Turbulent Fluid Motion Research Articles

A hierarchy of Poisson brackets in non-equilibrium thermodynamics

Reversible evolution of macroscopic and mesoscopic systems can be conveniently constructed from two ingredients: an energy functional and a Poisson bracket. The goal of this paper is to elucidate how the Poisson brackets can be constructed and what additional features we also gain by the construction. In particular, the Poisson brackets governing reversible evolution in one-particle kinetic theory, kinetic theory of binary mixtures, binary fluid mixtures, classical irreversible thermodynamics and classical hydrodynamics are derived from Liouville equation. Although the construction is quite natural, a few examples where it does not work are included (e.g. the BBGKY hierarchy). Finally, a new infinite grand-canonical hierarchy of Poisson brackets is proposed, which leads to Poisson brackets expressing non-local phenomena such as turbulent motion or evolution of polymeric fluids. Eventually, Lie–Poisson structures standing behind some of the brackets are identified.

On turbulence in dilatant dispersions

This paper presents a new theory on the behaviour of shear-thickening (dilatant) fluids under turbulent conditions. The structure of a dilatant colloidal fluid in turbulent motion may be characterized by (at least) four characteristic length scales: (i) the ‘statistically largest’ turbulent scale, , labeling the begin of the inertial part of the wavenumber spectrum; (ii) the energy-containing scale, (iii) Kolmogorov’s micro-scale, , related with the size of the smallest vortices existing for a given kinematic viscosity and forcing; (iv) the inner (‘colloidal’) micro-scale, , typically representing a major stable material property of the colloidal fluid. In particular, for small ratios , various interactions between colloidal structures and smallest turbulent eddies can be expected. In the present paper we discuss particularly that for turbulence (in the narrow, inertial sense) is strangled and chaotic but less mixing fluid motions remain. We start from a new stochastic, micro-mechanical turbulence theory without empirical parameters valid for inviscid fluids as seen in publications by Baumert in 2013 and 2015. It predicts e.g. von Karman’s constant correctly as . In its generalized version for non-zero viscosity and shear-thickening behavior presented in this contribution, it predicts two solution branches for the steady state: The first characterizes a family of states with swift (inertial) turbulent mixing and small , potentially approaching . The second branch characterizes a state family with and thus strangled turbulence, . Stability properties and a potential dynamic commuting between the two solution branches had to be left for future research.

Topology optimization for turbulent flow with Spalart–Allmaras model

In this research, a new finite element (FE) based topology optimization (TO) for turbulent flow was developed using the Spalart–Allmaras (S–A) equation, which is one of the Reynolds-Averaged Navier–Stokes (RANS) equations. Despite many innovative works on the subject of fluidic TO, it is rare to consider the influence of turbulent flow in TO. To consider the effect of complex turbulent fluid motion, this research considered the S–A model developed mainly for aerodynamic flows. For a successful TO, one primary issue is modification of the S–A turbulent model to account for topological evolution during the optimization process. To address this issue, we proposed the addition of penalization terms to the original governing equations. To show the validity of the present approach and the effect of turbulent flow on optimal layouts, some two dimensional benchmark designs studied for laminar flow were reconsidered. By considering the effect of turbulent flow, the eddy viscosity values were increased at some local regions due to the Boussinesq hypothesis, and naturally optimal layouts affected by the spatially varying viscosity were obtained in turbulent flow. It was also found that the balance between the inertia force and the viscosity force plays an important role in topological designs.

