Random Turbulent Flow Research Articles

Breaking of Josephson junction oscillations and onset of quantum turbulence in Bose–Einstein condensates

We analyse the formation and the dynamics of quantum turbulence in a two-dimensional Bose–Einstein condensate with a Josephson junction barrier modeled using the Gross–Pitaevskii equation. We show that a sufficiently high initial superfluid density imbalance leads to randomisation of the dynamics and generation of turbulence, namely, the formation of a quasi-1D dispersive shock consisting of a train of grey solitons that eventually breakup into chains of distinct quantised vortices of alternating vorticity followed by random turbulent flow. The Josephson junction barrier allows us to create two turbulent regimes: acoustic turbulence on one side and vortex turbulence on the other. Throughout the dynamics, a key mechanism for mixing these two regimes is the transmission of vortex dipoles through the barrier: we analyse this scattering process in terms of the barrier parameters, sound emission and vortex annihilation. Finally, we discuss how the vortex turbulence evolves for long times, presenting the optimal configurations for the density imbalance and barrier height in order to create the desired turbulent regimes which last as long as possible.

Development of rolled scaffold for high-density adherent cell culture.

Bioreactors for large-scale culture of mammalian cells are playing vital roles in biotechnology and bioengineering. Various bioreactors have been developed, but their capacity and efficiency are often limited by insufficient mass transfer rate and high shear stress. A rolled scaffold (RS) is a fully defined scaffold for high-density adherent culture of mammalian cells. The RS is a polymer film with spacers, that is rolled into a cylinder with a pre-determined gap between each turn. Cells are cultured on its inner surfaces, while media flows through the gap. The RS exhibits high surface-area-to-volume ratio over 100cm2/mL and can transport nutrients and gases with significantly reduced shear stress via convection in a unidirectional laminar flow, rather than diffusion and random turbulent flow as in stirred-tank bioreactors. In this paper, we expanded Chinese Hamster Ovary cells with RS bioreactors and demonstrated cell culture density over 60 million cells/mL with a growth rate higher than conventional suspension culture. Besides, murine embryonic stem cells were successfully expanded without losing their pluripotency. The RS will provide an affordable, scalable, and reliable platform for large-scale culture of recombinant cells in biopharmaceutical industries and shear-sensitive stem cells for tissue engineering.

Turbulent mixing of a critical fluid: The non-perturbative renormalization

Non-perturbative Renormalization Group (NPRG) technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi〉∼(Pji⊥+αPji∥)/kd+ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there is a new nonequilibrium regime (universality class) associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ) of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

On the genesis and evolution of barchan dunes: morphodynamics

Barchan dunes are crescent-shaped formations of sand that can dominate both desert and subaqueous landscapes when the supply of sand is scarce. Because of the complexity and scale of the underlying phenomena, the mechanisms governing the entire process from the genesis to the long-term evolution of barchan fields still remain to be better understood. Herein, we attempt to present a description of this process in a subaqueous environment by employing a large-eddy simulation approach that couples turbulent flow and sand-bed morphodynamics. We show that the seeds of the emergent structure in barchan fields are random turbulent flow motions near the initially flat bed. We also provide high-resolution insights into phenomena such as barchan migration and merging, and show how transverse sand waves are formed and migrate over the barchan horns. Furthermore, the transverse sand waves over the barchan horns are shown to be the seeds of the newly born barchans at the end points of the two horns of a barchan through the process known as calving. To show this, we examine the celerity, wavelength and amplitude of the transverse sand waves over the barchan as they approach the end of its horn. The celerity and wavelength of these transverse sand waves are shown to be the defining factors in determining the frequency of the calving process. The amplitude of the newly born barchans (through calving) is also shown to be associated with the amplitude of the transverse waves near the end of the horn. The simulation data also show that the wavelength of the newly born barchans (the distance between individual dunes) is closely related to that of the transverse sand waves over their maternal barchan. Finally, we use the simulation results to discuss past conclusions derived from theory, conventional models and field observations.

