Global injected power statistics in a turbulent system: degrees of freedom and aspect ratio effect

The properties of the global energy injection rate of a closed turbulent flow produced between two counter-rotating disks are studied. The statistics of this global quantity are measured when the aspect ratio (defined as the ratio of the disk diameter to the separating distance between both disks) is modified. It is shown that the non-Gaussian statistics obtained at a low aspect ratio becomes Gaussian for a large aspect ratio. This effect is accompanied with a large decrease of the fluctuation rate. These results indicate the total energy injection rate to obey the central limit theorem. It is also shown that the number of degrees of freedom of total injection rate may be related to the number of independent large scale structures present in the flow.     

Topology Trivialization and Large Deviations for the Minimum in the Simplest Random Optimization

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N?1)-dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the “trust region subproblem” or “constraint least square problem”. When both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field. We first identify and study two distinct large-N scaling regimes in which the linear term (magnetic field) leads to a gradual topology trivialization, i.e. reduction in the total number $\mathcal{N}_{tot}$ of critical (stationary) points in the cost function landscape. In the first regime $\mathcal{N}_{tot}$ remains of the order N and the cost function (energy) has generically two almost degenerate minima with the Tracy-Widom (TW) statistics. In the second regime the number of critical points is of the order of unity with a finite probability for a single minimum. In that case the mean total number of extrema (minima and maxima) of the cost function is given by the Laplace transform of the TW density, and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the TW law. Though the full form of that distribution is not yet known to us, one of its far tails can be inferred from the large deviation theory for the global minimum. In the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large-deviation approximation by finding both the rate function and the leading pre-exponential factor.     

Flow-induced oscillations of a cantilevered pipe conveying fluid with base excitation

It is known that a plain cantilevered pipe conveying fluid loses its stability by a Hopf bifurcation, leading to either planar or non-planar flutter for flow velocities beyond the critical flow velocity for Hopf bifurcation. If an external mass is attached to the end of the pipe (an end-mass), the resulting dynamics become much richer, showing 2D and 3D quasiperiodic and chaotic oscillations at high flow velocities. In this paper, a cantilevered pipe, with and without an end-mass, subjected to a small-amplitude periodic base excitation is considered. A set of three-dimensional nonlinear equations is used to analyze the pipe?s response at various flow velocities and with different amplitudes and frequencies of base excitation. The nonlinear equations are discretized using the Galerkin technique and the resulting set of equations is solved using Houbolt?s finite difference method. It is shown that for a plain pipe (with no end-mass), non-planar post-instability oscillations can be reduced to planar periodic oscillations for a range of base excitation frequencies and amplitudes. For a pipe with an end-mass, similarly to a plain pipe, three-dimensional period oscillations can be reduced to planar ones. At flow velocities beyond the critical flow velocity for torus instability, the three-dimensional quasiperiodic oscillations can be reduced to two-dimensional quasiperiodic or periodic oscillations, depending on the frequency of base excitation. In all these cases, a low-amplitude base excitation results in reducing the three-dimensional oscillations of the pipe to purely two-dimensional oscillations, over a range of excitation frequencies. These numerical results are in agreement with the previous experimental work.     

On mean flow universality of turbulent wall flows. I. High Reynolds number flow analysis

ABSTRACT

The universality and mathematical physical structure of wall-bounded turbulent flows is a topic of discussions over many decades. There is no agreement about questions like what is the physical mean flow structure, how universal is it, and how universal are theoretical concepts for local and global flow variations. These questions are addressed by using latest direct numerical simulation (DNS) data at moderate Reynolds numbers Re and experimental data up to extreme Re. The mean flow structure is explained by analytical models for three canonical wall-bounded turbulent flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Thorough comparisons with DNS and experimental data provide support for the validity of models. Criteria for veritable physics derived from observations are suggested. It is shown that the models presented satisfy these criteria. A probabilistic interpretation of the mean flow structure shows that the physical constraints of equal entropies and equally likely mean velocity values in a region unaffected by boundary effects impose a universal log-law structure. The structure of wall-bounded turbulent flows is much more universal than previously expected. There is no discrepancy between local logarithmic velocity variations and global friction law and bulk velocity variations. Flow effects are limited to the minimum: the difference of having a bounded or unbounded domain, and the variation range of mean velocity values allowed by the geometry.     

Langevin equation approach to granular flow in a narrow pipe

The gravity-driven flow of granular material through a rough, narrow vertical pipe is described using the Langevin equation formalism. Above a critical particle density the homogeneous flow becomes unstable with respect to short-wave length perturbations. In correspondence with experimental observations, we find clogging and density waves in the flowing material.     

