JFM Rapids
Phase-synchronization properties of laminar cylinder wake for periodic external forcings
- M. A. Khodkar, Kunihiko Taira
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- 05 October 2020, R1
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We investigate the synchronization properties of the two-dimensional periodic flow over a circular cylinder using the principles of phase-reduction theory. The influence of harmonic external forcings on the wake dynamics, together with the possible synchronization of the vortex shedding behind the cylinder to these forcings, is determined by evaluating the phase response of the system to weak impulse perturbations. These horizontal and vertical perturbations are added at different phase values over a period, in order to develop a linear one-dimensional model with respect to the limit cycle that describes the high-dimensional and nonlinear dynamics of the fluid flow via only a single scalar phase variable. This model is then utilized to acquire the theoretical conditions for the synchronization between the cylinder wake and the harmonic forcings added in the global near-wake region. Valuable insights are gained by comparing the findings of the present research against those rendered by the dynamic mode decomposition and adjoint analysis of the wake dynamics in earlier works. The present analysis reveals regions in the flow which enable phase synchronization or desynchronization to periodic excitations for applications such as active flow control and fluid-structure interactions.
Self-similarity in the breakup of very dilute viscoelastic solutions
- A. Deblais, M. A. Herrada, J. Eggers, D. Bonn
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- 06 October 2020, R2
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When pushed out of a syringe, polymer solutions form droplets attached by long and slender cylindrical filaments whose diameter decreases exponentially with time before eventually breaking. In the last stages of this process, a striking feature is the self-similarity of the interface shape near the end of the filament. This means that shapes at different times, if properly rescaled, collapse onto a single universal shape. A theoretical description based on the Oldroyd-B model was recently shown to disagree with existing experimental results. By revisiting these measurements and analysing the interface profiles of very diluted polyethylene oxide solutions at high temporal and spatial resolution, we show that they are very well described by the model.
Solitary magnetostrophic Rossby waves in spherical shells
- K. Hori, S. M. Tobias, C. A. Jones
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- 12 October 2020, R3
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Finite-amplitude hydromagnetic Rossby waves in the magnetostrophic regime are studied. We consider the slow mode, which travels in the opposite direction to the hydrodynamic or fast mode, in the presence of a toroidal magnetic field and zonal flow by means of quasi-geostrophic models for thick spherical shells. The weakly nonlinear long waves are derived asymptotically using a reductive perturbation method. The problem at the first order is found to obey a second-order ordinary differential equation, leading to a hypergeometric equation for a Malkus field and a confluent Heun equation for an electrical wire field, and is non-singular when the wave speed approaches the mean flow. Investigating its neutral non-singular eigensolutions for different basic states, we find the evolution is described by the Korteweg–de Vries equation. This implies that the nonlinear slow wave forms solitons and solitary waves. These may take the form of a coherent eddy, such as a single anticyclone. We speculate on the relation of the anticyclone to the asymmetric gyre seen in the Earth's fluid core, and in state-of-the-art dynamo direct numerical simulations.
Electric-field-induced transitions from spherical to discocyte and lens-shaped drops
- Brayden W. Wagoner, Petia M. Vlahovska, Michael T. Harris, Osman A. Basaran
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- 12 October 2020, R4
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When a poorly conducting drop that is surrounded by a more conducting exterior fluid is subjected to an electric field, the drop can deform into an oblate shape at low field strengths. Such drops become unstable at high field strengths and display two types of dynamics, dimpling and equatorial streaming, the physics of which is currently not understood. If the drop is more viscous, dimples form and grow at the poles of the drop and eventually the discocyte-shaped drop breaks up to form a torus. If the exterior fluid is more viscous, the drop deforms into a lens and sheds rings from the equator that subsequently break into a number of smaller droplets. A theoretical explanation as to why dimple- and lens-shaped drops occur, and the mechanisms for the onset of these instabilities, are provided by determining steady-state solutions by simulation and inferring their stability from bifurcation analysis. For large drop viscosities, electric shear stress is shown to play a dominant role and to result in dimpling. For small drop viscosities, equatorial normal stresses (electric, hydrodynamic and capillary) become unbounded and lead to the lens shape.