Anti-solvent crystallization of l-threonine in Taylor crystallizers and MSMPR crystallizer: Effect of fluid dynamic motions on crystal size, shape, and recovery

The influence of the fluid dynamic motions of a periodic Taylor vortex and random turbulent eddy on the anti-solvent crystallization of l-threonine was investigated. The Taylor vortex flow and random turbulent eddy flow were generated by the inner cylinder rotation in a Couette–Taylor (CT) crystallizer and the impeller agitation in a mixed-suspension mixed product removal (MSMPR) crystallizer, respectively. Furthermore, the circumferentially sinusoidal fluctuation of a Taylor vortex was induced in an elliptical Couette–Taylor (ECT) crystallizer .The periodic Taylor vortex flows in the CT and ECT crystallizers resulted in a smaller crystal size and higher crystal recovery ratio of l-threonine than the random turbulent flow in the MSMPR crystallizer due to induction of a higher supersaturation, resulting in a higher nucleation in the CT and ECT crystallizers than in the MSMPR crystallizer. Thus, the crystal size was reduced and the crystal recovery ratio enhanced when increasing the rotation/agitation speed and feed flow rate in the CT, ECT, and MSMPR crystallizers. When increasing the temperature, the crystal size and crystal recovery ratio were both increased due an enhanced mass transfer for crystal growth. The crystal morphology changes according to the fluid dynamic motion with various crystallization conditions were well correlated in terms of the supersaturation.

Polymorphic Crystallization of Sulfamerazine in Taylor Vortex Flow: Polymorphic Nucleation and Phase Transformation

The influence of a periodic Taylor vortex flow on the polymorphic crystallization of sulfamerazine (SMZ), including polymorphic nucleation and phase transformation, was investigated using a Couette–Taylor (CT) crystallizer, and also compared with the influence of a random turbulent flow in a mixing tank (MT) crystallizer. In the MT crystallizer, the induction of the metastable phase (form-I) occurred first, which was then followed by the induction of the stable phase (form-II) 10–85 h later. However, this whole process was significantly reduced to a half hour in the CT crystallizer, demonstrating the high efficiency of a Taylor vortex flow for the induction of polymorphic nucleation. The efficiency of the Taylor vortex flow was also enhanced when increasing the rotation speed. As a result, the stable and metastable phases were simultaneously nucleated at the first induction with a rotation speed above 300 rpm; plus the stable-phase fraction nucleated at the first induction increased when increasing the ro...

Spark ignition of turbulent recirculating non-premixed gas and spray flames: A model for predicting ignition probability

A model that synthesizes previous knowledge from experiments and simulations on spark ignition of gas and liquid-fuelled non-premixed recirculating flames has been developed. Attention is focused on the flame expansion process and the overall filling of the combustor volume with flame. The model is meant to provide a quick assessment of the ignition behaviour of a combustor. It uses information from the flow patterns before ignition and calculates possible trajectories that a flame emanating from a spark may experience. The calculation of these trajectories includes flame extinction to capture the experimentally-observed flame quenching, mixture fraction fluctuations to capture the non-premixed nature of the flame, convection by the mean and the random turbulent flow to capture the probabilistic nature of the flame evolution, and uses recent results on the laminar burning velocity in sprays. The model is applied to gas and spray flames and the calculated ignition probability distributions and the timescale of complete ignition agree reasonably well with experiment. The results of the model provide insights into spark ignition processes in complicated flow patterns.

Dark matter merging induced turbulence as an efficient engine for gas cooling

We have performed a cosmological numerical simulation of primordial baryonic gas collapsing onto a $3\times10^7$M$_{\odot}$ dark matter (DM) halo. We show that the large scale baryonic accretion process and the merger of few $\sim10^6$ M$_{\odot}$ DM halos, triggered by the gravitational potential of the biggest halo, is enough to create super sonic ($\mathcal{M}>10$) shocks and develop a turbulent environment. In this scenario the post shocked regions are able to produced both H$_2$ and HD molecules very efficiently reaching maximum abundances of $n_\mathrm{H_2}\sim10^{-2}n_\mathrm{H}$ and $n_\mathrm{HD}\sim \mathrm{few}\times10^{-6}n_\mathrm{H}$, enough to cool the gas below 100K in some regions. The kinetic energy spectrum of the turbulent primordial gas is close to a Burgers spectrum, $\hat{E}_k\propto k^{-2}$, which could favor the formation of low mass primordial stars. The solenoidal to total kinetic energy ratio is $0.65\la R_k\la0.7$ for a wide range of wave numbers; this value is close to $R_k\approx 2/3$ natural equipartition energy value of a random turbulent flow. In this way turbulence and molecular cooling seem to work together in order to produce potential star formation regions of cold and dense gas in primordial environments. We conclude that both the mergers and the collapse process onto the main DM halo provide enough energy to develop super sonic turbulence which favor the molecular coolants formation: this mechanism, which could be universal and the main route toward formation of the first galaxies, is able to create potential star forming regions at high redshift.

