Low-order models of the fluctuating wall pressure in an incompressible turbulent impinging jet

The fluctuating wall pressure field measured simultaneously at 137 points in an impinging jet with Re_D=23,000 and a nozzle-to-plate spacing of two diameters. A previous time averaged azimuthal decomposition¹ indicated that the fluctuating pressure field could be accurately described using few azimuthal modes, indicating this flow is an excellent candidate for a Low-Order Dynamical Systems (LODS) model. The present model was developed using a method similar as Ricaud,² whereby a general cubic order system of equations is fit to the experimentally determined Fourier coefficients. A LODS model developed using only azimuthal modes 0, 1 and 2 was able to reasonably accurately capture the behaviour of the fluctuating pressure field at r/D = 1.5. Downstream at r/D = 2.0, where the pressure field is more three-dimensional, the addition of azimuthal mode 3 is required to produce a stable system of equations, that again, reasonably captures the dynamics of the fluctuating pressure field. The success of this technique here, suggests that it may prove useful in high speed flow control applications where some degree of predictive ability is required.