A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions representing the global mode and a stochastic contribution representing the intrinsic turbulent forcing. Stochastic models are developed that account for the interaction between the two and that allow determining the dynamic properties of the flow from stationary data. The deterministic contributions are modelled by an amplitude equation, which describes the oscillatory dynamics of the instability, and in a second approach by a mean-field model, which additionally captures the interaction between the instability and the mean-flow corrections. The stochastic contributions are considered as coloured noise forcing, representing the spectral characteristics of the stochastic turbulent perturbations. The methodology is applied to a turbulent swirling jet with a dominant global mode. PIV measurements are conducted to ensure that the mode is the most dominant coherent structure and further pressure measurements provide long time series for the model calibration. The supercritical Hopf bifurcation is identified from the linear growthrate of the global mode and the excellent agreement between measured and estimated statistics suggest that the model captures the relevant dynamics. This work demonstrates that the sole observation of limit-cycle oscillations is not sufficient to determine the stability of turbulent flows since the stochastic perturbations obscure the actual bifurcation point. However, the proposed separation of deterministic and stochastic contributions in the dynamical model allows identifying the flow sate from stationary measurements.
We present a comparison of different particles' velocity and acceleration statistics in two paradigmatic turbulent swirling flows: the von Kármán flow in a laboratory experiment, and the Taylor-Green flow in direct numerical simulations. Tracers, as well as inertial particles, are considered. Results indicate that, in spite of the differences in boundary conditions and forcing mechanisms, scaling properties and statistical quantities reveal similarities between both flows, pointing to new methods to calibrate and compare models for particles dynamics in numerical simulations, as well as to cha…
We report numerical evidences of the influence of the blades' shape and of their direction of rotation on turbulent flows generated by counter-rotating bladed-disks enclosed in a cylinder, known as the von Kármán swirling flow. We show that, although the mean flows generated by stirrers with straight or curved blades can be topologically similar, turbulence production occurs in different zones. The structure and intensity of the turbulent fluctuating field also varies with the geometry, and retains significant anisotropy. From the direct numerical simulations fields, we analyse the dynamics of…
We study the three-dimensional clustering of velocity stagnation points, of nulls of the vorticity and of the Lagrangian acceleration, and of inertial particles in turbulent flows at fixed Reynolds numbers, but under different large-scale flow geometries. To this end, we combine direct numerical simulations of homogeneous and isotropic turbulence and of the Taylor-Green flow, with particle tracking velocimetry in a von Kármán experiment. While flows have different topologies (as nulls cluster differently), particles behave similarly in all cases, indicating that Taylor-scale neutrally buoyant …
We report the experimental observation of the alpha-effect. It consists in the generation of a current parallel to a magnetic field B0 applied to a turbulent swirling flow of liquid sodium. At low magnetic Reynolds number, Rm, we show that the magnitude of the alpha-effect increases like Rm2 and that its sign is determined by the flow helicity. It saturates and then decreases at large Rm, primarily because of the expulsion of the applied field B0 from the bulk of the flow. We show how this expulsion is affected by the flow geometry by varying the relative amplitudes of the azimuthal and axial …
Energy dissipation and pressure fluctuations are features inherent to turbulent fluid motion, and the internal origin of spatial and temporal temperature fluctuations. By measuring local velocity, pressure or temperature, it is possible to detect the presence of coherent structures ---like concentrated vortices--- and quantify their intensity. Here we report measurements of speed and temperature in a filamentary vortex lying in a strongly stretched turbulent airflow. The largest core temperature drop measured in our experiment was $ΔT = 9$ K, while the fastest measured air speed was $v_{max} =…