Effects of mixing and stirring on the critical behaviour

Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The stirring and mixing are modelled by a random external Gaussian noise with the correlation function $\propto\delta(t-t') k^{4-d-y}$ and the divergence-free (due to incompressibility) velocity field, governed by the stochastic Navier--Stokes equation with a random Gaussian force with the correlation function $\propto\delta(t-t') k^{4-d-y'}$. Depending on the relations between the exponents $y$ and $y'$ and the space dimensionality $d$, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there are three new nonequilibrium regimes (universality classes) associated with new nontrivial fixed points of the renormalization group equations. The corresponding critical dimensions are calculated in the two-loop approximation (second order of the triple expansion in $y$, $y'$ and $\epsilon=4-d$).

Response probability structure of a structurally nonlinear fluttering airfoil in turbulent flow

The stationary probability structure for the aeroelastic response of a structurally nonlinear fluttering airfoil subject to random turbulent flow is examined numerically. The airfoil is modelled as a two-dimensional flat plate with degrees of freedom in torsion and heave (vertical displacement). The nonlinearity is a hardening cubic stiffness force in the torsional direction. The aerodynamic force and moment are assumed to be linear, thus limiting the analysis to small oscillations; unsteady effects are retained. Furthermore, both parametric and external random coloured excitations are considered. It is found that depending on the value of turbulence variance and nonlinear cubic stiffness coefficient, the pitch marginal probability density functions (PDF) exhibits uni-, bi- or double bi-modality; the nature of the bi-modality is not unique. An explanation of the behaviour is provided via an analysis of the joint PDF in pitch and pitch rate for which both the deterministic and random responses are examined. More generally, it is found that the random excitation effectively ‘decouples’ the nonlinear responses such that the pitch, pitch rate, heave and heave rate marginal PDFs transition from uni- to bi-modality at different airspeeds. It is argued that a fundamental cause of the observed behaviour is the synergy between the nonlinearity and the random external excitation.

Star Formation from Galaxies to Globules

The empirical laws of star formation suggest that galactic-scale gravity is involved, but they do not identify the actual triggering mechanisms for clusters in the final stages. Many other triggering processes satisfy the empirical laws too, including turbulence compression and expanding shell collapse. The self-similar nature of the gas and associated young stars suggests that turbulence is more directly involved, but the small scale morphology of gas around most embedded clusters does not look like a random turbulent flow. Most clusters look triggered by other nearby stars. Such a prominent local influence makes it difficult to understand the universality of the Kennicutt and Schmidt laws on galactic scales. A unified view of multi-scale star formation avoids most of these problems. Ambient self-gravity produces spiral arms and drives much of the turbulence that leads to self-similar structures, while localized energy input from existing clusters and field supernovae triggers new clusters in pre-existing clouds. The hierarchical structure in the gas made by turbulence ensures that the triggering time scales with size, giving the Schmidt law over a wide range of scales and the size-duration correlation for young star fields. The efficiency of star formation is determined by the fraction of the gas above a critical density of around 10^5 m(H2)/cc. Star formation is saturated to its largest possible value given the fractal nature of the interstellar medium.

Transition to turbulent flow in aerodynamics

The difficult problem of understanding the physical mechanisms at work in the change from laminar, or smooth, flow to random turbulent flow, with its wide range of active time– and space–scales, has occupied engineers, physicists and mathematicians for the past century. When an airfoil is placed in and parallel to a current of fast–moving air, a so–called boundary layer forms on its surface as the velocity of the air at the surface must be reduced to zero. Near the front of the airfoil the boundarylayer flow is smooth and steady, but further downstream it is seen to become highly irregular, unsteady and turbulent, often at a well–defined front. Scientists working in transition prediction aim to answer the questions of where and why this transition occurs. It is a problem distinct from, but related to, that of understanding turbulent flow itself. It is of prime industrial importance. For example, a turbulent flow offers more drag resistance, and, indeed, an aircraft designed so that more of the flow over its wings is laminar can carry more passengers and much less fuel. Understanding the physical structures and flow patterns visible in the late end stage of transition and the initiation of turbulent spots, isolated patches of turbulence surrounded by laminar flow, should also throw much–needed light on the structures seen in fully developed wall turbulence and help in the equally difficult, distinct, problem of modelling turbulent flow. There are many possible routes through transition, depending on the flow configuration and geometry and the method in which transition is initiated by any of the range of possible background disturbances present, either in the free stream or in the form of roughness on the surface, for example. In the past 20 years, techniques for tracing the linear and nearly linear growth of small disturbances in the boundary layer have been developed that could form part of effective design tools for engineers. There has also been an increased theoretical understanding, made possible by the application of high Reynolds number asymptotic theories, of the myriad of possible interactions between disturbances driving this relatively slow stage of the transition process. Much important work remains to be done to include in any design tool the important processes occurring at the two ends of this process. Firstly, how do disturbances enter the boundary layer to be amplified, known as the receptivity problem, and secondly, what happens at the end stage, where the disturbances have grown so large that the nearly linear theories are no longer applicable? Recent experimental work has shown a remarkable similarity in the characteristics of this final breakdown among a variety of flows. Two–dimensional flows, such as that over a plate aligned with the flow or in a channel or pipe, gradually develop three–dimensional structures, known as lambda vortices. These then rapidly break down in two distinct ways, which are both active almost simultaneously. One gives rise to spikes: short–lived, large–amplitude pulses, which are practically deterministic in nature. The second involves a secondary instability and the initiation of random fluctuations. Three–dimensional flows, such as those on swept wings, develop cross–flow vortices, which themselves seem to break down via a secondary instability mechanism, possibly similar to that seen in lambda vortices. This article reviews recent developments in the field of transition research, concentrating on those related to the late stages of breakdown and the onset of random behaviour. It brings together results from young experimentalists, computationalists and theoreticians and looks forward to an increased understanding of this challenging and important problem.

