The prediction of trailing edge noise is a key element in the aeroacoustic
analysis of aircraft engines, and the design of quieter engines. The
prediction of trailing edge noise is particularly difficult because at a
fundamental level, it requires information about details of the vorticity
and velocity fluctuation fields produced by the trailing-edge boundary layer
(Howe, 1978). However, this information is usually not available. As a
result most predictions tend to rely heavily on empirical correlations
between noise and fairly simple boundary layer parameters such as thickness
(e.g. Schlinker and Amiet 1981, Brooks et al., 1989). Unfortunately, such
predictions cannot account for the detailed structure of the boundary layer,
such as can routinely be predicted using CFD solutions. Neither can they
provide any information about the specific features of the boundary layer
turbulence that contribute to the noise, and thus cannot be used as a basis
for manipulation of the boundary layer for the purposes of controlling that
noise.
The ultimate purpose of this work, in conjunction with the parallel effort
of Glegg (2001), is the development of trailing edge noise prediction
method, suitable for aircraft engine rotors, in which the velocity and
vorticity source terms are modeled directly using information from CFD
solutions. This approach would provide a dramatic reduction in the amount of
empirical input needed, and would couple the aeroacoustic prediction to the
best aerodynamic information available. Furthermore, the expression of the
acoustic problem in terms of the complete two-point vorticity correlation
function would allow the specific turbulent motions responsible for the
noise production to be identified as part of a calculation.
The method used is based on the premise that the form of the two point
velocity correlation function is largely determined by the requirement of
continuity and the inhomogeneity of the flow visible in the Reynolds stress
field. The two point velocity correlation is calculated from the double curl
of the two point vector potential correlation, guaranteeing that continuity
is satisfied. The vector potential correlation function is modeled by
analogy with homogeneous turbulence, i.e., as the product of a scaling
function determined from the Reynolds stress field, and a decay function
that controls the drop off of correlation with distance. Predictions can be
made after prescribing the Reynolds stress field, the form and lengthscale
of the decay function. Devenport et al. (2001) found the method to
accurately predict two-point correlations in wakes when a decay function
derived from the von Karman spectral form was used, in conjunction with a
constant lengthscale. This study concerns the adaptation of this method to
boundary layers, its extension to the prediction of vorticity correlations,
and its application to the trailing edge noise problem.
The method permits to obtain two-point correlations, proper orthogonal modes
and compact eddy structures. Example of comparison between experimental
results of a boundary layer on a flat plate (Adrian et al. (2000)) are shown
in the corresponding Figures.
More results can be found in Spitz et al. (2003).