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10:45   Vortex Dynamics and Structure Formation 1 10:45 15 mins #544 On the geometry of coherent structures in channel flow turbulence Abhishek Paraswarar Harikrishnan, Johannes von Lindheim, Nikki Vercauteren, Rupert Klein, Gitta Kutyniok Abstract: In this paper, we study the geometry of coherent structures and their spatial distribution in a three-dimensional channel flow at Re τ = 590. Particular focus is placed in the near-wall region at y + < 40. The scalar fields of interest composed of these ubiquitous structures are extracted using common vortex identification criteria: Q, ∆, λ 2 and the Finite-Time Lyapunov Exponent (FTLE). The first three, derived from the instantaneous velocity field, were normalized with <ε> /ν, where <ε> is the mean dissipation rate and ν is the kinematic viscosity and examined for multiple thresholds using the traditional box-counting method. As expected, low threshold values indicate larger, complex structures while at higher values they break down into simpler, filamentary vortices. The FTLE approach, which measures the separation of fluid particle trajectories, has no reliance on the threshold and as a result was investigated without it. To characterize the spatial distribution, box-counting is applied to the point sets of the barycenters of the structures. Finally, an alternative methodology based on a multi-scale representation of the data using the shearlet transform is proposed for the eduction of structures across a broad range of scales. Shearlets are closely related to wavelets and curvelets. They differ from wavelets in that they are a multiscale representation system with a parabolic scaling. This feature is important to capture anisotropic, meandering vortices in a turbulent flow oriented in arbitrary, grid-independent directions. In comparison with curvelets, their fundamental construction is substantially simpler, although equally powerful, and allows for a unified treatment of the continuum and digital world. This renders the shearlet technology amenable to rigorous analysis. Our aim is to identify characteristic patterns that appear across the scale hierarchy in the shearlet transform space by following an approach similar to that of Bermejo-Moreno and Pullin. This method should allow for a structural characterisation of turbulence at a multitude of scales, thereby enabling investigations of the life time of structures and other statistical properties. 11:00 15 mins #618 ON THE ENERGETICS OF SEPARATING AND REATTACHING FLOWS AND THEIR MODELING Andrea Cimarelli, Adriano Leonforte, Andrea Crivellini, Elisabetta De Angelis, Diego Angeli Abstract: The flow around a finite rectangular plate is recognized to be of overwhelming interest. It represents one of the simplest kind of flow reproducing very fundamental and distinct flow phenomena such as i) a laminar flow separation at the sharp leading-edge; ii) a free-shear layer instability and transition to turbulence; iii) a low frequency phenomenon of shedding of large scale vortices from the separated region; iv) flow reattachment and recirculation within the separation bubble; v) the shedding of large scale vortices in the wake; vi) the turbulent wake development. The consequent strongly inhomogeneous character of the problem and the combined presence of small scales, due to the development of turbulence, and large scales due to phenomena of shedding of large-scale vortices, challange for a rational approach able to give a clear picture of the interrelated physical processes. In this work, we face these issues by performing a detailed multiscale analysis of Direct Numerical Simulation data of the flow around a finite rectangular plate with chord-to-thickness ratio 5 and Reynolds number 3000, see figure 1. Two-point spatial correlation functions and energy spectra reveals the presence of a coupling mechanism between recirculating turbulent structures and the large-scale vortex shedding giving rise to a self-sustaining cycle [3]. Interestingly, the free-shear layer is recognized to be the site of negative turbulence production phenomena, i.e. a flow reversal of energy from the fluctuating field to the mean flow. The analysis of cospectra shows that negative production is a result of non-local phenomena taking place over long streamwise distances and associated with low-frequency shedding of vortices. All these mechanisms challange for turbulence closures. To this aim, an a priori analysis of filtered data is finally performed in order to understand the behaviour of the under-resolved field and to shed light on suitable and reliable turbulence modelling approaches. 11:15 15 mins #282 Large-eddy simulation of the fluidic oscillator jet Elizaveta Dauengauer, Rustam Mullyadzhanov Abstract: A fluidic oscillator emits a spatially oscillating jet which can be employed in many practical applications such as the control of separated flows or mixing efficiency enhancement. Although in the past the potential of this device has been shown for many applications, the details for its performance become the focus of the research only recently [1, 2]. Provided a number of experiments are available, advances in computations and technological needs suggest perform a series of eddy-resolving simulations to document the flow based on the described device. We study a fluidic oscillator jet with the geometry in accord with recent experiments [2] in the range of Reynolds numbers between 3 × 10^3 and 30 × 10^3 . For that purpose we use the accurate spectral-element Navier-Stokes solver Nek5000 [3] within Large-eddy simulation framework and dynamic Smagorinsky model for subgrid scales. Using for a coarse mesh around 