Flapping of heavy inverted flags: a fluid-elastic instability
- Mohammad Tavallaeinejad, Michael P. Païdoussis, Manuel Flores Salinas, Mathias Legrand, Mojtaba Kheiri, Ruxandra M. Botez
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- 13 October 2020, R5
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Wind tunnel experiments are described in this paper, aiming to examine the global dynamics of heavy inverted flags, with a specific focus on the underlying mechanism of large-amplitude flapping, which occurs at sufficiently high flow velocities. This problem is of interest because no consensus exists as to the mechanism, specifically whether it is a vortex-induced vibration or a self-excited vibration – the answer being not only of fundamental interest, but also important for energy harvesting applications. The effect of vortex shedding from both leading and trailing edges was investigated via experiments with flags modified by serrations to the leading edge and a long rigid splitter plate at the trailing edge, so as to disrupt leading- and trailing-edge vortices and to inhibit interactions between counter-rotating leading-edge vortices, if they exist. The relatively small quantitative changes in the critical flow velocity, amplitude and frequency of oscillations, as well as the near-identical qualitative behaviour, of plain and modified flags suggests that the global qualitative dynamics of heavy inverted flags is independent of vortex shedding from the leading and trailing edges, i.e. periodic vortex shedding is not the cause but an effect of large-amplitude flapping. Additional experiments showed that the dominant frequencies of flapping and the lift force on the flag are generally not synchronized, and multiple frequencies occur in the lift signal, reinforcing the conclusion that vortex shedding is not the cause of flapping. Our experimental results suggest that self-excited vibration through a fluid-elastic instability, i.e. flutter, is the underlying mechanism for the flapping of heavy inverted flags.
Focus on Fluids
A basis for flow modelling
- B. J. McKeon
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- 05 October 2020, F1
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Reduced-order models are often sought to efficiently represent key dynamical phenomena present among the broad range of temporal and spatial scales associated with unsteady and turbulent flow problems. Linear ‘input–output’ approaches and resolvent analyses reveal that important information about the most dangerous (most amplified) disturbances and the corresponding fluctuation response can be found with knowledge only of the base flow, or the turbulent mean field. In the work by Padovan et al. (J. Fluid Mech., vol. 900, 2020, A14), an important advance is made with regards to flows which have a periodically time-varying base flow, for example during unsteady vortex shedding from a body. By forming a harmonic resolvent relative to this base flow, limitations associated with the traditional linear resolvent are overcome to determine efficient bases for modelling of limit cycle flows and reveal novel information about key triadic (resonant) interactions.
JFM Papers
Rayleigh–Taylor unstable condensing liquid layers with nonlinear effects of interfacial convection and diffusion of vapour
- Tao Wei, Mengqi Zhang
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- 06 October 2020, A1
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We investigate the three-dimensional surface pattern and nonlinear dynamics of a condensing liquid layer suspended from a cooled substrate and in contact with a mixture of its vapour and an inert gas below. A vapour boundary layer (VBL) is introduced, to which the changes in gaseous composition and temperature are assumed to be confined. An interfacial transport equation is derived, which incorporates the physical effects of convection and diffusion of vapour within the VBL, coupled with a long-wave evolution equation for the location of the free surface. This work extends the study of Kanatani (J. Fluid Mech., vol. 732, 2013, pp. 128–149) on a sessile evaporating film to the Rayleigh–Taylor unstable condensing/evaporating case with nonlinear analyses which also accounts for the effect of vapour recoil due to mass transfer on interfacial evolution and that of gravity combined with buoyancy on the internal convection of pendent drops in a condensate layer. The coupled nonlinear evolutionary system is referred to as a $1.5$-sided model. It can be reduced to the conventional one-sided model when phase change is limited by processes in the liquid. An extended basic state is obtained, whose stability is investigated with pseudo-steady linear theory and time-dependent nonlinear simulations. With the one-sided model, the influences of vapour recoil and Marangoni effects are illustrated with three representative cases. In the one-sided simulations with a random perturbation, the interface is prone to finite-time rupture and the surface patterns feature isolated droplets when vapour recoil is significant, while it becomes more regular and even without rupture as vapour recoil is weakened relative to the Marangoni effect. This suggests that, in the absence of the convection and diffusion of vapour, the destabilizations of vapour recoil and negative gravity could prevail over the stabilizations of thermocapillarity, capillarity, viscous dissipation and mass gain. With an unsaturated initial interface concentration, $\tilde {x}_{A,I0}$, the $1.5$-sided model indicates that the liquid layer can be stabilized to a quasi-hexagon pattern and the Rayleigh–Taylor-driven rupture can be suppressed with the effects of vapour convection and diffusion near the interface. However, the initial dynamics is in contrast to the case with a saturated $\tilde {x}_{A,I0}$, where transition from weak evaporation to a condensation-dominated regime is seen in the later stage. The viewpoint of stability competition offers vital evidence for an induced Marangoni stabilization, which is a quintessential characteristic of the $1.5$-sided model. Comparisons of the theory and simulations with available experiments are included throughout.
