conductivity is interpolated in order to accommodate
differences in thermal conductivity of the solid and fluid phases. The
governing equations are discretised using stabilised finite elements and
topology optimisation is performed for two different problems using discrete
adjoint sensitivity analysis. The study shows that topology optimisation is a
viable approach for designing heat sink geometries cooled by natural convection
and micropumps powered by natural convection.Comment: Submitted to the 'International Journal for Numerical Methods in
Fluids' on 28th of August 2013 - currently under revie