37 × 10^3 spectral elements with the polynomial order N = 10 leading to the mesh of 37 × 10^6 nodes, we investigate the properties of oscillating jet. Figure 1 shows some preliminary results demonstrating the jet emerging from the nozzle with large-scale transverse oscillations. This dynamics results from the Coanda effect or a bistability state of the internal flow. The unsteady loop starts from any small perturbation causing an asymmetrical pressure difference in mixing chamber of oscillator. Consequently, part of the jet flow moves through the feedback channel back to the device inlet, where it pushes back the main stream. Then the process repeats itself on the other side of the device leading to some kind of a global instability with self-oscillations. Preliminary results provide an excellent agreement for the oscillation frequency which grows linearly with the Reynolds number increase. The full work will present the analysis of the phase-averaged fields, detailed comparison with experiments [2], turbulent kinetic energy budget as well as the application of various modal decomposition techniques. The work is supported by Russian Foundation for Basic Research grant No. 18-38-20167 and state contract with IT SB RAS. References [1] L.N. Cattafesta, M. Sheplak. Actuators for active flow control. Annual Review of Fluid Mechanics 43:247-272, 2011. [2] F. Ostermann, R. Woszidlo, C.N. Nayeri, C.O. Paschereit. Properties of a sweeping jet emitted from a fluidic oscillator. Journal of Fluid Mechanics 857:216-238, 2018. [3] S.G. Kerkemeier, P.F. Fischer , J.W. Lottes. Nek5000: Open source spectral element cfd solver. Available at http://nek5000.mcs.anl.gov, 2008. 11:30 15 mins #345 Direct numerical simulation of variable density starting turbulent jets Vladislav Ivashchenko, Rustam Mullyadzhanov Abstract: Starting jets represent an important class of flows from practical and fundamental point of view and are tightly connected with the dynamics of vortex rings [1]. Additional factors such as the inflow turbulence and variable density significantly complicate the situation. We study several cases of fully developed turbulent pipe jet entering an ambient gas environment using direct numerical simulations of the Navier-Stokes equations. To solve governing equations the computational code Nek5000 is used [2] featuring an accurate spectral element method with polynomial order N = 10 and around 126 × 10^3 spectral elements for this particular case resulting in 126 × 10^6 nodes while time discretization scheme corresponds to third order. We mainly consider an air jet entering an air medium, carbon dioxide or helium. The variable density is due to the mixing of two different gases while the overall temperature is assumed to be constant. The Reynolds number is set to Re = 5300 for all cases allowing the direct comparison. Figure 1 shows the evolution of the air jet in the carbon dioxide environment. A vortex ring on the jet front can be well-distinguished and is relatively resistent to the background turbulence. Comparison of different cases will help to describe the effects due to variable density resulting in the propagation speed as a function of time. A simplified analytical model will be presented capturing these differences. The work is supported by RFBR grant No. 19-08-01227 and state contract with IT SB RAS. References [1] K. Shariff, A. Leonard. Vortex rings. Annual Review of Fluid Mechanics 24:235-279, 1992. [2] M.O. Deville, P.F. Fischer, E.H. Mund. High-order methods for incompressible fluid flow. Cambridge University Press. 2002. 11:45 15 mins #604 Energy balance quantification and wake morphology description in collocated wind plants Hawwa Kadum, Mike Quigley, Sarah Smith, Gerard Cortina, Raul Bayoan Cal, Marc Calaf Abstract: Large eddy simulations approach is used to investigate the power production enhancement mechanisms in collocated wind plants in which twelve clusters of vertical axis wind turbines are collocated with a $3 \times 4$ horizontal axis wind turbine array. Three cases are studied: 1.) a standard wind plant (SWP), 2.) an aligned collocated wind plant (CWP$_{al}$), and 3.) a staggered collocated wind plant CWP$_{st}$. A control volume analysis is employed to examine the energy balance and relevant terms for the various characteristic compounded wakes. The results show that collocated configurations have an averaged 48.5\% higher power than the standard wind plant due to the faster wake recovery and improved vertical transport of mean kinetic energy. The collocated plants spatial heterogeneity is found to play a significant role in mean kinetic energy vertical transport advancement by increasing the dispersive stress with an average of 37.5\% increase in the vertical kinematic shear stress from the standard wind plant, consequently reinforcing the mean kinetic energy flux which is the lead term in mean kinetic energy budget. Furthermore, placing the vertical axis wind turbines cluster in proximity and upstream of a horizontal axis wind turbine increases its power production since an increase in the mean velocity is observed. This arrangement resulted in 4\% higher power production for the aligned configuration than the staggered even though the latter has faster wake recovery. It also leads to horizontal axis wind turbine and vertical axis wind turbine wake merging and generating a wake that is similar in structure to a horizontal axis wind turbine wake with heightened Reynolds shear stress. The staggered configuration, on the other hand, behaves as two interacting wakes generating a more confined and intensified skewed wake. Mean statistics for velocity and Reynolds shear stress are presented per single HAWT for the three cases investigated herein. Time averaging of a quantity is denoted with an over-bar ($\overline{.