Turbulent Dynamics Research Articles

Evaluation of advection schemes and surface tension model for algebraic and geometric VOF multiphase flow solvers

This paper addresses the validation and verification of numerical models for complex multiphase flows involving immiscible fluids. Specifically, the focus is on the dynamics of the interface between the fluids, which remains a challenge in many applications. Previous studies have primarily examined simpler flows with limited complexity, while real-world scenarios involve intricate interfaces and turbulent dynamics. To overcome this, a representative test case involving the motion of an oil cube within a water cube proposed by [12] is used. Different computational models using volume-of-fluid (VOF) approaches are validated and compared, with particular attention given to the influence of numerical schemes for convective terms. The impact of these schemes on integral quantities and interface dynamics is analyzed. Particular attention is paid at the surface tension contribution to the energy budgets, which is usually neglected in the available literature. Furthermore, it is shown here that, the model adopted for the surface tension is responsible for an additional contribution to numerical dissipation. To the authors' knowledge, it is the first time that a detailed analysis of such aspects is presented.

Turbulent dynamics in a two-dimensional paraxial fluid of light

Turbulent dynamics in a two-dimensional paraxial fluid of light

Characterizing Small-Scale Dynamics of Navier-Stokes Turbulence with Transverse Lyapunov Exponents: A Data Assimilation Approach.

Data assimilation (DA) of turbulence, which involves reconstructing small-scale turbulent structures based on observational data from large-scale ones, is crucial not only for practical forecasting but also for gaining a deeper understanding of turbulent dynamics. We propose a theoretical framework for DA of turbulence based on the transverse Lyapunov exponents (TLEs) in synchronization theory. Through stability analysis using TLEs, we identify a critical length scale as a key condition for DA; turbulent dynamics smaller than this scale are synchronized with larger-scale turbulent dynamics. Furthermore, considering recent findings for the maximal Lyapunov exponent and its relation with the TLEs, we clarify the Reynolds number dependence of the critical length scale.

Ozone Transport in 311 MVA Hydrogenerator: Computational Fluid Dynamics Modelling of Three-Dimensional Electric Machine

In this paper, a three-dimensional turbulent fluid dynamics numerical model of a 311 MVA full hydroelectric power plant unit is made, using the finite element method, to study and understand the ozone transport mechanisms inside the enclosured electric machine structure. In the real world, ozone is produced by partial discharges related to faults on stator bars. In order to analyse ozone transport from localised sources, a 3D fluid dynamic model of a complete hydrogenerator in operation is developed and presented for the first time. The model has a high level of geometric detail. Furthermore, a new proposal to simplify the modelling of radiators is implemented and validated. The modelled structure is based on a Campos Novos hydrogenerator electric machine and it consists of 378 coil-type stator bars made of copper covered by mica and, more externally, by a semiconductor coating layer. Other parts are also represented, including the stator core and air directors made of stainless steel, copper radiators, the rotor with its epoxy surface, and the concrete floor and concrete external walls. In the fluid dynamics model, a finite element mesh was designed to represent the air regions inside the hydrogenerator and the material surfaces that react with ozone (with their respective reaction rates), where the airflow and ozone transport are modelled using the Navier–Stokes equations and the mass conservation law. Partial discharge sources are represented by ozone sources with prismatic shapes, placed on surfaces of stator bars. Ozone concentrations have been calculated inside and around the generator machine. The rotor radius is 3.8075 m and its rotation frequency is 200 RPM. Radial air velocity due to interpole ventilation is also considered (2.2 m/s, as experimentally verified in loco. The radial velocity in the vicinity of the radiators is 3 m/s. It has been concluded that the ozone transport profile is influenced by the source positioning on the stator bars in such a way that source pinpointing is possible and it depends on determining the local and global maxima areas of ozone concentration at the radiators.

