Cross-Correlation of POD Spatial Modes for the Separation of Stochastic Turbulence and Coherent Structures

Abstract

This article describes a proper-orthogonal-decomposition (POD) based methodology proposed for the identification and separation of coherent and turbulent velocity fluctuations. Typically, POD filtering requires assumptions to be made on the cumulative energy content of coherent modes and can therefore exclude smaller, but important contributions from lower energy modes. This work introduces a suggested new metric to consider in the selection of POD modes to be included in a reconstruction of coherent and turbulent features. Cross-correlation of POD spatial modes derived from independent samples is used to identify modes descriptive of either coherent (high-correlation) or incoherent (low-correlation) features. The technique is demonstrated through application to a cylinder in cross-flow allowing appropriate analysis to be carried out on the coherent and turbulent velocity fields separately. This approach allows identification of coherent motions associated with cross-flow transport and vortex shedding, such as integral length scales. Turbulent flow characteristics may be analysed independently from the coherent motions, allowing for the extraction of properties such as turbulent length scale.

Analysis of Multi-Stream Fuel Injector Flow Using Zonal Proper Orthogonal Decomposition

“…A review of common criteria for cut-off mode are given by Brindise and Vlachos [17]. In the present work, the method of the cross-correlation of spatial modes between independent measurement sets, described by Butcher and Spencer [18] is used. This technique is shown to be an efficient filter for extracting the spatially coherent structures in a velocity flow field [19], since poorly correlating modes between independent tests suggest those modes are indicative of stochastic rather than coherent motion.…”

“…The cross-correlation method introduced by Butcher and Spencer [18] shall be used here to select the number of modes used for reconstruction of the velocity fields from the POD spatial modes and temporal coefficients. The technique is described in detail in [18], but the key points shall be outlined here for convenience. The velocity fields captured for Injector B are randomly ordered and split into two equal size sets.…”

“…This allows a single score for each mode which is presented in Figure 13. In line with [18], the cut-off is taken when the score falls below 0.5. For the case presented here, that is mode 12; therefore, all velocity field reconstructions in this section shall be based on the first 12 modes.…”

“…Firstly, the same underlying velocity set is used for POD and ZPOD, and therefore any spurious data would be present in both, and this is typically filtered by excluding the highest order modes. Turbulence is also contained within the higher order modes, and excluded in this approach by using the cross-correlation technique [18]. Therefore, the difference is the capturing of the movement of large structures, i.e., the pilot flow streams as a whole.…”

Recent Numerical Advances in Fluid Mechanics

“…The core idea is to utilize a second order accurate explicit filter in the presence of a discontinuity, and then gradually increase the order of explicit filter at the grid locations away from this discontinuity. The paper by Butcher and Spencer [7] takes up the concept of proper orthogonal decomposition (POD) for the identification of coherent structures. A new metric has been introduced for the selection of POD modes in reconstructing coherent or incoherent features.…”