We present experimental observations of the spatial distribution of large inertial particles suspended in a turbulent swirling flow at high Reynolds number. The plastic particles, which are tracked using several high speed cameras, are heavier than the working fluid so that their dynamics results from a competition between gravitational effects and turbulent agitation. We observe two different regimes of suspension. At low rotation rate, particles are strongly confined close to the bottom and are not able to reach the upper region of the tank whatever their size or density. At high rotation ra…
Modal linear stability analysis has proven very successful in the analysis of coherent structures of turbulent flows. Formally, it describes the evolution of a disturbance in the limit of infinite time. In this work we apply modal linear stability analysis to a turbulent swirling jet undergoing a control parameter transient. The flow undergoes a transition from a non-vortex breakdown state to a state with a strong recirculation bubble and the associated global mode. High-speed Particle Image Velocimetry (PIV) measurements are the basis for a local linear stability analysis of the temporarily e…
The LES/PDF methodology is applied to the Cambridge/Sandia turbulent stratified flame series under swirling conditions. The methane/air chemistry is represented by a 16-species reduced ARM1 mechanism, and the in situ adaptive tabulation method is adopted to accelerate the chemistry calculation. Effects of differential diffusion and heat loss through the bluffbody surface are taken into account. The simulations are conducted for premixed (SwB3), moderately and highly stratified (SwB7 and SwB11, respectively) cases under swirling conditions. The results from LES/PDF simulations are compared with…
We study the melting dynamics of large ice balls in a turbulent von Karman flow at very high Reynolds number. Using an optical shadowgraphy setup, we record the time evolution of particle sizes. We study the heat transfer as a function of the particle scale Reynolds number for three cases: fixed ice balls melting in a region of strong turbulence with zero mean flow, fixed ice balls melting under the action of a strong mean flow with lower fluctuations, and ice balls freely advected in the whole flow. For the fixed particles cases, heat transfer is observed to be much stronger than in laminar f…
We study the influence of the forcing on the steady turbulent states of a von Kármán swirling flow, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities with low-dimensional systems. We suggest that this forcing dependence may be an out- of-equilibrium analogue of the ensemble inequivalence, valid for long-range interacting statistical systems, and that it may be applicable to other turbulent systems.
We present an experimental study of a turbulent von Kármán flow produced in a cylindrical container using two propellers. The mean flow is stationary up to $Re = 10^4$, where a bifurcation takes place. The new regime breaks some symmetries of the problem, and is time-dependent. The axisymmetry is broken by the presence of equatorial vortices with a precession movement, being the velocity of the vortices proportional to the Reynolds number. The reflection symmetry through the equatorial plane is broken, and the shear layer of the mean flow appears displaced from the equator. These two facts app…
Linear stability analysis has proven to be a useful tool in the analysis of dominant coherent structures, such as the von Kármán vortex street and the global spiral mode associated with the vortex breakdown of swirling jets. In recent years, linear stability analysis has been applied successfully to turbulent time-mean flows, instead of laminar base-flows, \textcolor{black}{which requires turbulent models that account for the interaction of the turbulent field with the coherent structures. To retain the stability equations of laminar flows, the Boussinesq approximation with a spatially nonunif…
We evaluate the effect of two experimental parameters on the slow dynamics of a Von-Kármán swirling flow driven by two propellers in a closed cylinder. The first parameter is the inertia mo- mentum of the propellers, and the second parameter is the aspect ratio, i.e. the distance between the propellers $H$ divided by the diameter $D$. We use a cell with a fixed diameter $D$ but where the distance between the propellers can be turned continuously and where the inertia from the pro- pellers can also be changed using different gears. No change on the dynamics is observed when the momentum of iner…
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely the number of quasi-stationary states and transition rates among them, the effective dimensions, …
