Modelling of turbulent wakes

The dynamics of the turbulent three-dimensional wake generated by an axisymmetric bluff body with blunt trailing edge are experimentally and theoretically investigated at a diameter based Reynolds number of 188,000. A detailed analysis of the base pressure measurements shows that the large scale structures of the turbulent three-dimensional wake retain the structure of the laminar instabilities observed in the transitional regimes, in a statistical sense. These persisting instabilities at the turbulent regime, are associated with spatial and temporal symmetry breaking, giving rise to spatial reflectional symmetry and quasi-periodic vortex shedding. The influence of turbulence recovers the lost temporal and spatial symmetries in the long-time average. It is shown that the turbulent spatial dynamics are reproduced by a simple stochastic model the deterministic part of which accounts for the spatial symmetry breaking and gives rise to steady large scale structures through a supercritical pitchfork bifurcation, and the stochastic part modelling in a phenomenological sense the turbulent fluctuations acting on the large scale structures. The axisymmetric body wake is further investigated when axisymmetric slot-jet zero-net-mass-flux forcing is applied on the rear base. Landau-like models that capture the weakly nonlinear interaction between the global vortex shedding mode and axisymmetric forcing are derived from the phase-averaged Navier-Stokes equations. The Landau-like models describe accurately the forced response by means of measured base pressure of the global vortex shedding mode. With the present analysis it is demonstrated that the concept of weakly nonlinear global modes can be extended to a fully turbulent flow, far from the critical bifurcation Reynolds number, and a general framework for the description of systems with broken symmetries---giving rise to global dynamics---and turbulent dynamics is provided. The novel results presented here advance the understanding of the dynamics of three-dimensional turbulent wakes and pave the way for turbulence prediction and control.Open Acces

Nonlinear input/output analysis: application to boundary layer transition

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximise the drag are calculated using a gradient-based ascent algorithm. By including nonlinearity in the analysis, the proposed frequency-domain framework identifies the worst-case disturbances for laminar-turbulent transition. We demonstrate the framework on a flat-plate boundary layer by considering three-dimensional spanwise-periodic perturbations triggered by a few optimal forcing modes of finite amplitude. Two types of volumetric forcing are considered, one corresponding to a single frequency/spanwise wavenumber pair, and a multi-harmonic where a harmonic frequency and wavenumber are also added. Depending on the forcing strategy, we recover a range of transition scenarios associated with K-type and H-type mechanisms, including oblique and planar Tollmien–Schlichting waves, streaks and their breakdown. We show that nonlinearity plays a critical role in optimising growth by combining and redistributing energy between the linear mechanisms and the higher perturbation harmonics. With a very limited range of frequencies and wavenumbers, the calculations appear to reach the early stages of the turbulent regime through the generation and breakdown of hairpin and quasi-streamwise staggered vortices

Physics-Informed CNNs for Super-Resolution of Sparse Observations on Dynamical Systems

In the absence of high-resolution samples, super-resolution of sparse observations on dynamical systems is a challenging problem with wide-reaching applications in experimental settings. We showcase the application of physics-informed convolutional neural networks for super-resolution of sparse observations on grids. Results are shown for the chaotic-turbulent Kolmogorov flow, demonstrating the potential of this method for resolving finer scales of turbulence when compared with classic interpolation methods, and thus effectively reconstructing missing physics.Comment: Published in NeurIPS 2022: Machine Learning and the Physical Sciences Workshop. Code at https://github.com/magrilab/pisr. arXiv admin note: text overlap with arXiv:2210.1621

Weakly nonlinear modelling of a forced turbulent axisymmetric wake

A theory is presented where the weakly nonlinear analysis of laminar globally unstable flows in the presence of external forcing is extended to the turbulent regime. The analysis is demonstrated and validated using experimental results of an axisymmetric bluff-body wake at high Reynolds numbers, Re_D ∼1.88×10^5, where forcing is applied using a zero-net-mass-flux actuator located at the base of the blunt body. In this study we focus on the response of antisymmetric coherent structures with azimuthal wavenumbers m = ±1at a frequency St_D = 0.2 S, responsible for global vortex shedding. We found experimentally that axisymmetric forcing (m = 0) couples nonlinearly with the global shedding mode when the flow is forced at twice the shedding frequency, resulting in parametric subharmonic resonance through a triadic interaction between forcing and shedding. We derive simple weakly nonlinear models from the phase-averaged Navier–Stokes equations and show that they capture accurately the observed behaviour for this type of forcing. The unknown model coefficients are obtained experimentally by producing harmonic transients. This approach should be applicable in a variety of turbulent flows to describe the response of global modes to forcing

Turbulence model augmented physics informed neural networks for mean flow reconstruction

Experimental measurements and numerical simulations of turbulent flows are characterised by a trade-off between accuracy and resolution. In this study, we bridge this gap using Physics Informed Neural Networks (PINNs) constrained by the Reynolds-Averaged Navier-Stokes (RANS) equations and accurate sparse pointwise mean velocity measurements for data assimilation (DA). Firstly, by constraining the PINN with sparse data and the under-determined RANS equations without closure, we show that the mean flow is reconstructed to a higher accuracy than a RANS solver using the Spalart-Allmaras (SA) turbulence model. Secondly, we propose the SA turbulence model augmented PINN (PINN-DA-SA), which outperforms the former approach - up to 73% reduction in mean velocity reconstruction error with coarse measurements. The additional SA physics constraints improve flow reconstructions in regions with high velocity and pressure gradients and separation. Thirdly, we compare the PINN-DA-SA approach to a variational data assimilation using the same sparse velocity measurements and physics constraints. The PINN-DA-SA achieves lower reconstruction error across a range of data resolutions. This is attributed to discretisation errors in the variational methodology that are avoided by PINNs. We demonstrate the method using high fidelity measurements from direct numerical simulation of the turbulent periodic hill at Re=5600

Active Flow Control for Bluff Body Drag Reduction Using Reinforcement Learning with Partial Measurements

Active flow control for drag reduction with reinforcement learning (RL) is performed in the wake of a 2D square bluff body at laminar regimes with vortex shedding. Controllers parameterized by neural networks are trained to drive two blowing and suction jets. RL with full observability (sensors in the wake) successfully discovers a control policy which reduces the drag by suppressing the vortex shedding in the wake. However, a non-negligible performance degradation (~50\% less drag reduction) is observed when the controller is trained with partial measurements (sensors on the body). To mitigate this effect, we propose a dynamic, energy-efficient, maximum entropy RL control scheme. First, an energy-efficiency-based reward function is proposed to optimize the energy consumption of the controller while maximising drag reduction. Second, the controller is trained with an augmented state consisting of both current and past observations and actions, which can be formulated as a nonlinear autoregressive exogenous model, to alleviate the partial observability problem. Third, maximum entropy RL algorithms which promote exploration and exploitation in a sample efficient way are used and discover near-optimal policies in the challenging case of partial measurements. Complete stabilisation of the vortex shedding is achieved in the near wake using only surface pressure measurements on the rear of the body, resulting in similar drag reduction as in the case with wake sensors. The proposed approach opens new avenues for dynamic flow control using partial measurements for realistic configurations