Synthetic Inflow Condition for Large Eddy Simulation (Synthetic - KTH

CHAPTER 2. BACKGROUND
Subsequently Sagaut [34] proposed an extension of the original method of Lund
[45] to compressible turbulence using rescaling and recycling of the pressure and
temperature fluctuations in addition to the usual operations performed in the original
method.
Moreover a more robust variant of the original method of Lund was proposed by
Ferrante and Elghobashi [9] who noticed that Lund’s method was very sensitive to
the initialization of the flow field. In fact they were unable to generate fully developed
turbulence from the initialization procedure recommended in Lund [45](mean
velocity profile superimposed with random uncorrelated fluctuations). In their new
approach the flow field was initialized using synthetic turbulence with a prescribed
energy spectrum and shear stress profile.
Additionally, another modification was recently proposed by Spalart [35] to the
original method of Lund [45] regarding the reduction of the computational cost
of generating the inflow data. The recycling station should be taken much closer
to the inflow and the precursor simulation eliminated, carrying out in the main
simulation domain the recycling procedure so that it generates its own inflow data.
Li [32] proposed also another procedure to reduce the storage requirement and the
computational cost of running a precursor simulation prior to the main simulation.
2.4.3 Synthetic Turbulence
These methods synthetize inflow conditions using some kind of stochastic procedure
and don’t need precursor simulation or rescaling of a database created from
a precursor simulation. These stochastic procedures are referred to as synthetic
turbulence generation methods and use random number generators to construct
a random velocity signal which resembles turbulence. However, the synthesized
turbulence represents only a crude approximation of real turbulence. In fact the
underlying assumption on which they are based, is that a turbulent flow can be
approximated by reproducing a set of low order statistics such as mean velocity,
turbulent kinetic energy, Reynolds stresses, two-point and two-time correlations.
Higher order statistics such as the terms in the budget of the Reynolds stresses
(the rate of dissipation, the turbulent transport or the pressure-strain term) are not
usually reproduced. Additionally, the synthesized turbulence may show different
structures from the one corresponding to a real flow. It could also undergoe a transition
process before it developing towards a more physical state if the structure
of the turbulent eddies and their dynamics is not accurately reproduced. In recent
years several synthetic turbulence generation methods have been proposed which
are going to be discussed as following differentiating the ones working in physical
space (referred to as algebraic methods) from the methods working in Fourier space
(referred to as spectral methods).
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