A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing inertia, we predict that the injected power fluctuates twice less in the case of constant torque than in the case of constant angular velocity forcing. The model is further tested against experimental d…
We report the experimental observation of $1/f$ fluctuations in three different turbulent flow configurations: the large scale velocity driven by a two-dimensional turbulent flow, the magnetic field generated by a turbulent swirling flow of liquid sodium and the pressure fluctuations due to vorticity filaments in a swirling flow. For these three systems, $1/f$ noise is shown to result from the dynamics of coherent structures that display transitions between a small number of states. The interevent duration is distributed as a power-law. The exponent of this power-law and the nature of the dyna…
We present a novel moving immersed boundary method (IBM) and employ it in direct numerical simulations (DNS) of the closed-vessel swirling von Karman flow in laminar and turbulent regimes. The IBM extends direct-forcing approaches by leveraging a time integration scheme, that embeds the immersed boundary forcing step within a semi-implicit iterative Crank-Nicolson scheme. The overall method is robust, stable, and yields excellent results in canonical cases with static and moving boundaries. The moving IBM allows us to reproduce the geometry and parameters of the swirling von Karman flow experi…
We report an experimental investigation on the influence of an external magnetic field on forced 3D turbulence of liquid gallium in a closed vessel. We observe an exponential damping of the turbulent velocity fluctuations as a function of the interaction parameter N (ratio of Lorentz force over inertial terms of the Navier-Stokes equation). The flow structures develop some anisotropy but do not become bidimensional. From a dynamical viewpoint, the damping first occurs homogeneously over the whole spectrum of frequencies. For larger values of N, a very strong additional damping occurs at the hi…
We use laser-Doppler velocimetry (LDV) experiments and Reynolds-averaged Navier--Stokes (RANS) simulations to study the characteristic flow patterns downstream of a standardized clockwise swirl disturbance generator. After quantifying the impact of the mesh size, we evaluate the potential of various eddy-viscosity turbulence models in providing reasonable approximations with respect to the experimental reference. The choice of turbulent models reflects current industry practice. Our results suggest that models from the $k$-$ε$ family are more accurate in predicting swirling flows than models f…
Studies of magnetic induction in von Kármán swirling flows have so far linked the time-averaged induced magnetic field to the structure of the mean flow. They have evidenced the Omega and Parker mechanism generated respectively by the flow differential rotation and helicity, which underly the Duddley and James \cite{DuddleyJames} dynamos. Using an array of Hall probes we study here the dynamical regime. In the experimental flow, turbulence is fully developed and large fluctuations are observed in the magnetic induction processes. We find that the large scale turbulent fluctuations have differe…
We present the full three-dimensional numerical investigation of the von Karman swirling flow between two parallel plates using the Oldroyd-B model and characterize the onset and development of elastic turbulence. We quantify the flow state with the secondary-flow strength, a measure of the average strength of the velocity fluctuations, and then define an order parameter as the time average of the secondary-flow strength. The order parameter displays a subcritical transition from the laminar to a bistable flow that switches between weakly chaotic flow and elastic turbulence. The transition to …
The present study assesses the performance of the Wall Adapting SGS models along with the Dynamic Smagorinsky model for flows involving separation, reattachment and swirl. Due to the simple geometry and wide application in a variety of engineering systems, the Backward-Facing Step (BFS) geometry and Confined Swirling Flow (CSF) geometry are invoked in the present case. The calculation of the SGS stresses employs three models, namely, the Dynamic Smagorinsky model, the Wall Adapting Local Eddy viscosity (WALE) model and the Dynamic WALE model. For studying the effect of the grid sensitivity, th…
We present direct numerical simulations of reversals of the magnetic field generated by swirling flows in a spherical domain. In agreement with a recent model, we observe that coupling dipolar and quadrupolar magnetic modes by an asymmetric forcing of the flow generates field reversals. In addition, we show that this mechanism strongly depends on the value of the magnetic Prandtl number.
