Analysis of the wall pressure trace downstream of a separated region using extended proper orthogonal decomposition

Abstract

Multipoint wall pressure measurements and Laser Doppler Velocimetry (LDV) measurements of the velocity field generated over a 30° forward facing ramp are discussed in this paper. Mean and fluctuating signals are analyzed both in the mean separated region and in the recovering boundary layer flow. We present an analysis based on proper orthogonal decomposition (POD). The choice of a “POD region” as a subset of the sensor array is discussed. In a “POD region” restricted to the mean separated region, we show that the spatio-temporal coherence of the signal is efficiently captured by the POD decomposition. Extended POD is then introduced to extract in an objective way the part of the surface pressure signal, downstream of the mean reattachment point, which is correlated with the pressure signal under the separated region. The properties of this decomposition are demonstrated. We show that the power spectral density of the correlated part always displays a peak in the frequency domain associated with vortex shedding while the high frequency region is dominated by the uncorrelated part. A physical model is proposed to link large scale vortex structures and the correlated surface pressure fluctuations. We prove that the correlated pressure signal downstream of the mean separation length carries the properties of the distorted mixing layer eddies being advected and dissipating into the outer boundary layer flow. Finally, the spectral content of the correlated pressure signal is studied and we show that the first extended mode is able to capture the normalized power spectral density of the correlated pressure accurately. The method proposed here is therefore able to extract the contribution of separated shear layer eddies from the complex pressure trace in the recovering boundary layer near the mean reattachment point. The fast convergence of the POD decomposition in the separated region and the properties of the first extended mode downstream of the reattachment may be used to obtain an efficient reduced description for control or analysis purposes.

Wall pressure and conditional flow structures downstream of a reattaching flow region

“…Our observed distribution may be a consequence of such a distribution in the separated shear layer upstream of reattachment but the interaction with the wall has to be taken into account here. Hoarau et al (2006) have shown that the fluctuating pressure upstream of a reattachment is strongly correlated with that downstream of the reattachment. Therefore a simple convection of the vortices emanating from the separated shear layer could lead to such a distribution.…”

“…Following the same reasoning, we clearly expect the coherence of the structure to decrease when moving downstream. Hoarau et al (2006) have conjectured that these structures, generated in the separated shear layer, lose their kinetic energy in one turn over time scale while being transported along the wall in the outer layer. These authors have proposed a simple model equation for the decrease of the coherent kinetic energy based on an equilibrium between advection and dissipation that can be easily solved for constant length scale and transport velocity.…”

Statistical properties of wall pressure fluctuations over a forward-facing step

“…In the central region, several authors suggested that the flow can be considered two dimensional ͑2D͒ at least in a statistical sense. In this regard, Hoarau et al 17 stated that the use of end plates to ensure a 2D flow is not feasible due to the induced disturbances but, without end plates, the flow is 2D in the central region. Other authors ͑e.g., Moss and Baker 18 and Kiya and Sasaki 5 ͒ confirmed this point and suggested a ratio larger than 10 between the spanwise extension of the step and its height in order to neglect the 3D effects in the central region.…”

Unsteady wall pressure field of a model A-pillar conical vortex

“…Note that a long tube of 2 m length is connected to each sensor to adapt the impedance and to avoid acoustic resonances. For each probe, the frequency response is measured (magnitude and phase) with a B&K UA 0922 coupler and a reference microphone (see Hoarau et al, 2006 for more details). The signal/noise ratio of the pressure probe is 50 dB.…”