Large-Eddy Simulation: Application to Bypass Transition
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Philipp Schlatter
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Linné Flow Centre, KTH Mechanics, Stockholm, Sweden
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The governing equations for laminar, transitional and turbulent flows are
the Navier-Stokes equations, which have been known for almost 200 years.
Except for a few simple laminar flow cases, no closed analytical solutions
to these nonlinear equations are known. Therefore, one needs to resort to
numerical simulation techniques in order to get at least an approximate
solution of a given fluid dynamics problem. Increasing the Reynolds number
(i.e. the relative importance of inertial and viscous forces) leads to the
excitation of smaller and smaller turbulent scales down to a lower limit.
These smallest, so-called Kolmogorov scales need to be resolved or
appropriately modelled in numerical simulations based on the Navier-Stokes
equations; the simulation accuracy strongly depends on the spatial and
temporal resolution employed. Tremendous research progress has been achieved
during the past decades in fluid simulations, with the help of growing power
of computers, increasing efficiency of algorithms and refined turbulence
models. Nowadays, numerical fluid dynamics can be considered an equal and
valuable complement to experimental studies.
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The talk will be focussed on a more detailed description of the specific
flow case of bypass transition detailed below. After formalising the
different modelling approaches to the Navier-Stokes equations, the concept
of large-eddy simulation (LES) is introduced. In LES, only the large-scale,
energy-carrying vortices of a flow are resolved and discretised on the grid,
whereas the effect of the unresolved is only modelled by an appropriate
subgrid-scale closure. Thereby, the stringent resolution requirements by a
full direct numerical simulation (DS) are loosened to a considerable extent.
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For a wide range of technical applications, the accurate prediction of flows
that undergo transition to turbulence is of great importance. In flat-plate
boundary layers, classical transition is initiated by weak disturbances
close to the wall. The strength of these disturbances grows exponentially as
they travel downstream, which finally leads to turbulent breakdown. However,
for ambient free-stream turbulence intensities of 1% or more, transition
occurs more rapidly, bypassing the classical transition process. This
scenario is denoted bypass transition and is characterised by the appearance
of streamwise-elongated streaky structures. The strength of these streaks
grows linearly with downstream distance, which eventually makes them become
unstable. This leads to the appearance of intense turbulent motion close to
the wall. Bypass transition has been chosen for the present project since
(i) it involves several challenges for successful flow modelling
(receptivity of the free-stream modes, prediction of transitional flow
structures and wall-bounded turbulence), (ii) it is relevant for technical
applications (mainly in turbo-machinery), and (iii) several open questions
concerning the exact mechanisms causing the instability of the streaks and
the appearance of turbulent spots still exist. It is expected that by using
LES on that flow case, through the reduction of the necessary CPU time for a
single run while maintaining the simulation accuracy, an important
contribution to the present research can be gathered.
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