Scrupulous measurements and detailed data analysis of the torque in a swirling turbulent flow driven by counter-rotating bladed disks reveals an apparent breaking of the law of similarity. Potentially, such breakdown could arise from several possible factors, including dependence on dimensionless numbers other that $Re$ or velocity coupling to other fields such as temperature. However, careful redesign and calibration of the experiment showed that this unexpected result was due to background errorscaused by minute misalignments which lead to a noisy and irreproducible torque signal at low rota…
Turbulent characteristics within shear layer have been studied, recently, within vegetative canopy, buildings, dunes. Kevin-Helmholtz instability triggered hairpin vortex shedding has been widely concluded as the "signature" of mixing layer analogy. However, convoluted roughness types complicate the observing practice of turbulent evolving progress. To simplify that, spanwise homogeneous roughness has been adopted in this work to capture the streamwise flow alternations under different streamwise roughness element distances. Streamwise successive object distance $λ_x$ is used to show the rough…
We investigate the statistics of phase fluctuations of an acoustic wave propagating through a turbulent flow in line of sight (LOS) configuration. Experiments are performed on a closed von Karman swirling flow whose boundaries are maintained at a constant temperature. In particular, we analyze the root mean square (RMS) and the power spectrum density (PSD) of phase fluctuations. A model is developed and analytical predictions obtained for these quantities using geometrical acoustics are shown to be in agreement with experimental observations.
In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for uncertainty quantification is applied to the two-step simulation of the mechanical design of a swirling jet flow generated by a rotating pipe (\textit{Simulation 1}) impinging on a flat plate to provide convective heat transfer (\textit{Simulation 2}). The first approach is the Stochastic Collocation Method (SCM) with Clenshaw-Curtis sparse grids. The concl…
We compute numerically the threshold for dynamo action in Taylor-Green swirling flows. Kinematic calculations, for which the flow field is fixed to its time averaged profile, are compared to dynamical runs for which both the Navier-Stokes and the induction equations are jointly solved. The kinematic instability is found to have two branches, for all explored Reynolds numbers. The dynamical dynamo threshold follows these branches: at low Reynolds number it lies within the low branch while at high kinetic Reynolds number it is close to the high branch.
A new rotational flamelet model with inward swirling flow through a stretched vortex tube is developed for sub-grid modeling to be coupled with the resolved flow for turbulent combustion. The model has critical new features compared to existing models. (i) Non-premixed flames, premixed flames, or multi-branched flame structures are determined rather than prescribed. (ii) The effects of vorticity and the related centifugal acceleration are determined. (iii) The strain rates and vorticity applied at the sub-grid level can be directly determined from the resolved-scale strain rates and vorticity …
We study the flow response to an externally imposed homogeneous magnetic field in a turbulent swirling flow of liquid sodium -- the VKS2 experiment in which magnetic Reynolds numbers Rm up to 50 are reached. Induction effects are larger than in the former VKS1 experiment. At Rm larger than about 25, the local amplitude of induced field components supersedes that of the applied field, and exhibits non-Gaussian fluctuations. Slow dynamical instationarities and low-frequency bimodal dynamics are observed in the induction, presumably tracing back to large scale fluctuations in the hydrodynamic flo…
This paper experimentally analyzes the simultaneous influence of heat release and coherent vortex structures on the transfer of kinetic energy across scales around the laminar flame thickness $δ^0_\mathrm{L}$ in a turbulent premixed swirl flame and a non-reacting swirl flow. High-resolution tomographic particle image velocimetry and formaldehyde planar laser induced fluorescence measurements are used to obtain 3D velocity fields and estimates of the progress variable and density fields. The kinetic energy transfer across a filter scale of $Δ= 1.5 δ^0_\mathrm{L}$ was then quantified using physi…
The Precessing Vortex Core (PVC) is a coherent structure that can arise in swirling jets from a global instability. In this work, the PVC is investigated under highly turbulent conditions. The goal is to characterize the receptivity of the PVC to active flow control, both theoretically and experimentally. Based on stereoscopic particle image velocimetry and surface pressure measurements, the experimental studies are facilitated by Fourier decomposition and proper orthogonal decomposition. The frequency and the mode shape of the PVC are extracted and a very good agreement with the theoretical p…