Rayleigh–Bénard convection in viscoelastic liquid bridges
- Marcello Lappa, Alessio Boaro
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- 05 October 2020, A2
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Rayleigh–Bénard convection in a floating zone held by the surface tension between two supporting disks at different temperatures is considered. Through direct numerical solution of the mixed parabolic–elliptic–hyperbolic set of governing equations in complete time-dependent and nonlinear form, we investigate the still unknown patterns and spatio-temporal states that are produced when the fluid has viscoelastic properties. The following conditions are examined: Prandtl number Pr = 8, aspect ratio (A = length/diameter) in the range 0.17 ≤ A ≤ 1 and different values of the elasticity number (0 ≤ θ ≤ 0.2). It is shown that, in addition to elastic overstability, an important ingredient of the considered dynamics is the existence of multiple solutions i.e. ‘attractors’ coexisting in the space of phases and differing with respect to the basin of attraction. We categorize the emerging states as modes with dominant vertical or horizontal vorticity and analyse the related waveforms, generally consisting of standing waves with central symmetry or oscillatory modes featuring almost parallel rolls, which periodically break and reform in time with a new orientation in space. In order to characterize the peculiar features of these flows, the notions of disturbance node and the topological concept of ‘knot’ are used. Azimuthally travelling waves are also possible in certain regions of the space of parameters, though they are generally taken over by convective modes with dominant pulsating nature as the elasticity parameter is increased. The case of an infinite horizontal layer is finally considered as an idealized model to study the asymptotic fluid-dynamic behaviour of the liquid bridge in the limit as its aspect ratio tends to zero.
The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability
- M. M. Mansoor, S. M. Dalton, A. A. Martinez, T. Desjardins, J. J. Charonko, K. P. Prestridge
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- 05 October 2020, A3
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We investigate the late-time Richtmyer–Meshkov instability (RMI) growth of sinuous perturbations on an air/sulphur hexafluoride interface (Atwood number, $A \sim 0.67$) subjected to a Mach 1.2 planar shock wave at Los Alamos National Laboratory's vertical shock tube facility. Interface perturbations are established using a novel membraneless technique where cross-flowing air and SF$_6$ separated by an oscillating splitter plate create a perturbed density interface. The interface formed has multi-modal features and residual small perturbations, however, a dominant mode is still noticeable. The late-time perturbation growths scale with $ka_0$ initial conditions (where $k$ is the wavenumber and $a_0$ is the initial amplitude of the dominant mode) as measured at the pre-shock interface. Past nonlinear models based on potential-flow theory, heuristic/interpolation approaches, Padé approximants and numerical simulations are evaluated against present experimental results. Accounting for an explicit $ka_0$ dependence in Sadot et al.'s (Phys. Rev. Lett., vol. 80, issue 8, 1998, pp. 1654–1657) model, we propose an empirical rational function that captures the asymptotic behaviour of perturbation growth for a broad range of initial conditions ($0.30 \leq ka_0 \leq 0.86$). The onset of mixing transition and its initial condition dependence are investigated with respect to the minimum state criterion ($Re = 1.6 \times 10^5$) for unsteady flows by Zhou (Phys. Plasmas, vol. 14, 2007, 082701). Earlier mixing transitions for higher $ka_0$ initial conditions are noted from local and global Reynolds number estimates which are corroborated by the existence of an inertial sub-range and formation of mixing regions indicating the physical significance of the minimum state criterion in RMI flows. The transition is accompanied by the increasing teapot-like appearance of joint probability density functions of $p$–$q$ (invariants of the reduced velocity gradient tensor), establishing the technique as a useful tool for turbulence detection in two-dimensional diagnostics.
Solitary waves on constant vorticity flows with an interior stagnation point
- V. Kozlov, N. Kuznetsov, E. Lokharu
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- 06 October 2020, A4
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The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we construct a solution with the following properties. The corresponding flow is unidirectional at infinity and has a solitary wave of elevation as its upper boundary; under this unidirectional flow, there is a bounded domain adjacent to the bottom, which surrounds an interior stagnation point and is divided into two subdomains with opposite directions of flow by a critical level curve connecting two stagnation points on the bottom.
