Anisotropic filter for synthetic turbulence
Summary
A technique of synthetic turbulence is proposed by developing a general
form of anisotropic filter, which can realize the desired velocity spectra
of three-dimensional anisotropic turbulence. The anisotropic filter can
be directly implemented instead of obtaining the non-Gaussian energy
spectra through Gaussian superposition, which is then combined with
linearised Euler equations to predict the leading edge noise.
To develop a new method of synthetic anisotropic turbulence by
deriving a general form of anisotropic filter that generates the
homogeneous anisotropic turbulence. To investigate the influence of anisotropy on turbulence-airfoil
interaction noise by applying various stretching ratios.
The effectiveness of pseudo three-dimensional anisotropic filter is
verified by comparing with Amiet’s analytical solution. The turbulent
velocity field induced by the anisotropic filters can be regarded as the
pseudo three-dimensional anisotropic turbulence, which will reproduce
the major statistics of three-dimensional turbulence
Through an integral solution of the three-dimensional FW-H equation,
the far-field SPL spectra is obtained, which shows good agreement
with the theoretical solution, to within 1.5 dB accuracy. It can be
concluded that doubling of the tangential turbulent length scale leads
to 9 dB increase in SPL spectra, which is attributed to the octupling of
one-dimensional energy in the transverse direction.