Maximum drag enhancement asymptote in turbulent Taylor–Couette flow of dilute polymeric solutions

Direct numerical simulations in a wide-gap turbulent viscoelastic Taylor–Couette flow in the Reynolds number (Re) range of 1500 to 8000 reveals the existence of a maximum drag enhancement (MDE) asymptote. The statistical properties associated with the turbulent and polymer dynamics demonstrate that the turbulent drag enhances with the increase of the Weissenberg number (Wi) and eventually saturates above a critical Wi, namely, the flow reaches the MDE state. The mean velocity profile in MDE state closely follows a logarithmic-like law with an identical slope (κK=2.32) and a Re-dependent intercept. A detailed analysis of flow structures reveals that the MDE asymptote results from the creation and eventual saturation of small-scale elastic and inertio-elastic Görtler vortices in the inner- and outer-wall regions, respectively. These vortical structures arise due to competing effects of polymer-induced stresses that either suppress or promote turbulent vortices. A close examination of competing forces in the azimuthal direction shows that the ratio of polymeric to turbulent stresses reaches a large plateau, underscoring the elastic nature of the MDE state. Moreover, the energy production mechanism in the MDE state further supports: (1) the universal interplay between polymers and turbulent vortices in a broad range of curvilinear and planar turbulent flows, and (2) the fact that the elastically induced asymptotic saturation of drag modification is an inherent property of elasticity-driven and/or elasto-inertial turbulence flow states. Overall, this study provides concrete evidence for our earlier postulate that asymptotic flow states in unidirectional turbulent viscoelastic flows are of elastic nature.

Sinc method for generating and extending phase screens of atmospheric turbulence.

We present a method, based on sinc series approximation, for generating and extending phase screens of atmospheric turbulence in real time to arbitrary lengths. Unlike phase screen representations based on the Fourier series, the sinc approximation is naturally suited to problems on infinite domains and thus avoids the problem of artificial periodicity inherent in the Fourier series. In particular, phase screens generated using the sinc method have accurate non-periodic statistics throughout the computational domain. They can also be extended using a conditional probability distribution without having to deal with artifacts of periodicity. This is a crucial feature for long time-dependent simulations of dynamic turbulence that require very long phase screen realizations. Both the generation and extension methods take advantage of special structures inherent in the sinc approximation, leading to light memory footprints and fast computations based on the FFT. Numerical results demonstrate the accuracy of the sinc method, reproducing the correct ensemble averaged statistics as well as the sample statistics of single realizations. In other words, the sinc method preserves ergodicity when this is a feature of the turbulence model. We also verify the computational efficiency of the proposed methods.

Turbulence via intermolecular potential: Uncovering the origin

In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed spontaneously emerge from a laminar initial condition, as observed in nature and experiments. To study the origin of turbulent dynamics, in the current work we examine the equations of a two-dimensional inertial flow, linearized around a large scale constant vorticity state. Remarkably, even in this simplified setting, we find that turbulent dynamics emerge as linearly unstable fluctuations of the velocity divergence.In particular, for the linearized dynamics at a high Reynolds number, we find that, at short time scales, the coupling of the mean field potential with the large scale background vorticity creates linearly unstable and rapidly oscillating fluctuations of the divergence of velocity at inertial scales. In the asymptotic time limit, we find a persistent eigenvector, also aligned largely with the divergence of velocity, which allows these fluctuations to propagate in the form of traveling waves in the Fourier domain. Remarkably, these traveling waves decay at a constant, scale-independent exponential rate. Furthermore, it appears that the Kolmogorov scaling of the kinetic energy is produced by this persistent velocity divergence, due to a cubic relation between the physical time variable, and a pseudo-time variable, in which the dynamics become autonomous. These effects vanish when the mean field potential is removed.

New simulations improves interpretation of high-resolution satellite imagery of surface water

Researchers investigate dynamics of surface ocean turbulence at the submesoscale.

