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CIRA
Capua 13 Luglio 2006
Daniela Tordella, POLITECNICO DI TORINO
Simulazioni di Larga Scala di Flussi
Turbolenti
Confronti con le altre metodologie
Applicazioni e aspetti innovativi
Risultati attesi
DNS and LES
• In the past 15-20 years, DNS and LES become viable tools to treat
transitioning and turbulent flows
--- Improvements in numerical methods
--- Improvements in computers – speed, memory, cost
today is not unusual to have capabilities equivalent of Cray 1 in a small
group
• Successful application to a number of problems
• Tremendous potential in the future for:
Understanding transition and turbulence
Prediction in applications
DNS
Numerical calculation that solves for the time development
of the detailed, unsteady structures in a transitioning or a
turbulent flow field
NOT a numerical solution of Reynolds- or Favreaveraged equations
It is a numerical experiment analogous to a laboratory
experiment
• statistical scatter
• researcher must think like an experimentalist and ask
proper questions, etc.
Strengths of Approach
Compared to laboratory experiments
* know all the variables at each point in space and time
can follow large-scale structures
can in theory comoute any statistic of interest, e.g. pressure-velocity
correlation
can readily compare with theory
* Easy to control parameters to respect experimental conditions
Compared to theory
* Circumvent the closure problem
Weaknesses of Approach
Limited spatial and temporal resolution
Limits Reynolds number (and other key paramenters) without
resorting to modeling
Considers physics depending mainly on the large-scale
motions, difficult to treat Kolmogorov-scale processes
•
Opinion – complementary to laboratory experiment, theory
in any particular problem (whether fundamental or applied) use
methods (laboratory, theory, etc.) best suited for the problem.
Full Turbulence Simulation FTS
Calculation in which all of the dynamically significant lenghth and
time scales are included
L_e -- energy-containing scale (e.g., integral scale)
L_ k -- Kolmogorov scale (viscous dissipation scale)
L_k = ( ³/ )¼
L_e / L_ k = Re ¾
N -- number of grid poits in one direction ~ Re ¾
Ntot ~ N³ ~ ( Re ¾)³
Number of time steps increases with Re as well
Large Eddy Simulation LES
Motivated by the desire to remove Reynolds number limitations
Prior to numerical integration are spatially filtered to eliminate
the scales of motion smaller than those resolvable on the
computational mesh.
The effect of the subgrid-scale (SGS) motion is modeled
u = ū + u’
ū – grid-scale (computed) motions
u’ – subgrid-scale (modeled) motions
Several approaches – model using analogies with Reynoldsaveraged models
LES compared to FTS
Advantages:
potential to treat very high Reynolds number flows;
fast reaction, etc.
possibility of use in applied problems
Disadvantages:
ad hoc models are necessary to close euqations
introduces some uncertainty into validity of results
LES compared to Reynolds-averaging approach
Advantages:
Large-scale motions treated directly;
Can follow large-scale structures
Only small scales are modeled
Less energy in modeled scale; more universality
Expected to provide more realistic results
Disadvantages:
3D, time-dependent, high resolution
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