16:15
Instability, Transition and Control of Turbulent Flows 3
16:15
15 mins
#134
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Feedback stabilization of a Plane Couette Flow Exact Coherent Structure
GEOFFROY C. P. CLAISSE, ATI S. SHARMA
Abstract: The idea of turbulence as a finite dimensional dynamical system was introduced by Hopf (1948). Each solution of the Navier-Stokes equations is associated to a point motion in a state-space, where its phase motion can be followed. This theory was strengthened by the discovery of Exact Coherent Structures (ECS) in shear flows. They correspond to invariant solutions of the Navier-Stokes equations. The turbulent inertial manifold is depicted as a network of Exact Coherent Structures acting as unstable attractors of the turbulent dynamical state and interlinked via heteroclinic connections.
Nonetheless, the mechanism by which the turbulent dynamical state remains and leaves the neighbourdhood of an ECS is still unknown. It is supposed that the turbulent dynamical state escapes the neighbourhood of an ECS along its unstable eigenspace (Gibson & al. 2008), although recent work suggests that the non-normality of its stable eigenspace may help the turbulent trajectory to leave along stable directions (Farano & al. 2019).
In the light of this, we focused here on the stabilization via state-space control theory of the unstable eigenspace of the Nagata (1990) lower-branch (referred to as EQ1), known as the least unstable Plane Couette Flow ECS.
The application of state-space control theory to ECS requires a linearised state-space model. Yet, the linearisation around an ECS is very high-dimensional. To reduce the state dimension, we developed a divergence-free model (the Orr-Sommerfeld Squire model Extended for an ECS as baseflow, or OSSE), which resulted in a boundary actuated full-matrix state-space model. The derivation follows from the Orr-Sommerfeld Squire model, but no longer diagonalises with Fourier wave-numbers due to the breaking of translational symmetry of the baseflow. We calculated the leading eigenmodes of different equilibria and validated them against the literature (Bewley & Liu 1998; Gibson & al. 2008). The OSSE model depicts faithfully the dynamical evolution of the flow in the neighbourhood of an ECS for small perturbations and it enables access to linear control theory. We then built a full-information state-feedback Linear Quadratic Regulator (an optimal controller) actuating via wall-transpiration and targeting the unstable eigenmodes of EQ1. We showed that these modes are controllable with this actuation type and determined their most effective actuation modes (see fig.1). The optimal control derives from the solution of a high-dimensional Riccati equation, which is computationally expensive but now accessible thanks to the OSSE model. Finally, we were able to stabilize EQ1 within a linear simulation.
We are in the process of determining the radius of stability of the stabilized EQ1 in non-linear simulation. This result will give direct insights on the mechanisms responsible for the chaotic evolution of the turbulent state.
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16:30
15 mins
#226
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Optimal forcing to destabilise turbulence in a pipe flow
Elena Marensi, Ashley P. Willis, Rich R. Kerswell
Abstract: See uploaded file
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16:45
15 mins
#535
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Towards an extension of Barkley's pipe-flow model to transitional plane Couette flow.
Cristobal Arratia
Abstract: Abstract text in the attached pdf.
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17:00
15 mins
#539
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Wavy Instability in pulsating pipe flow
Atul Varshney, Duo Xu, Xingyu Ma, Bjorn Hof
Abstract: We report that fluid flows when subjected to periodic velocity modulations (e.g. cardiovascular flow) exhibit hydrodynamic instabilities and early turbulence depending on frequency and amplitude of pulsation. At low amplitudes the flow has the same qualitative features as turbulent pipe flow with steady driving and the transition occurs via typical puff like structures. However, at high amplitudes a qualitative different transition scenario is observed. The former case (transition to puffs) was investigated by Xu et al.[1] and a delay in the transition point to turbulence with increasing amplitude was reported. Remarkably, at high amplitudes a wavy Kelvin-Helmholtz type instability is observed, shown by snapshots in Fig. 1. Further, we find that the instability and turbulence only persist during flow deceleration and disappear during the acceleration cycle (phase locked turbulence). Interestingly, with increasing amplitude this new wavy instability sets in at Reynolds number much lower than the steady case (critical Reynolds number for pipe flow ~2000). Our observations show that this instability typically occurs downstream of (modestly) curved pipe sections and at stenosis. In order to investigate the relevance of this instability to cardiovascular flows we report experiments carried out with blood as the working fluid.
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17:15
15 mins
#545
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Interscale energy transport for turbulent stripe in rotating plane Couette flow
Tomohiro Nimura, Takuya Kawata, Takahiro Tsukahara
Abstract: Turbulent stripe is spatial intermittent structure and often occurs in subcritical transition of wall-bounded shear flow. Turbulent stripe is composed of large-scale flow and small-scale structure. The large-scale flows as well as the stripe pattern are steadily oblique to the mean flow direction and may decide the patterning of localized turbulence. The large-scale flow is also essential for the growth of a turbulent spot. The small-scale structures correspond to rather disordered motions in the localized turbulence. The interactions between the large-scale flows and small-scale structures are complicated, but of importance to understand the physics relevant to the pattern formation of localized turbulence. To authors' knowledge, no one has discussed the interscale transport of the Reynolds stresses, including momentum transport, between the large-scale flow related to small-scale structures.