An augmented invariant-based model of the pressure Hessian tensor using a combination of physics-assisted neural networks

Modeling the velocity gradient dynamics in incompressible turbulence requires modeling two unclosed quantities: the pressure Hessian tensor and the viscous Laplacian tensor. In this work, we model the pressure Hessian tensor using a combination of two different physics-embedded deep neural networks. The first neural network is trained specifically to predict the alignment tendencies of the eigen-vectors of the pressure Hessian tensor, whereas the second neural network is trained only to predict the magnitude of the tensor. This separation of tasks allows us to define mathematically optimal and physics-informed customized loss functions separately for the two aspects (alignment and magnitude) of the tensor. Both neural networks take invariants of the velocity gradient tensor as inputs. Even though the training of the two networks is performed using direct numerical simulation database of an incompressible stationary isotropic turbulence at a particular Reynolds number, we extensively evaluate the model at different Reynolds numbers and in different kinds of flow fields. In incompressible flows, the proposed model shows significant improvements over the existing phenomenological model (the recent fluid deformation closure model or the RFD model) of the pressure Hessian tensor. While the improvements in the alignment tendencies are convincingly evident in the shapes of the probability density functions of the cosines of various angles between eigenvectors, the improvements in the prediction of the magnitude of the pressure Hessian tensor using the new model are quantifiable in the range of 28%–89% (depending on the type of the flow field) compared to the RFD model.

Statistics of inhomogeneous turbulence in large-scale quasigeostrophic dynamics.

A remarkable feature of two-dimensional turbulence is the transfer of energy from small to large scales. This process can result in the self-organization of the flow into large, coherent structures due to energy condensation at the largest scales. We investigate the formation of this condensate in a quasigeostropic flow in the limit of small Rossby deformation radius, namely the large-scale quasigeostrophic model. In this model potential energy is transferred up-scale while kinetic energy is transferred down-scale in a direct cascade. We focus on a jet mean flow and carry out a thorough investigation of the second-order statistics for this flow, combining a quasilinear analytical approach with direct numerical simulations. We show that the quasilinear approach applies in regions where jets are strong and is able to capture all second-order correlators in that region, including those related to the kinetic energy. This is a consequence of the blocking of the direct cascade by the mean flow in jet regions, suppressing fluctuation-fluctuation interactions. The suppression of the direct cascade is demonstrated using a local coarse-graining approach allowing us to measure space dependent interscale kinetic energy fluxes, which we show are concentrated in between jets in our simulations. We comment on the possibility of a similar direct cascade arrest in other two-dimensional flows, arguing that it is a special feature of flows in which the fluid element interactions are local in space.

Enhancing turbulence modeling: Machine learning for pressure-strain correlation and uncertainty quantification in the Reynolds stress model

This research study delves into the realm of enhancing the Reynolds stress model through the remarkable capabilities of machine learning. Focusing on two key aspects, we investigate the modeling of fluctuating pressure-rate-of-strain tensor and uncertainty quantification in turbulent fluid flows. In the first part of our investigation, a neural network is employed to predict the pressure-strain correlation term for the frictional Reynolds number, even in cases where it was not trained. Through the use of high-fidelity datasets, we surpass the limitations of traditional numerical methods, achieving more accurate results with reduced computational costs. Going beyond conventional analysis, we explore the isotropic and anisotropic components of the pressure-strain correlation term. Intriguingly, our findings unveil the significant influence of production and redistribution terms on the anisotropic component by 50% and viscous dissipation impacts the isotropic part by 65% in wall-bounded turbulent flows. The second part introduces a novel approach for uncertainty quantification in the Reynolds stress model. Leveraging a binary classification model, we identify error-prone points within the simulation domain with an impressive accuracy of up to 95%. This critical step paves the way for a deeper understanding of uncertainties in turbulent flows for more reliable predictions. By harnessing the power of machine learning, our study provides two compelling ways to enhance the Reynolds stress model, contributing to a more efficient and dependable prediction of turbulent fluid dynamics.