}$), while angular brackets ($\langle . \rangle)$ are used to express spatial averaging. Figure \ref{fig1} shows the streamwise mean velocity component $\overline{u}$ through consecutive slices upstream and downstream the rotor. The slices represent the velocity in $zy$ planes at several streamwise locations. Mean velocity $\overline{u}$ at $x/D$= -0.1 is 9.5 $ms^{-1}$ on average for the standard plant layout and the wake extends to $x/D$=4. The aligned collocated configuration demonstrates increased velocity surrounding the swept area of the rotor when compared to the SWP layout. The velocity deficit is mild at locations larger than $x/D$=3.5, yet the deficit extends up until $x/D$=5. Cases CWP$_{al}$ and CWP$_{st}$ are similar as they possess an increase in the streamwise velocity around the rotor compared to the standard case. However, the wake for CWP$_{st}$ is shorter than in the aligned case as the wake deficit becomes marginal after $x/D$=4. Consequently, the CWP$_{st}$ case exhibits a faster wake recovery than the aligned case. The minimum velocity of 8 $ms^{-1}$ assigned orange color in figure \ref{fig1} can be last marked at $x/D$=2.6 in the aligned configuration, while it is no longer present after $x/D$=2.3 in the staggered case, thus representing a slower rate of recovery. Furthermore, around the rotor, $\overline{u}$ is more homogeneous in the collocated plants suggesting better flow mixing even in the near wake. In contrast, the standard configuration contains a significant velocity gradient between the flow above and below the hub height. The enhanced flow mixing caused by the VAWTs results in a significant increase in flow velocity of a collocated wind plant. 12:00 15 mins #334 MAGNETIC DISSIPATION OF COHERENT STRUCTURES AND PARTICLE DEPOSITION IN MAGNETOHYDRODYNAMIC TURBULENCE AT LOW MAGNETIC REYNOLDS NUMBERS Bruno Magacho, Luca Moriconi Abstract: We discuss the problem of particle deposition and relaminarization in wall-bounded magnetohydrodynamic (MHD) turbulent flows subject to external static magnetic fields, from a unifying structural point of view. Our study is focused on flow regimes characterized by low magnetic Reynolds numbers, a meaningful assumption for most of laboratory and industrial applications, where electrolytes or liquid metals are the fluids of interest. Even though the connection between vortex suppression by magnetic fields and particle deposition is clearly indicated from numerical investigations, a deeper phenomenological understanding of the particle-vortex dynamics involved in the deposition process is still in order. We are able to recover, through a simple structural model of deposition based on particle transport induced by quasi-streamwise vortices, some important qualitative features observed in numerical simulations, as the dependence of the deposition rate with the particle Stoke’s number for arbitrary orientations of the external magnetic field with respect to the normal to the wall direction. It is noted, furthermore, that deposition phase diagrams, can be of great help in the prediction and control of deposition. Motivated by these suggestive results, which provide support for the relevance of the structural approach to MHD turbulence, we put forward, from very energy balance arguments, a criterion for the relaminarization of turbulent flows at high Hartman’s numbers, which turns out to agree reasonably well with long-established experimental data. 12:15 15 mins #442 Turbulence dynamics transition of flow past a circular cylinder and the prediction of vortex-induced forces Bernat Font Garcia, Gabriel Weymouth, Vinh-Tan Nguyen, Owen Tutty Abstract: We investigate the transition of three-dimensional (3D) to two-dimensional (2D) turbulence of incompressible viscous flow past a circular cylinder as the span is constricted. The inclusion of a bluff body provides novel information with respect to previous work on free turbulent flow [1, 2, 3]. The coexistance of both turbulence dynamics can be found at the mid wake region for highly anisotropic geometries as shown in figure 1 (left). Both 3D and 2D turbulence (-5/3 decay rate and -3 decay rate respectively) are captured on the inertial subrange for the Lz=0.5 case, where Lz is the cylinder span relative to its diameter. Small-scale 3D structures detach from the wall even on very constricted domains. These structures are rapidly two-dimensionalised by the large-scale rotation of the Kármán vortices when the span is 50% of the diameter or less. The large-scale rotation as a mechanism of two-dimensionalisation is in agreement with other studies such as [3, 4]. On the other hand, the constriction of the span induces larger forces on the cylinder as displayed in figure 1 (right). There is a quasi-linear relation between the r.m.s value of the lift coefficient (CL) and the turbulence kinetic energy (TKE). Higher values are found on both parameters as the span is reduced because of the emerging energised 2D vortical structures. Evidencing the strong relation of the forces induced to the cylinder and the turbulence statistics, a regression model is included to provide an a priori analysis given a sufficiently large data set. 12:30 15 mins #352 Motion of helical vortices : a dynamical system approach maurice Rossi, Ivan Delbende, Can Selcuk Abstract: We reduce the three-dimensional dynamics of helical vortices in terms of a dynamical system. It is shown that some complex dynamics can be captured by these simplified models such as leapfrogging or overtaking of interlaced helical vortices.

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