Correlated turbulence modelling: An advancing Fourier series method

• Parametric spectral models can be used to define a flowfield in terms of a few fitting parameters.
• Calculating turbulence for a general point in space by interpolating between known grid points produces incorrect correlations for large spacings.
• The AFS method allows the generation of correctly correlated velocity time histories for a point moving through a non-uniform flowfield.

The simulation of correlated non-uniform flowfields in the time domain is required for the study of many time-dependent aeroelastic phenomena. A novel method for achieving representative spatially- and temporally-correlated flow simulation for a moving point in space, such as a point on a helicopter rotor, is discussed herein. This method uses the Fourier series to take frequency-domain information and from it reconstructs a time-domain velocity signal. It differs, however, from the traditional application in that the coefficients and phase angles for the Fourier components are modified at each time step to accommodate changing flowfield characteristics and achieve the correct correlations between one point in space and the next. This method is named the advancing Fourier series method. This paper covers the specifics of the method, including its advantages and disadvantages relative to other correlated flow modelling techniques.