The effect of turbulent motions on particle spatial distribution in high-Reynolds-number particle-laden flows

The spatial relationship between turbulent and particle concentration structures is investigated based on the turbulent velocity and particle concentration data obtained synchronously at the Qingtu Lake Observation Array site. In addition to the observation of particle concentration structures that contain not only large-scale coherence but also significant energy in the high-Reynolds-number atmospheric surface layer (ASL), the scale of turbulent motions that have the most significant coherence with particle concentration is found to follow a 1/2 power scaling law with the local height and ASL thickness. Moreover, large-scale turbulent velocity fluctuations have a significant amplitude modulation effect on particle concentration fluctuations, but the modulating influence is different for small dust particles and large saltating particles. Based on the interphase amplitude modulation, there exists a particle–turbulence structure phase difference that varies with height, which further makes the structure inclination angle of the particle concentration larger than that of the turbulence. In this scenario, a conceptual model reflecting the relationship between the two is proposed, and a quantitative formulation is further derived and found to be in good agreement with the experimental results. These findings and the proposed model contribute insights into particle–turbulence interactions, thereby providing theoretical support for a unified model of turbulence dynamics and particle kinematics.

Effect of a Control Mechanism on the Interaction between a Rectangular Jet and a Slotted Plate: Experimental Study of the Aeroacoustic Field

The aeroacoustic field of a rectangular subsonic jet impinging on a slotted plate was investigated experimentally using microphones and stereoscopic particle image velocimetry (S-PIV). The study was carried out with a Reynolds number of 6700 and an impact distance of 4 cm. The current configuration represents a benchmark standpoint, featuring high levels of generated noise. A control mechanism consisting of a thin rod was introduced downstream from the jet exit to suppress the self-sustained tones. A total of 1085 positions of the rod between the jet exit and impinging plate were tested to identify positions of optimal noise reduction. Two zones were distinguished in terms of control efficacy: a zone where the sound pressure level (SPL) dropped by up to 19 dB and another zone where the SPL increased by up to 14 dB. The velocity fields show that the presence of the rod divides the jet into two lateral secondary jets on both sides of the main jet axis. The outer part of the secondary jets expanded radially with less interaction with the plate compared to the case without the control. This behavior affected the deformation of vortices against the slot. Proper orthogonal decomposition was applied to the velocity field for a better understanding of the turbulence dynamics with and without the control rod.

Nonlinear interaction of Alfvénic instabilities and turbulence via the modification of the equilibrium profiles

Nonlinear simulations of Alfvén modes (AMs) driven by energetic particles (EPs) in the presence of turbulence are performed with the gyrokinetic particle-in-cell code ORB5. The AMs carry a heat flux, and consequently they nonlinearly modify the plasma temperature profiles. The isolated effect of this modification on the dynamics of turbulence is studied by means of electrostatic simulations. We find that turbulence is reduced when the profiles relaxed by the AM are used, with respect to the simulation where the unperturbed profiles are used. This is an example of indirect interaction of EPs and turbulence. First, an analytic magnetic equilibrium with circular concentric flux surfaces is considered as a simplified example for this study. Then, an application to an experimentally relevant case of ASDEX Upgrade is discussed.

Sensitivity Analysis of an Unsteady Flow Around a Pitching Airfoil

Various ways to control the loads and thus the output of the wind turbine by pitching the blades and by controlling the rotational speed already exist. However, adverse pressure gradient leading to flow separation at the trailing edge, with relatively high angles of attack (AOA) due to blade-pitching motion, largely affects the airfoil aerodynamic performance. This work presents the results of a numerical study of the unsteady flow around a pitching FFA-W3-301 airfoil at a Reynolds 1.6 × 106 using OpenFOAM®, as obtained by first performing 2D Unsteady Reynolds-Averaged Navier- Stokes (URANS) simulations whereby the flow characteristics are simulated by the shear stress transport (SST) k − ω model and Spalart-Allmaras (SA). The influence of various parameters on the numerical results is investigated, namely y+, computational grid resolution, dynamic mesh technique, time step and turbulence model. Integral aerodynamic forces and detailed flow patterns are compared with experimental measurements presented in the literature. A range of angles of attack, including early stalls, are examined. For best-performing parameters, an adequate refinement close to the wall was imperative in order to match experiments, especially during the upstroke motion of the airfoil, while for the downstroke phase, some differences still appeared. The agreement was greatly improved by using a 2.5D hybrid RANS-LES approach with enhanced delayed-Detached Eddy Simulation (DES) capabilities.