The Effect of Turbulence on Flow of Natural Gas Through Porous Reservoirs

Abstract The nature and the limits of validity of Darcy's law as applied to the flow of natural gas through reservoirs has been considered in order to resolve some controversial aspects of the effect of turbulence on pressure drops. The equivalence between various concepts and viewpoints advanced in the past by several investigators to explain how and why a gas well does not necessarily perform according to Darcy's law is shown. Starting with generalized equations of flow of fluids through porous media, a partial differential equation has been derived which accurately represents the flow at all rates. This equation has been numerically solved using an IBM 704 digital computer. The results permit plots of unsteady radial pressure distribution curves from which specific isochronal backpressure curves may be constructed. These back-pressure curves show the effect of the fl factor on the slope of the back-pressure curve. The calculations further indicate that the drainage radius for a gas well in turbulent flow propagates at a rate dependent upon the rate of production at the wellbore. This is quite different from the case with liquid flow or natural-gas flow in laminar regime. Additionally, the effect of reservoir inhomogeneities and crossflow between layers of different permeability on the back-pressure performance of gas wells has been considered red. In light of the current numerical results the significance and limitation of the rate of flow function Y proposed by Smith has been discussed. Introduction The relationship between the pressure drop and flow rate in problems of fluid flow through porous media is known to be affected by the nature of flow through the porous matrix. It has been observed by many that, for a range of flow rates, the pressure drop remains proportional to the rate of flow. When some flow rate is reached, however, it is usually observed that the pressure drop gradually begins to increase more than proportionally to the flow rate. It is well known that this phenomenon was first observed by Osborne Reynolds in 1901 in experimenting with flow through pipes. In his classical experiments. Reynolds made visual observations on the condition of streamlines evidenced by injecting a dye into water flowing through glass tubes. In these experiments, the abrupt transition between steady, "streamline, laminar" flow and unsteady random turbulent flow was found to be a function of the dimensionless group (D / ), now known as the Reynolds number. During these experiments, in addition to observations on the nature of flow regimes, the proportionality between flow rate and pressure drop in laminar flow was contrasted with the nonlinearity between these variables in turbulent flow. Fancher and Lewis reported data on various consolidated and unconsolidated sands in 1933. Their conclusions were that ". . . the flow of fluids through these porous materials closely resembles that through pipes; that there is a condition of flow in porous systems which resembles viscous flow, another which corresponds to turbulent; that the change from one type to the other takes place at a definite and reproducible condition for each system". In 1947, Brownell and Katz published a method to predict the laminar and turbulent flow behavior from the particle size, bed porosity and the particle sphericity, employing the friction factor-Reynolds number charts for pipes. Several investigators have verified the work of Fancher, Lewis and Barnes and presented their data as friction factor-vs-Reynolds number plots. The equation which would represent the pressure gradient over the whole range of velocity must have an added term over that represented by Darcy's law. Accordingly, the pressure gradient necessary to sustain flow at the velocity (v) through a porous medium may be represented by the following equation, suggested by Forscheimer. = ..........(1) The nature and the range of validity of Darcy's law has been the subject of studies by many investigators over the past years. While everyone seemed to agree on the need for a quadratic correction term to Darcy's law to make it effective over the range of velocities, the concept of inception of turbulence and the use of the term "turbulent flow" remained controversial. JPT P. 799^