In this study using direct numerical simulation, we investigate turbulent stripes in the plane Couette flow with a spanwise cyclonic system rotation (the cyclonic rotating plane Couette flow, CRPCF). In this system, the Coriolis force stabilizes the Couette flow, and various turbulent stripes that have never formed in the non-rotation case are observed in a wider range of the Reynolds number in this flow. We performed direct numerical simulations for the PCF/CRPCF at Reynolds number Re = Uw δ/ν = 375, 500, 750, and 1000 (Uw, δ, and ν are the half of relative wall speed, the channel half width, and the kinematic viscosity, respectively) with increasing the system rotation rate Ω to final state, i.e. laminar flow. As shown in Figure 1, variety of flow regimes are classified. Total volume-averaged turbulent kinetic energy (TKE) and energy ratio of the large-scale flow and small-scale structures change, even with keeping the turbulent stripe, depending on Re and Ω. At fixed Re, the large-scale flow grows from Ω = 0 to a certain Ω while the interscale transport term exhibits energy transport from the small-scale structures to the large-scale flow. This result may imply that the small-scale structures can sustain the large-scale flow. The Reynolds-number and rotation-rate dependencies of the interscale transport term would be discussed.
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17:30
15 mins
#162
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System identification using Neural Networks applied to experimental noise-amplifier flows characterized by real-time optical flow velocimetry
Antonios Giannopoulos, Jean-Luc Aider
Abstract: In noise amplifiers flows initial random upstream perturbations are selectively amplified by convective instabilities via the receptivity process and convected downstream. A possible approach in flow control is to reduce the numbers of degrees of freedom of the system through the use of a Reduced Order Model (ROM). This approach alone is challenging, especially when dealing with noise amplifiers flows. A more realistic approach has been proposed by Guzman et al.[1] who propose an identification method to capture the dynamics of the flow through local sensors (velocity/ vorticity/ vortex identification criteria like swirling strength) which are linked to the full POD reduced order model to be identified and predicted. This information can be later used in a control law targeting the kinetic energy of the perturbation field calculated from the POD model. In this study, time-delay artificial feed-forward Neural Networks (NN) are used for the multi-input/ multi- output(MIMO) identification process in the form of a non-linear regression. The optimum network architecture is discussed and the results are compared to a traditional N4SID method [1]. Two examples of amplifier flows are used as benchmarks: the Backward Facing Step (BFS) and the transitional flat plate Boundary Layer (BL) flow. The goal is to create a dynamic observer to predict the full POD coefficients of a ROM from local measurements extracted from 2D-2C (two-components in a 2D plane) velocity fields using an optical flow PIV code [2] implemented on a GPU (Graphics Processor Unit). The PIV experiments are carried out in a 80 cm long, low Reynolds number, hydrodynamic channel driven by gravity. The efficiency of the training process of the system identification regarding the position and the nature of the sensor (local velocity, vorticity, swirling strength criterion or combinations) is discussed. The importance of noise filtering in the velocity time-series in the reduced order modelling as well as the identification process is discussed.
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17:45
15 mins
#265
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MEAN FLOW ANALYSIS OF A TURBULENT WIND TURBINE WAKE
Giovanni De Cillis, Stefania Cherubini, Onofrio Semeraro, Stefano Leonardi, Pietro De Palma
Abstract: In this work, we investigate the instability of wake flows generated by three-bladed wind turbines through a mean flow analysis. A wind turbine model, already considered for previous analyses, is simulated by an incompressible LES approach, which employs the actuator line method for mimicking the aerodynamic forcing exerted by the turbine blades and an immersed boundary method for tower and nacelle. The stability of such flows is studied relying on the analysis of their optimal frequency response to external harmonic excitations, using the linear resolvent operator with a bi-local approach. Since the flow is highly turbulent (Re = 6.3*10^5 ), the diffusive effect of fluctuations has to be taken into account in order to obtain meaningful results. Qualitative results are obtained employing the Boussinesq approximation for the Reynolds stresses, and assuming the eddy viscosity is uniform at each streamwise location. This is equivalent to considering an “effective” Reynolds number into the base flow stability equation. Within such an approximation, the Reynolds number needs to be reduced by two orders of magnitudine in order to obtain nearly stable spectra, as expected from a mean flow stability analysis. A more accurate approach takes into account the spatial distribution of the eddy viscosity as proposed by Tammisola & Juniper. Such an approach is based on a triple decomposition of the unsteady flow, as proposed in Reynolds & Hussain, and employs again the Boussinesq approximation, which allows one to calculate the eddy viscosity from the Reynolds stresses obtained by the LES. The analysis is carried out at several streamwise positions in the wake. We begin by only considering the wake of the turbine, such that the bottom-wall boundary layer is discarded. This simplified geometry is aimed at validating our results with previous ones available in the literature, according to which the most spatially amplified fluctuation is a single helical mode. We are also interested into the calculation of POD modes which can provide useful information for interpretation and validation of the resolvent analysis.
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18:00
15 mins
#138
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What can we learn from the Edge about bypass transition?
Miguel Beneitez, Yohann Duguet, Philipp Schlatter, Dan S. Henningson
Abstract: Attached in pdf
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