Bipolar Solitary Wave Interactions within the Schamel Equation

Pair soliton interactions play a significant role in the dynamics of soliton turbulence. The interaction of solitons with different polarities is particularly crucial in the context of abnormally large wave formation, often referred to as freak or rogue waves, as these interactions result in an increase in the maximum wave field. In this article, we investigate the features and properties of bipolar solitary wave interactions within the framework of the non-integrable Schamel equation, contrasting them with the integrable modified Korteweg-de Vries (mKdV) equation. We show that in bipolar solitary wave interactions involving two solitary waves with significantly different amplitudes in magnitude, the behavior closely resembles what is observed in the mKdV equation. However, when solitary waves have similar amplitudes in modulus, the maximum value of their interaction remains less than the sum of their initial amplitudes. This distinguishes these interactions from integrable models, where the resulting impulse amplitude equals the sum of the soliton amplitudes before interaction. Furthermore, in the Schamel equation, smaller solitary waves can transfer some energy to larger ones, leading to an increase in the larger soliton amplitude and a decrease in the smaller one amplitude. This effect is particularly prominent when the initial solitary waves have similar amplitudes. Consequently, large solitary waves can accumulate energy, which is crucial in scenarios involving soliton turbulence or soliton gas, where numerous solitons interact repeatedly. In this sense, non-integrability can be considered a factor that triggers the formation of rogue waves.

Simulating Microscale Urban Airflow and Pollutant Distributions Based on Computational Fluid Dynamics Model: A Review.

Urban surfaces exert profound influences on local wind patterns, turbulence dynamics, and the dispersion of air pollutants, underscoring the critical need for a thorough understanding of these processes in the realms of urban planning, design, construction, and air quality management. The advent of advanced computational capabilities has propelled the computational fluid dynamics model (CFD) into becoming a mature and widely adopted tool to investigate microscale meteorological phenomena in urban settings. This review provides a comprehensive overview of the current state of CFD-based microscale meteorological simulations, offering insights into their applications, influential factors, and challenges. Significant variables such as the aspect ratio of street canyons, building geometries, ambient wind directions, atmospheric boundary layer stabilities, and street tree configurations play crucial roles in influencing microscale physical processes and the dispersion of air pollutants. The integration of CFD with mesoscale meteorological models and cutting-edge machine learning techniques empowers high-resolution, precise simulations of urban meteorology, establishing a robust scientific basis for sustainable urban development, the mitigation of air pollution, and emergency response planning for hazardous substances. Nonetheless, the broader application of CFD in this domain introduces challenges in grid optimization, enhancing integration with mesoscale models, addressing data limitations, and simulating diverse weather conditions.

Experimental investigation on the turbulent wake flow in fully established transonic buffet conditions