About One Discrete Mathematical Model of Perfect Fluid

In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical objects: circles and spheres for two-dimensional and three-dimensional cases, respectively. The mechanism of interaction between the liquid particles on a binary level and on the level of the n-cluster is formulated. This mechanism has previously been found by the author as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived and investigated the potential interaction of pairs of liquid particles, which contained a singularity of the branch point. Exactly, this is possible to build in this article discrete stochastic-deterministic model of an ideal fluid. The results of computational experiment to simulate various kinds of flows in two-dimensional and three-dimensional ensembles of liquid particles are presented. Modeling was carried out in the areas of quadratic or cubic form. On boundary of a region satisfies the condition of elastic reflection liquid particles. The flows with spontaneous separation of particles in a region, various kinds of eddy streams, with the quite unexpected statistical properties of an ensemble of particles characteristic for the Fermi-Pasta-Ulam effect were found. We build and study the flow in which the velocity of the particles is calibrated. It was possible using the appropriate flows of liquid particles of the ensemble to demonstrate the possibility to reproduce any prescribed image by manipulating the parameters of the interaction. Calculations of the flows were performed with using MATLAB software package according to the algorithms presented in this article.

Global-in-time existence of weak solutions to Kolmogorov's two-equation model of turbulence

We consider Kolmogorov's model for the turbulent motion of an incompressible fluid in R3. This model consists in a Navier–Stokes-type system for the mean flow u and two further partial differential equations: an equation for the frequency ω and for the kinetic energy k each. We investigate this system of partial differential equations in a cylinder Ω×]0,T[ (Ω⊂R3 cube, 0<T<+∞) under spatial periodic boundary conditions on ∂Ω×]0,T[ and initial conditions in Ω×{0}. We present an existence result for a weak solution {u,ω,k} to the problem under consideration, with ω, k obeying the inequalities c1+t≤1ω≤t+c2 and k1/2ω≥c3t1/2 (c1,c2,c3=const>0).

Experimental study of global-scale turbulence in a librating ellipsoid

We present laboratory experimental results demonstrating that librational forcing of an ellipsoidal container of water can produce intense motions through the mechanism of a libration driven elliptical instability (LDEI). These libration studies are conducted using an ellipsoidal acrylic container filled with water. A particle image velocimetry method is used to measure the 2D velocity field in the equatorial plane over hundreds libration cycles for a fixed Ekman number, E = 2 × 10−5. In doing so, we recover the libration induced base flow and a time averaged zonal flow. Further, we show that LDEI in non-axisymmetric container geometries is capable of driving both intermittent and saturated turbulent motions in the bulk fluid. Additionally, we measure the growth rate and amplitude of the LDEI induced excited flow in a fully ellipsoidal container at more extreme parameters than previously studied [Noir et al., “Experimental study of libration-driven flows in nonaxisymmetric containers,” Phys. Earth Planet. Inter. 204-205, 1 (2012); Cébron et al., Phys. Fluids 24, 061703, “Libration driven elliptical instability,” (2012)]. Excitation of bulk filling turbulence by librational forcing provides a mechanism for transferring rotational energy into turbulent fluid motion and thus can play an important role in the thermal evolution, interior dynamics, and magneto-hydrodynamics of librating bodies, as appear to be common in solar system settings [e.g., Comstock and Bills, “A solar system survey of forced librations in longitude,” J. Geophys. Res. Planets 108, 1 (2003)].

Introduction to quantum turbulence

The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.

Quantifying energetics and dissipation in magnetohydrodynamic turbulence

We perform a suite of two- and three-dimensional magnetohydrodynamic (MHD) simulations with the Athena code of the non-driven Kelvin-Helmholtz instability in the subsonic, weak magnetic field limit. Focusing the analysis on the non-linear turbulent regime, we quantify energy transfer on a scale-by-scale basis and identify the physical mechanisms responsible for energy exchange by developing the diagnostic known as spectral energy transfer function analysis. At late times when the fluid is in a state of MHD turbulence, magnetic tension mediates the dominant mode of energy injection into the magnetic reservoir, whereby turbulent fluid motions twist and stretch the magnetic field lines. This generated magnetic energy turbulently cascades to smaller scales, while being exchanged backwards and forwards with the kinetic energy reservoir, until finally being dissipated. Incorporating explicit dissipation pushes the dissipation scale to larger scales than if the dissipation were entirely numerical. For scales larger than the dissipation scale, we show that the physics of energy transfer in decaying MHD turbulence is robust to numerical effects.