Pressure-driven flows in helical pipes: bounds on flow rate and friction factor
- Anuj Kumar
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- 06 October 2020, A5
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In this paper, we use the well-known background method to obtain a rigorous lower bound on the volume flow rate through a helical pipe driven by a pressure differential in the limit of large Reynolds number. As a consequence, we also obtain an equivalent upper bound on the friction factor. These bounds are also valid for toroidal and straight pipes as limiting cases. By considering a two-dimensional background flow with varying boundary layer thickness along the circumference of the pipe, we obtain these bounds as a function of the curvature and torsion of the pipe and therefore capture the geometrical aspects of the problem. In this paper, we also present a sufficient criterion for determining which pressure-driven flow and surface-velocity-driven flow problems can be tackled using the background method.
Lift and drag forces acting on a particle moving with zero slip in a linear shear flow near a wall
- Nilanka I. K. Ekanayake, Joseph D. Berry, Anthony D. Stickland, David E. Dunstan, Ineke L. Muir, Steven K. Dower, Dalton J. E. Harvie
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- 08 October 2020, A6
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The lift and drag forces acting on a small spherical particle in a single wall-bounded linear shear flow are examined via numerical computation. The effects of shear rate are isolated from those of slip by setting the particle velocity equal to the local fluid velocity (zero slip), and examining the resulting hydrodynamic forces as a function of separation distance. In contrast to much of the previous numerical literature, low shear Reynolds numbers are considered ($10^{-3} \lesssim Re_{\gamma } \lesssim 10^{-1}$). This shear rate range is relevant when dealing with particulate flows within small channels, for example particle migration in microfluidic devices being used or developed for the biotech industry. We demonstrate a strong dependence of both the lift and drag forces on shear rate. Building on previous theoretical $Re_{\gamma } \ll 1$ studies, a wall-shear-based zero-slip lift correlation is proposed that is applicable when the wall lies both within the inner and outer regions of the disturbed flow. Similarly, we validate an improved wall-shear-based zero-slip drag correlation that more accurately captures the drag force when the particle is close to, but not touching, the wall. Application of the new correlations to predict the movement of a force-free particle shows that the examined shear-based lift force is as important as the previously examined slip-based lift force, highlighting the need to accurately account for shear when predicting the near-wall movement of force-free particles.
Concentration banding instability of a sheared bacterial suspension
- Laxminarsimharao Vennamneni, Piyush Garg, Ganesh Subramanian
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- 06 October 2020, A7
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We demonstrate a novel shear-induced mechanism for growth of concentration fluctuations in a bacterial suspension. Using a linear stability analysis, a homogeneous bacterial suspension, subject to a simple shear flow, is shown to be susceptible to exponentially growing layering perturbations in the shear rate and bacterial concentration. A semi-analytical expression for the growth rate of concentration perturbations is first obtained using the method of multiple scales, in the limit where the time scales characterizing the positional and orientation degrees of freedom are well separated. Next, the eigenspectrum obtained numerically from a full linear stability analysis is used to validate and extend the multiple scales result, and draw a contrast with the known orientation-shear instability. Finally, fully nonlinear simulations, but restricted to one-dimensional variations of the relevant fields (velocity, concentration and swimmer orientation distribution) show that the initial instability leads to gradient-banded velocity profiles, with a local depletion of bacteria at the interface between the homogeneous shear bands. Our results demonstrate that long-ranged hydrodynamic interactions serve as an alternate explanation for recent observations of shear bands in bacterial suspensions.
A minimal Maxey–Riley model for the drift of Sargassum rafts
- F. J. Beron-Vera, P. Miron
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- 06 October 2020, A8
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Inertial particles (i.e. with mass and of finite size) immersed in a fluid in motion are unable to adapt their velocities to the carrying flow and thus they have been the subject of much interest in fluid mechanics. In this paper we consider an ocean setting with inertial particles elastically connected forming a network that floats at the interface with the atmosphere. The network evolves according to a recently derived and validated Maxey–Riley equation for inertial particle motion in the ocean. We rigorously show that, under sufficiently calm wind conditions, rotationally coherent quasigeostrophic vortices (which have material boundaries that resist outward filamentation) always possess finite-time attractors for elastic networks if they are anticyclonic, while if they are cyclonic provided that the networks are sufficiently stiff. This result is supported numerically under more general wind conditions and, most importantly, is consistent with observations of rafts of pelagic Sargassum, for which the elastic inertial networks represent a minimal model. Furthermore, our finding provides an effective mechanism for the long range transport of Sargassum, and thus for its connectivity between accumulation regions and remote sources.
