2014 Doctoral Student Summer Institute Supplemental
Application
Pieces
Francois Cadieux
April 28, 2014
1 Benefits of participating
I will benefit from participating in the doctoral student summer
institute in a number of ways:financial support, greater structure,
mentorship, and opportunities to expand my network
acrossdisciplines with a wide range of scholars. Financial support
is key, because it would allow me tofocus entirely on completing a
part of my thesis project. Summer funding being limited, I
wouldotherwise have to find another source of income and divide my
time. The greater structure ofthe program, such as the written
expectations outlined in this proposal will help me ensure that100%
of the time I gain from having financial support is used towards
obtaining and analyzingresults that I can then publish. The
opportunity to be mentored by another faculty is both rareand
coveted. My personal and research interests cross many disciplines.
Being able to explorethese interests with a faculty member from
another discipline, with a different outlook, could leadto many
unexpected realizations, avenues for future work, and the potential
for interdisciplinarycollaboration (beyond this particular
faculty). I hope to learn from faculty members and advisorsways to
improve the exposure and reach of my research. Their experience in
the job market willalso be valuable for me to hear about. I hope to
improve the quality and clarity of my writingby applying what I
have learned from academic and professional development writing
workshopsI attended these past two semesters. I plan to take full
advantage of the availability of furtherwriting workshops during
the program to iterate on a first draft for a publication based on
theresults I will obtain this summer. The diverse and
interdisciplinary group of students and facultyparticipating will
enable me to broaden my horizons and extend my professional
network. Eachtime I explain concepts related to my research in
conversations with scholars outside my field Igain in both
perspective and insight - from finding new ways to relate and from
listening to theirthought process. This process helps to hone my
communication skills. Conversely, learning aboutother scholars
research often opens my mind to possibilities I had not explored.
By breaking downthese barriers and exploring new perspectives, I am
convinced this opportunity will help me growpersonally and
professionally.
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April 28, 2014 2014 Doctoral Student Summer Institute
Application Francois Cadieux
2 Proposed Summer Project Description
2.1 Context & Motivation
Flow separation, transition to turbulence, and turbulent
reattachment coined laminar separationbubble (LSB) because of the
recirculating region the phenomena create together directly affect
theperformance of a number of increasingly important applications
in the aerospace, defense and energyindustries. Flow separation
without reattachment can have disastrous consequences such as loss
oflift on the performance of these applications (e.g. unmanned and
micro-aerial vehicles) and waysto delay it are sought at the design
stage. LSB often favorably delay loss of lift by promoting
earlytransition to turbulence and reattachment. Faster, more
accurate computational fluid dynamicstools are necessary to enable
the design optimization of technologies to better understand
andcontrol this phenomenon.
Standard turbulence modeling methods used for the aviation
industry (Reynolds Averaged Navier-Stokes) were shown to be
inadequate for such LSB flows [2]. Direct numerical simulation
(DNS)is the most reliable but also the most computationally
expensive alternative. In previous work([1]), we assessed the
capability of large eddy simulations (LES) to drastically reduce
the resolutionrequirements for such flows. Flow over a flat plate
with suitable velocity boundary conditions awayfrom the plate to
produce a separation bubble was considered. Benchmark DNS data for
thisconfiguration were generated with the resolution of 59 10 6
mesh points; also used is a differentDNS database with 15 10 6
points [2]. LES results are in good agreement with DNS and
indicatethat accurate LES is possible using O(1%) of the DNS
resolution. However, contamination ofthe results by numerical
dissipation preclude any strong conclusions. Numerical dissipation
is theprocess by which energy is not entirely conserved in a
simulation due to any approximation errorsinherent to the scheme
used to integrate the partial differential equations governing the
flow inspace and time. A preliminary attempt at quantifying the
numerical dissipation in the simulationindicated that it was on the
same order of magnitude as the physical dissipation predicted bythe
subgrid scale (SGS) model. Since numerical dissipation is present
in all numerical simulationsof fluid flow, and is expected to be
larger at coarse resolutions, a method to better quantify itwas
developed by Domaradzki et al. Applying this method to quantify
numerical dissipation indifferent parts of the flow (laminar,
transitional, and turbulent regions) should yield insight intothe
reliability of very coarse LES as well as implicit LES and
under-resolved DNS.
2.2 Objectives
The primary objective will be to quantify numerical dissipation
by comparing theoretical expectedphysical energy dissipation based
on the independent variables (velocities, pressure, energy), tothe
dissipation calculated when running the simulation. This comparison
will be carried out byanalyzing a number of instants in time, as
well as different regions in the flow. It is expectedthat different
values of numerical dissipation will be obtained for different
regions of the flow. Forexample, dissipation should be larger in
turbulent areas, where we also expect numerical dissipationto be
larger due to sharp gradients being approximated on a coarse
mesh.
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April 28, 2014 2014 Doctoral Student Summer Institute
Application Francois Cadieux
2.3 Method
A number of snapshots in time of the flow field will be
generated. These snapshots will be usedas input to calculate the
expected theoretical energy dissipation rate. This will be obtained
bycomputing an energy balance with spectral accuracy using Fourier
transforms in different controlvolumes of the flow field. The
energy rate of change is directly obtained from the
simulationvariables as the change in time of the energy. The
difference between the rate of change of energyobtained from the
simulation and that obtained from theory should be the dissipation
due tonumerical error for a given control volume. This method of
quantifying energy losses due tonumerics has been validated
previously by Domaradzki et al.
2.4 Expected outcome
The hypothesis is that dissipation due to numerics is
detrimental to the reliability of very coarseLES results because it
is not consistent with the physics, but rather depends on the
precise grid andnumerical scheme used. Furthermore, numerical
errors are not limited to regions where physicaldissipation is
expected to be present. In other words, modeling physical
dissipation to heat asnumerical losses from derivative
approximations may introduce significant dissipation in areas
wherethere should be little to none. These effects should be
limited to under-resolved simulations.Unfortunately, such
simulations are routinely performed in industrial and commercial
settings tosave on computational cost, without any indication on
the reliability of the results. The hope is thatthis technique will
help determine whether using a SGS model should improve or worsen
accuracyof the results.
3 Proposed Summer Project Timeline
References
[1] F. Cadieux, J. A. Domaradzki, T. Sayadi, and T. Bose. DNS
and LES of laminar separationbubbles at moderate Reynolds numbers.
J. Fluids Eng., 136, 2014.
[2] P.R. Spalart and M.K. Strelets. Mechanisms of transition and
heat transfer in a separationbubble. J. Fluid Mech., 403:329349,
2000.