Even in the absence of externally applied temperature gradients, spontaneously generated temperature fluctuations arise in turbulent flows. We experimentally study these fluctuations in a closed von Karman swirling flow of air at Mach number of order $10^{-3}$, whose boundaries are maintained at a constant temperature. We observe intermittent peaks of low temperature correlated with pressure drops within the flow and show that they are caused by vorticity filaments. The measured ratio of temperature to pressure fluctuation agrees with the prediction based on adiabatic cooling within vortex cor…
We report the observation of dynamo action in the VKS experiment, i.e., the generation of magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number Rm \sim 30. A mean magnetic field of order 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number …
We discuss the role of elastic stress in the statistical properties of elastic turbulence, realized by the flow of a polymer solution between two disks. The dynamics of the elastic stress are analogous to those of a small scale fast dynamo in magnetohydrodynamics, and to those of the turbulent advection of a passive scalar in the Batchelor regime. Both systems are theoretically studied in literature, and this analogy is exploited to explain the statistical properties, the flow structure, and the scaling observed experimentally. Several features of elastic turbulence are confirmed experimentall…
We suggest a new approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average modeling of turbulent time series. We introduce a new index $Υ$ that measures the distance from a Kolmogorov-Obukhov model in the Auto-Regressive Moving-Average models space. Applying our analysis to Particle Image Velocimetry and Laser Doppler Velocimetry measurements in a von Kármán swirling flow, we show that $Υ$ is proportional to the traditional intermittency correction computed from the structure function. Therefore it provides the same infor…
We experimentally study the susceptibility to symmetry breaking of a closed turbulent von Kármán swirling flow from $Re = 150$ to $Re \simeq 10^{6}$. We report a divergence of this susceptibility at an intermediate Reynolds number $Re = Re_χ\simeq 90\,000$ which gives experimental evidence that such a highly space and time fluctuating system can undergo a "phase transition". This transition is furthermore associated with a peak in the amplitude of fluctuations of the instantaneous flow symmetry corresponding to intermittencies between spontaneously symmetry breaking metastable states.
Data-driven methods for modelling purposes in fluid mechanics are a promising alternative given the continuous increase of both computational power and data-storage capabilities. Highly non-linear flows including turbulence and reaction are challenging to model, and accurate closures for the unresolved terms in large eddy simulations of such flows are difficult to obtain. In this study, we investigate the use of artificial neural networks for modelling an important unclosed term namely the unresolved stress tensor, in a highly demanding turbulent and reacting flow, which additionally includes …
We present a detailed study of of a global bifurcation occuring in a turbulent von Kármán swirling flow. In this system, the statistically steady states progressively display hysteretic behaviour when the Reynolds number is increased above the transition to turbulence. We examine in detail this hysteresis using asymmetric forcing conditions --- rotating the impellers at different speeds. For very high Reynolds numbers, we study the sensitivity of the hysteresis cycle --- using complementary Particle Image Velocimetry (PIV) and global mechanical measurements --- to the forcing nature, imposing …
We investigate the ability of 4D Particle Tracking Velocimetry measurements at high particle density to explore intermittency and irreversibility in a turbulent swirling flow at various Reynolds numbers. For this, we devise suitable tools to remove the experimental noise, and compute the statistics of both Lagrangian velocity increments and wavelet coefficients of the Lagrangian power (the time derivative of the kinetic energy along a trajectory). We show that the signature of noise is strongest on short trajectories, and results in deviations from the regularity condition at small time scales…
The pressure strain correlation plays a critical role in the Reynolds stress transport modelling. Accurate modelling of the pressure strain correlation leads to proper prediction of turbulence stresses and subsequently the other terms of engineering interest. However, classical pressure strain correlation models are often unreliable for complex turbulent flows. Machine learning based models have shown promise in turbulence modeling but their application has been largely restricted to eddy viscosity based models. In this article, we outline a rationale for the preferential application of machin…