Direct numerical simulation of turbulent conjugate heat transfer in a porous-walled duct flow
- Y. Kuwata, K. Tsuda, K. Suga
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- 06 October 2020, A9
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In this study, the effects of permeable porous walls on momentum and heat transfer in a rectangular duct were studied by means of direct numerical simulation of the turbulent conjugate heat transfer. For this purpose, airflow through a rectangular duct, partially filled with a porous medium consisting of aluminium square bars, was simulated at a bulk mean Reynolds number of 3500, where the geometry of the duct used was identical to that employed in the experimental study of Suga et al. (J. Fluid Mech., vol. 884, 2020, A7). It was found that the large-scale perturbations arising from the Kelvin–Helmholtz type of instability developed over the porous medium wall, and the turbulence intensity, particularly in the porous wall-normal component, was enhanced significantly. The secondary flow was enhanced by a factor of three compared to that in a smooth-walled square duct flow, and could be characterized by a strong upward flow along the lateral walls and downward flow in the symmetry plane. The convection by the secondary flow considerably contributed to the momentum and heat transfer in the top half of the clear flow region, whereas the enhanced turbulence over the porous wall largely affected the momentum and heat transfer just above the porous medium wall, as seen in the case of a porous-walled channel flow. It should be noted that in the porous medium region, the mean temperature at the surface of the porous medium is non-uniform, with the solid- and fluid-phase temperatures reaching the equilibrium state. This could be correctly reproduced only with the conjugate heat transfer. It was found that the mean velocity dispersion as well as the turbulent velocity fluctuation contributed significantly to the energy transfer below the porous wall, which demonstrated the importance of the dispersion heat flux for heat transfer modelling of porous medium flows. Furthermore, it was observed that the secondary flow penetrated the porous medium region resulting in large-scale mean flow currents, which enhanced heat transfer inside the porous medium region.
Optimal growth of counter-rotating vortex pairs interacting with walls
- Daniel Dehtyriov, Kerry Hourigan, Mark C. Thompson
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- 06 October 2020, A10
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The transient growth of a counter-rotating equal strength vortex pair, which descends under mutual induction towards a ground plane, is examined through non-modal linear stability analysis and direct numerical simulation. The vortex pair is studied at a height of five vortex spacing distances above the wall, consistent with the first mode of vortex instability/wall interaction observed by experiment. Three regimes are identified in which the optimal mode topology and non-modal growth mechanisms are distinct, correlated with the widely studied Crow and elliptic instabilities, alongside a wall-modified long-wavelength-displacement-type instability. The initial optimal amplification mechanisms are found to be weakly influenced by the wall, with the long- and short-wave mechanisms consisting of anti-symmetric amplification at the leading hyperbolic point and symmetric amplification at the trailing hyperbolic point, respectively, as observed by out-of-wall studies previously. The linear growth of the Crow instability is found to be impeded by the wall, and the evolution results in the suppression of both the secondary structure formation and vortex rebound. The linear elliptic mode remains largely uninhibited however, and substantially outgrows the long-wave modes, illustrating the importance of the elliptic instability on the wall-bounded interaction. Both the wall-modified long-wave and elliptic optimal growth modes show substantial amplification in the secondary vortices. At finite perturbation amplitudes, the nonlinear formation of both long- and short-wavelength secondary vortex tongues are shown to play a critical role in the vortex dynamics as the pair strongly interacts with the wall.
Spectral energetics of a quasilinear approximation in uniform shear turbulence
- Carlos G. Hernández, Yongyun Hwang
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- 06 October 2020, A11
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The spectral energetics of a quasilinear (QL) model is studied in uniform shear turbulence. For the QL approximation, the velocity is decomposed into a mean averaged in the streamwise direction and the remaining fluctuation. The equations for the mean are fully considered, while the equations for the fluctuation are linearised around the mean. The QL model exhibits an energy cascade in the spanwise direction, but this is mediated by highly anisotropic small-scale motions unlike that in direct numerical simulation mediated by isotropic motions. In the streamwise direction the energy cascade is shown to be completely inhibited in the QL model, resulting in highly elevated spectral energy intensity residing only at the streamwise integral length scales. It is also found that the streamwise wavenumber spectra of turbulent transport, obtained with the classical Reynolds decomposition, statistically characterizes the instability of the linearised fluctuation equations. Further supporting evidence of this claim is presented by carrying out a numerical experiment, in which the QL model with a single streamwise Fourier mode is found to generate the strongest turbulence for $L_x/L_z=1\sim 3$, consistent with previous findings ($L_x$ and $L_z$ are the streamwise and spanwise computational domains, respectively). Finally, the QL model is shown to completely ignore the role of slow pressure in the fluctuations, resulting in a significant damage of pressure-strain transport at all length scales. This explains the anisotropic turbulence of the QL model throughout the entire wavenumber space as well as the inhibited nonlinear regeneration of streamwise vortices in the self-sustaining process.