Flow acoustics modelling and implications for ultrasonic flow measurement based on the transit-time method

A comparison between three mathematical models frequently used in flow acoustics is presented and discussed with respect to ultrasonic flow-meter performance based on the transit-time method. The flow-meter spoolpiece geometry is assumed to be a cylindrical pipe. Semi-analytical calculations employing the Frobenius power series expansion method are shown for the cases of a constant-, linear-, parabolic-, and cubic-flow profiles although the Frobenius method presented can be applied to any smooth flow profile. It is shown that the so-called deviation of measurement, often used as a measure of the flow-meter accuracy, is strongly dependent on the acoustic mode excited and the flow profile. Furthermore, differences with respect to deviation of measurement results exist among the three mathematical models analyzed.     

A composite model of the plastic flow of amorphous covalent materials

A model based on the data available in the literature on the computer simulation of amorphous silicon has been proposed for describing the specific features of the plastic flow of amorphous covalent materials. The mechanism of plastic deformation involves homogeneous nucleation and growth of inclusions of a liquidlike phase under external shear stress. Such inclusions experience plastic shear, which is modeled by glide dislocation loops. The energy changes associated with the nucleation of these inclusions at room and increased temperatures have been calculated. The critical stress has been found, at which the barrierless nucleation of inclusions becomes possible. It has been shown that this stress decreases with an increase in temperature. According to the calculations, the heterogeneous (homogeneous) plastic flow of an amorphous material should be expected at relatively low (high) temperatures. Above the critical stress, the homogeneous flow is gradually replaced by the heterogeneous flow.     

Direct numerical simulation of transitional flow in a finite length curved pipe

Transition to turbulent flow in a curved pipe has been well studied through experiments and numerical simulations. Numerical simulations often use a helical pipe with an infinite length such that the inlet and outlet boundary conditions can be modelled as periodic which greatly reduces computational time. In this study, we examined a finite length curved pipe with Poiseuille flow imposed at the inlet and a stress-free boundary condition at the outlet. Direct numerical simulation of the Navier-Stokes equations for rigid walls and a Newtonian fluid was performed using nek5000. Straight extensions were added to the inlet and outlet such to diminish the impact of boundary conditions on the flow field in the region with curvature. The examined model has a pipe radius of curvature that is three times the pipe radius. The model has ～355 million nodes and required an order of magnitude greater computational time when compared with an infinite length curved pipe. Results show that the critical Reynolds number, the lowest value with instabilities present in the flow, is much greater than that of a straight pipe and occurs near Re=5000–5200. This is larger than the critical Reynolds number typically reported for an infinite length curved pipe (Re=4200–4300).     

Universal dynamic fragmentation in D dimensions

A generic model is introduced for brittle fragmentation in D dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for D=2. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for D=3. In the experiments the nonzero grain size of rock causes deviation from the ideal model distribution in the small-size limit. The size of the cutoff seems to diverge at the minimum energy sufficient for fragmentation to occur, but the scaling exponent is not universal.     

Some interesting consequences of the maximum entropy production principle

Two nonequilibrium phase transitions (morphological and hydrodynamic) are analyzed by applying the maximum entropy production principle. Quantitative analysis is for the first time compared with experiment. Nonequilibrium crystallization of ice and laminar-turbulent flow transition in a circular pipe are examined as examples of morphological and hydrodynamic transitions, respectively. For the latter transition, a minimum critical Reynolds number of 1200 is predicted. A discussion of this important and interesting result is presented.     

End correction at the interface between a plain and a perforated pipe

This paper considers the plane-wave end correction that should be applied at the junction between a plain and a perforated pipe of equal diameter in the absence of mean flow. A general theory is developed that results in an equation for the end correction of all such junctions. The theory is verified by experimental results for the end correction obtained via the measurement of resonant frequency of a Helmholtz resonator whose neck is formed of a plain section and then a perforated section of pipe, before termination into free space. It is shown that in most practical situations within automotive silencers the perforated pipe will be long enough for the nature of the termination to be irrelevant. A simple formula is developed to evaluate this long-length limit and from it the dependence of the end correction upon all the parameters within the problem becomes explicit.     

Quantum-chemical interpretation of spectral and photochemical properties of complexes of metalloporphyrins with pyridine anions

A quantum-chemical study is made of the energy minima and profiles of the potential surface of complexes of Zn-porphyrin with dilithiumpyridine in different energy states. It is shown that the axial distribution of dilithiumpyridine relative to the porphyrin ring corresponds to the energy minimum pertaining to the lower singlet state. A radically different geometry is obtained for the lower triplet state of charge transfer, and at this energy minimum the latter state represents, according to calculation data, the ground state. Based on an investigation of the profiles of potential surfaces between the energy minima, an explanation is given for the photochemical behavior of the complex. “S. I. Vavilov Institute of Optics” All-Russia Scientific Center, 12, Birzhevaya Liniya, St. Petersburg, 199034. Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 38–41, January–February, 1997.     

Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method

The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function $K$ (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function $K$ for plane Couette flow is derived. The result indicates that $K$ reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high $\operatorname{Re}$ for given same level of normalized perturbation in the domain. The critical value of $K$ at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of $K$ at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).     

Improved composite-boson theory of monolayer and bilayer quantum Hall ferromagnets

An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.     

Visualization of molten pools and invisible laser beam profiles using an ultraviolet CCD camera

Experiments were conducted on the effects of a wall distance and velocity ratio of suction flow to injection flow on the flow and heat transfer characteristics of a circular impinging jet accompanying an annular suction flow. As a result, it is found that in the case of accompanying suction flow, a higher Nusselt number can be obtained compared with in the case without suction flow, under a condition of the wall distance within eight times of injection pipe diameter from the near pipe exit edge. In addition, when the effect of velocity ratio is examined at a fixed arbitrary wall distance, it is found that there exists an optimum velocity ratio where the Nusselt number becomes the maximum. It is shown that these heat transfer characteristics are closely associated with the fluctuating velocity and the mean velocity in the two-dimensional velocity field observed by Particle Image Velocimetry (PIV).     

Peculiarities of propagation of the dispersed phase in a gas-droplet flow downstream of a pipe sudden expansion

The results of numerical simulation of the propagation of the dispersed phase in a gas-droplet flow downstream of a pipe sudden expansion for small initial mass concentrations of particles (M _L1 = 0–0.1) are presented. Fine-dispersed droplets with the Stokes numbers Stk < 1 are entrained by a separated flow and are present in the whole cross section of the pipe. The near-wall region of the pipe is free of fine particles due to intense evaporation. Heavy particles (Stk > 1) do not get in the recirculation flow region and are present only in the mixing layer and in the flow core. It is shown that the addition of fine-dispersed droplets suppresses the energy of the gaseous phase turbulence in the separated flow. The results are compared with the experimental data for two-phase separated flows and are found to be in the conformity with these data.     

弯管内气液固三相流中液膜区流场的PIV测量

为了深入认识螺旋管内多相流相分离现象,应用粒子图象测速仪(PIV),对组合弯管内气水砂三相流底部水平段和上升段中液膜区的流场进行了测量。研究表明:底部水平段流动主流速度分布比较均匀,颗粒跟随流体运动;二次流十分微弱,颗粒在离心力作用下由内弯侧向外弯侧运动;速度脉动强烈,不利于相分离。上升段中流动受到重力的阻碍,同底部平段相比主流速度降低,离心力作用减弱,颗粒径向时均速度较低;流动的间歇性更强,两相速度脉动更剧烈。     

Bifurcational behavior of potential energy in a particle system

The paper considers a one-dimensional crystal model consisting of pairwise interacting particles. The critical points of potential energy for the crystal system under tension are studied on the assumption that the pair interaction potential has a single minimum. It is shown that new critical points of potential energy appear in a bifurcational manner.     

Deformation of Two-Dimensional Nonuniform-Membrane Red Blood Cells Simulated by a Lattice

To study two-dimensional red blood cells deforming in a shear flow with the membrane nonuniform on the rigidity and mass, the membrane is discretized into equilength segments. The fluid inside and outside the red blood cell is simulated by the D2Q9 lattice Boltzmann model and the hydrodynamic forces exerted on the membrane from the inner and outer of the red blood cell are calculated by a stress-integration method. Through the global deviation from the curvature of uniform-membrane, we find that when the membrane is nonuniform on the rigidity, the deviation first decreases with the time increases and implies that the terminal profile of the red blood cell is static. To a red blood cell with the mass nonuniform on the membrane, the deviation becomes more large, and the mass distribution affects the profile of the two sides of the flattened red blood cell in a shear flow.     

Elucidating the mechanism of nucleation near the gas-liquid spinodal

We have constructed a multidimensional free energy surface of nucleation of the liquid phase from the parent supercooled and supersaturated vapor phase near the gas-liquid spinodal. In particular, we remove the Becker-Doring constraint of having only one growing cluster in the system. Close to the spinodal, the free energy, as a function of the size of the largest cluster, develops surprisingly a minimum at a subcritical cluster size. It is this minimum at intermediate size that is found to be responsible for the barrier towards further growth of the nucleus at large supersaturation. An alternative free energy pathway involving the participation of many subcritical clusters is found near the spinodal where the growth of the nucleus is promoted by a coalescence mechanism. The growth of the stable phase becomes collective and spatially diffuse, and the significance of a "critical nucleus" is lost for deeper quenches.