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the interface, and we develop a model that describes wave-induced perturbation turbulent stresses (PTS). We demonstrate the effect of the PTS on the stability properties of the system in two cases: for a laminar thin film, and for deep-water waves. In the first case, we find that the PTS have little effect on the growth rate of the waves, although they do affect…
A formulation is developed to assimilate ocean-wave data into the Numerical Flow Analysis (NFA) code. NFA is a Cartesian-based implicit Large-Eddy Simulation (LES) code with Volume of Fluid (VOF) interface capturing. The sequential assimilation of data into NFA permits detailed analysis of ocean-wave physics with higher bandwidths than is possible using either other formulations, such as High-Order Spectral (HOS) methods, or field measurements. A framework is provided for assimilating the wavy and vortical portions of the flow. Nudging is used to assimilate wave data at low wavenumbers, and th…
We propose a model for assessing the unresolved wrinkling factor in LES of turbulent premixed combustion. It relies essentially on a power-law dependence of the wrinkling factor to the filter size and an original expression for the active corrugating strain rate. The latter is written as a product of an efficiency function which accounts for viscous effects and the kinematic constraint of Peters, by a recent expression for the turbulent strain intensity. Yields functional expressions for the fractal dimension and the inner cut-off length scale, the latter being (i) filter-size independent and …
We study the problem of mixing between core and annular flow in a pipe, examining the effect of a swirling core flow. Such flows are important across a range of applications, including jet pumps, combustion chambers and aerospace engineering. Previous studies show that swirl can increase shear layer growth rates and, in the case of confining walls, reduce flow separation. However, the effect of swirl on pressure loss in a confined flow is uncertain. To address this, we develop a simplified model that approximates the axial flow profile as a linear shear layer separating uniform-velocity core a…
All previous experiments in open turbulent flows (e.g. downstream of grids, jet and atmospheric boundary layer) have produced quantitatively consistent values for the scaling exponents of velocity structure functions. The only measurement in closed turbulent flow (von Kármán swirling flow) using Taylor-hypothesis, however, produced scaling exponents that are significantly smaller, suggesting that the universality of these exponents are broken with respect to change of large scale geometry of the flow. Here, we report measurements of longitudinal structure functions of velocity in a von Kármán …
The swirling secondary flow in curved pipes is studied in three-space dimensions using a weakly compressible Smoothed Particle Hydrodynamics (WCSPH) formulation coupled to new non-reflecting outflow boundary conditions. A large-eddy simulation (LES) model for turbulence is benchmarked with existing experimental data. After validation of the present model against experimental results for a 90 grades pipe bend, a detailed numerical study aimed at reproducing experimental flow measurements for a wide range of Reynolds numbers has been performed for different pipe geometries, including U pipe bend…
We suggest that the dynamical spontaneous symmetry breaking reported in a turbulent swirling flow at $Re=40~000$ by Cortet et al., Phys. Rev. Lett., 105, 214501 (2010) can be described through a continuous one parameter family transformation (amounting to a phase shift) of steady states and could be the analogue of the Goldstone mode of the vertical translational symmetry in an ideal system. We investigate a possible mechanism of emergence of such spontaneous symmetry breaking in a toy model of our out-equilibrium system, derived from its equilibrium counterpart. We show that the stationary st…
We analyse and compare various empirical models of wall pressure spectra beneath turbulent boundary layers and propose an alternative machine learning approach using Artificial Neural Networks (ANN). The analysis and the training of the ANN are performed on data from experiments and high-fidelity simulations by various authors, covering a wide range of flow conditions. We present a methodology to extract all the turbulent boundary layer parameters required by these models, also considering flows experiencing strong adverse pressure gradients. Moreover, the database is explored to unveil import…
We describe the structure and dynamics of turbulence by the scale-dependent perceived velocity gradient tensor as supported by following four tracers, i.e. fluid particles, that initially form a regular tetrahedron. We report results from experiments in a von Kármán swirling water flow and from numerical simulations of the incompressible Navier-Stokes equation. We analyze the statistics and the dynamics of the perceived rate of strain tensor and vorticity for initially regular tetrahedron of size $r_0$ from the dissipative to the integral scale. Just as for the true velocity gradient, at any i…