Comparative Study on the Reynolds Shear Stress in CTAC Drag-Reducing Flow by Experiment and DNS

In this paper, both experimental and numerical studies were carried out for fully developed water and CTAC solution channel flows in order to understand the different distribution of Reynolds shear stress appeared in experiments and DNS. Quadrant analysis were carried out according to the categorization of turbulent fluid motions. The studies indicates that the elastic force of the additives' structures will cause the fluids moving back and forth in the wall-normal direction in experiment and the symmetric distribution of Reynolds shear stress in all quadrants. However, Giesekus model in DNS only applies the elastic force inhibiting the transverse fluctuations.

Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition

The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form of spatially localized structures (e.g., eddies) filling the flow field, a tendency to occupy such a structured state of the flow cannot be ruled out as a driving force for turbulent transition. To examine this possibility, we propose a simple analytical model that treats the flow as a collection of localized spatial structures, each of which consists of elementary cells in which the behavior of the particles (atoms or molecules) is uncorrelated. This allows us to introduce the Reynolds number, associating it with the ratio between the total phase volume for the system and that for the elementary cell. Using the principle of maximum entropy to calculate the most probable size distribution of the localized structures, we show that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains turbulent transition and some other general properties of turbulent flows. An important feature of the present model is that a bridge between the spatial-statistical description of the flow and hydrodynamic equations is established. We show that the basic assumptions underlying the model, i.e., that the particles are indistinguishable and elementary volumes of phase space exist in which the state of the particles is uncertain, are involved in the derivation of the Navier-Stokes equation. Taking into account that the model captures essential features of turbulent flows, this suggests that the driving force for the turbulent transition is basically the same as in the present model, i.e., the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow at high Reynolds numbers can then be a mechanism to initiate structural rearrangement of the flow to find this state.

Direct numerical simulation of elastic turbulence and its mixing-enhancement effect in a straight channel flow

In this paper, we present a direct numerical simulation (DNS) of elastic turbulence of viscoelastic fluid at vanishingly low Reynolds number (Re=1) in a three-dimensional straight channel flow for the first time, using the Giesekus constitutive model for the fluid. In order to generate and maintain the turbulent fluid motion in the straight channel, a sinusoidal force term is added to the momentum equation, and then the elastic turbulence is numerically realized with an initialized chaotic velocity field and a stretched conformation field. Statistical and structural characteristics of the elastic turbulence therein are analyzed based on the detailed information obtained from the DNS. The fluid mixing enhancement effect of elastic turbulence is also demonstrated for the potential applications of this phenomenon.

Physically-Based Feature Tracking for CFD Data

Numerical simulations of turbulent fluid flow in areas ranging from solar physics to aircraft design are dominated by the presence of repeating patterns known as coherent structures. These persistent features are not yet well understood, but are believed to play an important role in the dynamics of turbulent fluid motion, and are the subject of study across numerous scientific and engineering disciplines. To facilitate their investigation a variety of techniques have been devised to track the paths of these structures as they evolve through time. Heretofore, all such feature tracking methods have largely ignored the physics governing the motion of these objects at the expense of error prone and often computationally expensive solutions. In this paper, we present a feature path prediction method that is based on the physics of the underlying solutions to the equations of fluid motion. To the knowledge of the authors the accuracy of these predictions is superior to methods reported elsewhere. Moreover, the precision of these forecasts for many applications is sufficiently high to enable the use of only the most rudimentary and inexpensive forms of correspondence matching. We also provide insight on the relationship between the internal time stepping used in a CFD simulation, and the evolution of coherent structures, that we believe is of benefit to any feature tracking method applicable to CFD. Finally, our method is easy to implement, and computationally inexpensive to execute, making it well suited for very high-resolution simulations.