The wake structure of a propeller operating upstream of a hydrofoil
- Antonio Posa, Riccardo Broglia, Elias Balaras
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- 06 October 2020, A12
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Large eddy simulations are presented on the wake flow of a notional propeller (the INSEAN E1658), upstream of a NACA0020 hydrofoil of infinite spanwise extent, mimicking propeller–rudder interaction. Results show that the flow physics is dominated by the interaction between the coherent structures populating the wake of the propeller and the surface of the hydrofoil. The suction and pressure side branches of the tip vortices move towards inner and outer radii, respectively. The hub vortex is split into two branches at the leading edge of the hydrofoil. The two branches of the hub vortex shift in the opposite direction, compared to the tip vortices, towards the rudder suction sides. As a result, a contraction of the propeller wake on the suction sides occurs, leading to increased levels of shear stress and turbulence. At downstream locations along the hydrofoil the spanwise deflection of the suction side branches of the tip vortices affects the trajectory of the overall propeller wake, including also the smaller helical vortices across the span of the wake of each blade and the two branches of the hub vortex on the two sides of the hydrofoil. This cross-stream shift persists, producing a strong anti-symmetry of the overall wake.
On the spectral behaviour of the turbulence-driven power fluctuations of horizontal-axis turbines
- Georgios Deskos, Grégory S. Payne, Benoît Gaurier, Michael Graham
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- 06 October 2020, A13
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In this article we consider the spectral behaviour of turbulence-driven power fluctuations for a single horizontal-axis turbine. To this end, a small-scale instrumented axial-flow hydrokinetic turbine model ($\textrm {diameter}=0.724\ \textrm {m}$) is deployed in the long water flume situated in the laboratory facilities of IFREMER in Boulogne-sur-Mer, France, and synchronous measurements of the upstream velocity and the rotor are collected for different tip-speed ratios. The study confirms previous findings suggesting that the power spectra follow the velocity spectra behaviour in the large scales region and a steeper power law slope behaviour ($-11/3$) over the inertial frequency sub-range. However, we show that both the amplitude of the power spectra and low-pass filtering effect over the inertial sub-range also depend on the rotor aero/hydrodynamics (e.g. $\mathrm {d}C_L/\mathrm {d}\alpha$) and the approaching flow deceleration and not solely on the rotational effects. In addition, we present a novel semi-analytical model to predict the dominant blade-passing frequency harmonics in the high-frequency regime using the rotationally sampled spectra technique. For all calculations, the distortion of incoming turbulence is taken into account.
Evaporation-driven turbulent convection in water pools
- William A. Hay, Miltiadis V. Papalexandris
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- 08 October 2020, A14
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In this paper we study turbulent thermal convection driven by free-surface evaporation at the top and a uniformly heated wall at the bottom. More specifically, we report on direct numerical simulations over 1.25 decades of Rayleigh number, Ra. At the top of the cubic domain, a shear-free boundary condition acts as an approximation of a free surface, and different evaporation rates form the basis of a temperature gradient assigned as a non-zero Neumann boundary condition. The corresponding lower wall temperature is fixed and we assess the thermal mixing on the water side of the air–water interface. The set-up is considered a simplified model of the turbulent natural convection in the upper volumes of spent-fuel pools of nuclear power plants. Surface temperatures are investigated over a range of 40 K, resulting in a sixteenfold increase in evaporation rates. Our work allows, for the first time, analysis of the features and mean flow statistics of this particular thermal convection configuration. Results show that a shear-free surface increases heat transfer within the domain; however, the exponent in the diagnosed power-law relation between the Nusselt and Rayleigh numbers, $Nu = 0.178Ra^{0.301}$, is similar to that of classical turbulent Rayleigh–Bénard convection. Further, the free slip accelerates the fluid after impingement on the upper boundary, significantly affecting the structure of the large-scale circulation in the container. Analysis of the flow statistics then shows how the shear-free surface introduces inhomogeneities in thermal boundary layer heights. Overall, the investigated turbulent convection configuration shows unique traits, borrowing from both turbulent Rayleigh–Bénard convection and evaporative cooling.