Stochastic estimation of a separated-flow field using wall-pressure-array measurements

Abstract

Concurrent, surface-pressure and planar, particle image velocimetry ͑PIV͒ measurements were obtained in the separating/reattaching flow region downstream of an axisymmetric, backward-facing step at a Reynolds number of 8081, based on step height. The surface-pressure and PIV measurements were used to investigate the evolution of coherent structures in the flow field by employing proper orthogonal decomposition ͑POD͒ and multipoint, linear, stochastic estimation ͑mLSE͒ analysis techniques. POD was used to determine the dominant modes in the pressure signature, while mLSE was used to estimate the dominant flow structures above the wall from the wall-pressure POD modes over a series of time steps. It was found that a large-scale, coherent structure develops in place ͑i.e., temporally͒ at approximately half the reattachment distance. Once this structure reaches a height equivalent to the step, it sheds and accelerates downstream. This growth in place, and then shedding, resembles the evolution of the flow structure in the wake of bluff bodies. Such a "wake mode" has been observed in numerical-simulation studies of long cavities and backward-facing steps, where flow two dimensionality is controllable. The present study shows for the first time evidence for the existence of a wake mode in an experimental study of a backward-facing step. This is believed to relate to the quality of the two dimensionality ͑i.e., axisymmetry͒ of the test geometry and the ability to track the temporal evolution of structural features through mLSE.

Unsteady Behavior of a Pressure-Induced Turbulent Separation Bubble

“…At this position, the coherent vortices have attained their maximum size and are shed downstream of the separation bubble at a nondimensional frequency St s ≃ 0.7. Recently, another possible mechanism has been proposed by Sigurdson [16], Wee et al [43], and Hudy et al [9]. These authors argue that the shedding mode can be explained by an absolute instability akin to the formation of von Kármán vortex streets in the wake of a cylinder.…”

“…Results from detailed experimental and numerical investigations on backward-facing steps [1][2][3][4][5][6][7][8][9], fence-andsplitter-plate configurations [10][11][12][13], and blunt-plate flows [14][15][16] are available in the literature. They have revealed that the fluctuations of pressure and velocity in turbulent, reattaching flows are characterized by two dominant unsteady modes: one mode is associated with the roll-up of spanwise vortices in the shear layer above the recirculating region and their shedding downstream of the separated zone, and another, lower-frequency mode, is associated with a global motion of the separation bubble, described as "flapping motion" in the literature.…”

Wave Packets of Controlled Velocity Perturbations at Laminar Flow Separation

“…To estimate the backflow component, which could not be accurately resolved with the hot-wire method of the present study, PIV data on flow separation behind backward-facing steps seem helpful [3,7,11]. The most close to the present conditions are those of experiments [3] where the maximum of backflow was found as 5% of U 0 at Re h = 1060.…”

“…In experimental work, the intrinsic dynamics of separation bubbles is explained in terms of the "shedding" type instability [12] or the "wake mode" of velocity perturbations [7], emphasizing their essential difference from the convective instability of the separated shear layer. Theoretically, the oscillations synchronized over the entire separated-flow region are approached through stability analysis of local velocity profiles within the concept of their absolute / convective instability and global stability solutions [2,6,9,10,13,14,15].…”

Comparison of stochastic estimation methods with conditional events optimization for the reconstruction of the flow around a supercritical airfoil in transonic conditions

“…Once the Taylor expansion coefficients calculated, one only needs conditional event samples (for instance a wall pressure sensor) to obtain the approximation of the conditional average. SE has been extensively used to describe several turbulent flows: shear layer [1] [2], turbulent boundary layer [3], cavity flows [4] [5], jets [6] [7], separated flows [8]. And several extensions to the classical Linear Stochastic Estimation (LSE) [1] have been developed: Quadratic Stochastic Estimation (QSE) [9], Multi-Time-Delays SE (MTD-SE) [10] [11], spectral SE [6] [12], modified SE (SE combined with Proper Orthogonal Decomposition (POD), also called SE-POD) [13] [14] [15], Extended POD (EPOD) [16]...…”