Characterisation and estimation of the flow over a forward-facing step

Abstract

The turbulent flow over a forward-facing step is studied using two-dimensional time-resolved Particle Image Velocimetry and simultaneously sampled wall-pressure fluctuations. The structure and behaviour of the separation region in front of the step is investigated using conditional averages based on the area of reverse flow present. The relation between the position of upstream separation and the two-dimensional shape of the separation region is presented. It is shown that when of ‘closed’ form, the separation region can become unstable resulting in the ejection of fluid over the corner of the step. The conditional averages are traced backwards in time to identify the average behaviour of the boundary layer displacement thickness leading up to such events. It is shown that these ejections are preceded by the convection of low velocity regions from upstream, resulting in a three-dimensional interaction within the separation region. The ejections are also shown to be linked to instances of increased swirling motion downstream. A mechanism for this process is proposed based on observations of the flow angle and magnitude over the step corner. The velocity field is then estimated using wall-pressure measurements. A linear model of the flow is created using Optimal Mode Decomposition (OMD), which is a generalisation of Dynamic Mode Decomposition (DMD). A comparison between OMD and DMD is made using both a synthetic waveform and the PIV data. In both instances it is shown to provide a model with a lower residual error and, for the synthetic waveform, an improved estimate of the system eigenvalues. The weights of the OMD modes are then used as the system states in a Kalman Filter with the pressure measurements as the system output. The performance of the Kalman Filter is shown to be superior to that of pseudo-inverse techniques such as Linear Stochastic Estimation.