The transonic flight regime is often dominated by transonic buffet, a highly unsteady and complex shock-wave/boundary-layer interaction involving major parts of the flow field. The phenomenon is associated with a large-amplitude periodic motion of the compression shock coupled with large-scale flow separation and intermittent re-attachment. Due to the resulting large-scale variation of the global flow topology, also the turbulent wake of the airfoil or wing is severely affected, and so are any aerodynamic devices downstream on which the wake impinges. To analyze and understand the turbulent structures and dynamics of the wake, we performed a comprehensive experimental study of the near wake of the supercritical OAT15A airfoil in transonic buffet conditions at a chord Reynolds number of 2×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\ imes 10^{6}$$\\end{document}. Velocity field measurements reveal severe global influences of the buffet mode on both the surface-bound flow field on the suction side of the airfoil and the wake. The flow is intermittently strongly separated, with a significant momentum deficit that extends far into the wake. The buffet motion induces severe disturbances and variations of the turbulent flow, as shown on the basis of phase-averaged turbulent quantities in terms of Reynolds shear stress and RMS-values. The spectral nature of downstream-convecting fluctuations and turbulent structures are analyzed using high-speed focusing schlieren sequences. Analyses of the power spectral density pertaining to the vortex shedding in the direct vicinity of the trailing edge indicate dominant frequencies one order of magnitude higher than those associated with shock buffet (Stc=O(1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$St_c=\\mathcal {O}({1})$$\\end{document}) vs. Stc=O(0.1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$St_c=\\mathcal {O}({0.1})$$\\end{document}). It is shown that the flapping motion of the shear layer is accompanied by the formation of a von Kármán-type vortex street of fluctuating strength. These wake structures and dynamics will impact any downstream aerodynamic devices affected by the wake. Our study, therefore, allows conclusions regarding the incoming flow of devices such as the tail plane.

Land Cover Control on the Drivers of Evaporation and Sensible Heat Fluxes: An Observation‐Based Synthesis for the Netherlands

AbstractLand cover controls the land‐atmosphere exchange of water and energy through the partitioning of solar energy into latent and sensible heat. Observations over all land cover types at the regional scale are required to study these turbulent flux dynamics over a landscape. Here, we aim to study how the control of daily and midday latent and sensible heat fluxes over different land cover types is distributed along three axes: energy availability, water availability and exchange efficiency. To this end, observations from 19 eddy covariance flux tower sites in the Netherlands, covering six different land cover types located within the same climatic zone, were used in a regression analysis to explain the observed dynamics and find the principle drivers. The resulting relative position of these sites along the three axes suggests that land cover partly explains the variance of daily and midday turbulent fluxes. We found that evaporation dynamics from grassland, peatland swamp and cropland sites could mostly be explained by energy availability. Forest evaporation can mainly be explained by water availability, urban evaporation by water availability and exchange efficiency, and open water evaporation can almost entirely be explained by exchange efficiency. We found that the sensible heat flux is less sensitive to land cover type. This demonstrates that the land‐atmosphere interface plays an active role in the shedding of sensible heat. Our results contribute to a better understanding of the dynamics of evaporation over different land cover types and may help to optimize, and potentially simplify, models to predict evaporation.

The NexGen burner: Non-Reacting gaseous and spray dynamics

This paper reports the results of a comprehensive investigation to identify turbulent multiphase fluid dynamics through the NexGen burner used for fireworthiness certifications by the Federal Aviation Administration. The burner geometry consists of a draft tube, a stator to swirl the incoming air, a turbulator that is placed immediately downstream of the stator to increase the turbulence intensity of the swirling flow, and a burner cone that exhausts into the atmosphere. A Delavan type-W fuel nozzle, attached downstream of the turbulator injects Jet A into the burner cone, where it mixes with the turbulent swirling air, vaporizes and subsequently burns. The operating conditions consist of air and fuel mass flow rates of 0.0384 kg/s and 2.5 Gph at room temperature and pressure conditions. In this paper, we report on non-reacting fluid dynamics; the reacting flow analysis will be presented in a subsequent manuscript. To systematically analyze the flow configuration, three calculations are conducted. First, to validate our large eddy simulation-based framework, a case without the burner cone is conducted—our results are in reasonable agreement with experimental measurements. In the second configuration, to isolate the effect of liquid injection on turbulent flow physics, simulations are conducted with the burner cone but without fuel spray. Detailed analyses are conducted, including identification of flow structures, swirl generation, and the turbulent kinetic energy budget. Finally, Jet A is injected into the burner, and the spray and gaseous flow fields are quantified and compared with the flow structures developed without spray injection.