Abstract
The present talk is concerned with the application of topology
optimization to creeping flow problems in 3D. This research is
driven by the fact that topology optimization has proven very
successful as a tool in academic and industrial design problems.
Success stories are reported from such diverse fields as solid
mechanics and optics and is due to the method's flexibility in the
(rough) parametrization of the design, see [1] and the reference
therein for an overview.
Borrvall and Petersson [2] is the seminal reference for topology
optimization in fluid flow problems. They considered design of
energy efficient devices for 2D Stokes flow. Creeping flow problems
are described by the Stokes equations which model very viscous
fluids at macro scales or ordinary fluids at very small scales. The
latter gives the motivation for topology optimization problems based
on the Stokes equations being a model for the fluid behavior in a
micro fluidic device. Such a device has finite size and a large
degree of freedom for the design of geometry.
Physically Stokes flow is an exotic inertia free flow. This,
however, complicates mixing by passive devices. Passive devices,
that is, devices without moving parts, are often of practical
interest since they are easily manufacturable and maintenance free.
In order to tackle such a challenging problem a robust method is
needed which we approach by this contribution.
The finite size of a micro fluidic device calls for 3D modelling of
the equations, in particular when the design geometry is non-trivial
as typically seen in topology design. The presentation elaborates on
effects caused by 3D fluid modelling on the design. Numerical
examples relevant for optimal micro fluidic mixer design are shown
where the design is planar - compliant with micro fabrication
techniques - and where the designs are 3D. Moreover, preliminary
results show that a formulation of an optimization problem that
maximizes mixing with a constraint on the pressure drop across the
device gives promising results. To measure the mixing a step
temperature profile is convected through the design and the
resulting temperature profile at the outlet boundary is measured.
The closer the outlet temperature profile is to the average inlet
temperature the better mixing occurs in the device. For this problem
the P$\acute{\textrm{e}}$clet number $Pe\gg1$ such that mixing by
pure diffusion is not an option. Instead, the optimizer suggests a
design that stretches the hot-cold interface, which is encouraging
since "stretching and folding" is known to be key ingredients in
efficient mixing. The modelling is performed using a finite element
based solver, with analytically derived sensitivities that drives a
gradient based optimization algorithm.
Secondly, this talk also has its focus on the parallel
implementation of the solution procedures, using OpenMP [3] on
medium to large SMP computers. The necessary setup to achieve a good
performance is described in detail. Further, issues such as
scalability and portability are discussed.
[1] M.P. Bendsøe and O. Sigmund. Topology
optimization - theory, methods and applications, 2nd Edition, Springer 2003.
[2] T. Borrvall, J. Petersson. Topology optimization
of fluids in Stokes flow. Int. J. Num. Meth. Fluids, Vol. 41, 77-107, 2003. DOI:10.1002/fld.426
[3] The OpenMP Application Program Interface,
http://www.openmp.org/
Original language | English |
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Publication date | 2006 |
Publication status | Published - 2006 |
Event | European Conference on Computational Fluid Dynamics - Egmond aan Zee, Netherlands Duration: 5 Sept 2006 → 8 Sept 2006 https://www.certh.gr/47A6297A.en.aspx |
Conference
Conference | European Conference on Computational Fluid Dynamics |
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Country/Territory | Netherlands |
City | Egmond aan Zee |
Period | 05/09/2006 → 08/09/2006 |
Internet address |