Modal energy flow analysis of a highly modulated wake behind a wall-mounted pyramid

Abstract

We experimentally investigate the highly modulated turbulent wake behind a wall-mounted square-base pyramid protruding through the boundary layer. We present the first modal energy flow analysis of a time-resolved three-dimensional velocity field from experimental particle image velocimetry data. The underlying low-order representation is optimized for resolving the base-flow variation as well as the first and second harmonics associated with vortex shedding – generalizing the triple decomposition of Reynolds & Hussain (J. Fluid Mech., vol. 54, 1972, pp. 263–288). This analysis comprises not only a detailed modal balance of turbulent kinetic energy as pioneered by Rempfer & Fasel (J. Fluid Mech., vol. 275, 1994, pp. 257–283) for proper orthogonal decomposition (POD) models, but also the companion energy balance of the mean flow. The experimental results vividly demonstrate how constitutive elements of mean-field theory (Stuart, J. Fluid Mech., vol. 4, 1958, pp. 1–21) near laminar Hopf bifurcations remain strongly pronounced in a turbulent wake characterized by highly modulated, quasi-periodic shedding. The study emphasizes, for instance, the stabilizing role of mean-field manifolds, as explored in the pioneering POD model of Aubry et al. (J. Fluid Mech., vol. 192, 1988, pp. 115–173). The presented low-order representation of the flow and modal energy flow analyses may provide important insights and reference data for computational turbulence modelling, e.g. unsteady Reynolds-averaged Navier–Stokes simulations.

Interscale energy transfer in the merger of wakes of a multiscale array of rectangular cylinders

“…This can be linked to the fact that both are evaluated in the vicinity of the fluctuations intensity peaks of particular wakes. A similar energy balance is also reported by Hosseini et al [15], who considered a flow past a wall-mounted pyramid, focusing at the area around shedding intensity peak. The authors show that the entire gain of the mean energy is due to the convection term, whereas the loss splits between the production term and the pressure term in the proportion of 30 % and 70 %.…”

“…40 % − 60 % and the former two account for further 20 % − 40 %. Hosseini et al [15] reported a similar tendency in the flow past a pyramid. The energy balance of its first shedding harmonic was driven entirely by the production term, while losses were caused by the convection term (20 %) and the stochastic fluctuations production (70 %, referred to as residual in Hosseini et al [15]).…”

“…Since we consider a number of simultaneous coherent fluctuations, a new, suitable form of these equations is derived and further applied to the analysis of the gathered data. This approach is similar to an intermodal energy flow study presented by Couplet et al [14] (an energy exchange between a number of POD modes is considered therein) or, more recently, by Hosseini et al [15] (an energy exchange between a slowly-varying base flow; the first and the second harmonic of a wall-mounted pyramid's shedding are studied).…”

Cartographing dynamic stall with machine learning

“…In particular, there is abundant literature using Singular Value Decomposition (SVD) based methods such as POD/PCA (Taira et al, 2017), DMD (Schmid, 2010;Kutz et al, 2015;, SPOD (Sieber et al, 2015). These methods generally do not perform well in cases with any kind of traveling wave behavior (Taira et al, 2017;Riches et al, 2018;Hosseini et al, 2016). The reason for this lies in the creation of fixed spatial functions/basis functions.…”

Cartographing dynamic stall with machine learning

“…The concept of transfer learning exploits the fact that once a model has been trained for one task, it can be easily remolded to complete similar tasks (Brownlee, 2017). In practice this means that a neural network can be trained for a specific computer vision task and then easily be reused; i.e., a network originally trained for classifying breeds of dogs within photographs can be easily reused on aerodynamics data (the FASTAI project has a lecture series expanding at length on this theme; Howard et al, 2019). This may seem like an exotic claim but there is solid reasoning underpinning the claim.…”