Inertial Frame Independent Forcing for Discrete Velocity Boltzmann Equation: Implications for Filtered Turbulence Simulation

AbstractWe present a systematic derivation of a model based on the central moment lattice Boltzmann equation that rigorously maintains Galilean invariance of forces to simulate inertial frame independent flow fields. In this regard, the central moments, i.e. moments shifted by the local fluid velocity, of the discrete source terms of the lattice Boltzmann equation are obtained by matching those of the continuous full Boltzmann equation of various orders. This results in an exact hierarchical identity between the central moments of the source terms of a given order and the components of the central moments of the distribution functions and sources of lower orders. The corresponding source terms in velocity space are then obtained from an exact inverse transformation due to a suitable choice of orthogonal basis for moments. Furthermore, such a central moment based kinetic model is further extended by incorporating reduced compressibility effects to represent incompressible flow. Moreover, the description and simulation of fluid turbulence for full or any subset of scales or their averaged behavior should remain independent of any inertial frame of reference. Thus, based on the above formulation, a new approach in lattice Boltzmann framework to incorporate turbulence models for simulation of Galilean invariant statistical averaged or filtered turbulent fluid motion is discussed.

Synthesis of Nanocrystals of Gadolinium Carbonate by Reaction Crystallization

The formation of nano-sized crystals of gadolinium carbonate via reaction crystallization was studied in a semi-batch crystallizer using gadolinium chloride and ammonium hydrogen carbonate as the reactants. The gadolinium carbonate crystals were formed by the aggregation of primary particles sized about 5 nm. Thereby, the crystallization parameters acting directly on the aggregation of the primary particles, such as the reactant concentrations, non-stoichiometry of the reactants, solution pH, acoustic energy, and agitation speed, were mechanistically investigated. As such, increasing the reactant concentrations enhanced the crystal size due to higher nucleation of the primary particles for the aggregation. Non-stoichiometric reactant concentrations resulted in a significant reduction of the crystal size, due to the adsorption of the excess species on the primary particles. Similarly, the surface charge of the primary particles depended on the solution pH. Thus, the crystal size was reduced when the pH deviated from the neutral point. The acoustic cavitation of the ultrasound was much more effective than the turbulent fluid motion of the agitation in inhibiting the primary particle aggregation. Thus, the crystal size was remarkably reduced, even at a low acoustic energy of 6 watts.

Acoustic Effect on Induction of Cerium Carbonate in Reaction Crystallization

The influence of ultrasonication and agitation on the induction of nucleation in the reaction crystallization of cerium carbonate has been investigated in a semi-batch crystallizer. When the cerium chloride and sodium carbonate reactants are constantly injected, the induction time depends significantly on ultrasonication and agitation. Due to the acoustic cavitation of ultrasonication promoting micromixing of the reactants, the induction time of cerium carbonate is markedly reduced. Simultaneously, the acoustic cavitation appears to reduce the energy barrier of nucleation, inducing nucleation at a lower supersaturation level than with the turbulent fluid motion of agitation. However, the acoustic stream of ultrasonication does not promote the induction of nucleation. Meanwhile, agitation also facilitates the induction of nucleation due to turbulent mixing of the reactants. The micromixing resulting from agitation meant the supersaturation in the solution increases rapidly when increasing the agitation speed, thereby reducing the induction time. The influence of ultrasonication and agitation on the induction of nucleation has also been compared in terms of the energy dissipation. With the same energy dissipation, ultrasonication is much more effective than agitation for induction, possibly due to its unique feature of acoustic cavitation.

A one-way coupled, Euler–Lagrangian simulation of bubble coalescence in a turbulent pipe flow

A bubble coalescence model is developed using an Euler–Lagrangian approach for unstructured grids. The Eulerian carrier fluid is solved using large-eddy simulation (LES) and the Lagrangian particle motion is solved with equations relating the turbulent motion of the carrier fluid to forces on each discrete bubble. The collision process is deterministic; bubble–bubble collisions are assumed to be binary and are modeled using a hard-sphere approach. A stochastic approach is used to model coalescence, with the probability of coalescence being a function of the bubble–bubble interaction timescale and the time to drain fluid between the colliding bubbles. The intention is to develop and validate the collision and coalescence model, neglecting two-way coupling turbulent subgrid stress transport of bubbles and the modification of the subgrid stress by the bubbles. Coalescence in a bubbly, turbulent pipe flow in microgravity is simulated with conditions similar to experiments by Colin et al. (Colin, C., Fabre, J., Dukler, A.E., 1991. Gas–liquid flow at microgravity conditions – I. Dispersed bubble and slug flow. Int. J. Multiphase Flow 17 (4), 533–544.) and excellent agreement of bubble size distribution is obtained between simulation and experiment. With increasing downstream distance, the number density of bubbles decreases due to coalescence and the average probability of coalescence decreases slightly due to an increase in overall bubble size.

Examples of the Potential of DNS for the Understanding of Reactive Multiphase Flows

The objective of this article is to point out the ability of the multiphase flow DNS (Direct Numerical Simulation) to help to understand basic physics and to interpret some experimental observations. To illustrate the DNS' potential to give access to key phenomena involved in reactive multiphase flows, several recent results obtained by the authors are summed up with a bridge to experimental results. It includes droplet dispersion, laminar spray flame instability, spray combustion regimes or acoustic modulation effect on a two-phase flow Bunsen burner. As a perspective, two-phase flow DNS auto-ignition is considered thanks to a skeletal mechanism for the n-heptane chemistry involving 29 species and 52 reactions. Results highlight evaporating droplet effects on the auto-ignition process that is generally dramatically modified by spray distribution resulting from the turbulent fluid motion. This paper shows that DNS is a powerful tool to understand the intricate coupling between the evaporating spray, the turbulent fluid motion and the detailed chemistry, inseparable in the experimental context.

Energy budget of cosmological first-order phase transitions

The study of the hydrodynamics of bubble growth in first-order phasetransitions is very relevant for electroweak baryogenesis, as thebaryon asymmetry depends sensitively on the bubble wall velocity, andalso for predicting the size of the gravity wave signal resulting frombubble collisions, which depends on both the bubble wall velocity andthe plasma fluid velocity. We perform such study in different bubbleexpansion regimes, namely deflagrations, detonations, hybrids (steadystates) and runaway solutions (accelerating wall), without relying ona specific particle physics model. We compute the efficiency of thetransfer of vacuum energy to the bubble wall and the plasma in allregimes. We clarify the condition determining the runaway regime andstress that in most models of strong first-order phase transitionsthis will modify expectations for the gravity wave signal. Indeed, inthis case, most of the kinetic energy is concentrated in the wall andalmost no turbulent fluid motions are expected since the surroundingfluid is kept mostly at rest.

High‐speed jet noise: A two source model.

Recent experiments on high‐speed jets indicate that jet noise is made up of two components. One component dominates in a conical sector surrounding the jet axis in the downstream direction. Experimental evidence suggests that this noise component is generated by the large turbulence structures of the jet flow. The other component is dominant in the sideline and upstream directions. There is ample experimental evidence showing that this noise component is generated by the fine scale turbulence of the jet. Optical observations confirm that there is a separation of turbulence scales in jets. Jet turbulence consists of large structures with length scale of the order of the jet diameter and fine scale turbulence with a much smaller length scale. These two types of turbulent fluid motions, with large disparate length scales, co‐exist in the first one and half core length of the jet. In this presentation, extensive far field noise and direct correlation data are provided to support the two‐noise source model. The validity of the two‐noise source model is also strongly supported by near acoustic field measurements.

G203 遷移チャネル流れに発現する乱流縞内のエネルギ輸送に関するDNS解析(GS2 乱流の諸問題,一般セッション)

A regular pattern of turbulent and quasi-laminar fluid motions is known to appear in a plane Poiseuille flow at very low Reynolds numbers for which turbulence can be sustained. We focused on this transitional structure, so-called the turbulent stripe, and investigated its energy transport process in each region, using a direct numerical simulation. We obtained the budget for Reynolds stresses, including v'w' and w'v', and considered a self-sustaining mechanism of the stripe inclining pattern.