Quantitative evaluation of PIV peak locking through a multiple Δ<Emphasis Type="Italic">t</Emphasis> strategy: relevance of the rms component

The possibility of using different times between laser pulses (Δt) in a PIV (Particle Image Velocimetry) measurement of the same real flow field for error assessment has already been proposed by the authors in a recent paper Nogueira et al. (Meas Sci Technol 20, 2009). It is a simple procedure that is available with the usual PIV setup. In that work, peak locking was considered basically as a bias error. Later measurements indicated that, using appropriate processing algorithms, this error is not the main peak-locking effect. Scenarios with the rms (root mean square) error due to peak locking as the most relevant contribution are more common than initially expected and require a differentiated approach. This issue is relevant due to the impact of the rms error in the evaluation of flow quantities like turbulent kinetic energy. The first part of this work is centred on showing that peak-locking error in PIV is not always a measurement bias towards the closest pixel integer displacement. Insight in the subject indicates that this is the case only for algorithm-induced peak locking. The peak locking coming out of image acquisition limitations (i.e. resolution) is not ‘a priory’ biased. It is a random error with a peculiar probability density function. Discussion on the subject is offered, and a particular approach to use a simple multiple Δt strategy to asses this error is proposed. The results reveal that in real images where amplitude of the peak-locking bias error is assessed to be as small as 0.02 pixels, rms errors can be in the order of 0.1 pixels. As PIV approaches maturity, providing a quantitative confidence interval by estimating measurement error seems essential. The method developed is robust enough to quantify these values in the presence of turbulence with rms up to ~0.6 pixels. This proposal constitutes a relevant step forward from the traditional histogram-based considerations that only reveal whether strong peak-locking error is present or not, without any information on its magnitude or whether its origin is bias or rms.     

Biological control of a predator–prey system through provision of a super predator

In this paper, we make a systematic analysis of the dynamics of a predator–prey system with type-II functional response, in which the predator growth rate is affected by the presence of a super predator. The main aim of this research is to study the consequences of the presence of a super predator on the system dynamics. The existence and stability of the different possible equilibrium points are studied, and we conclude that the maximum consumption rate of a super predator plays a key role in determining the eventual state of the ecosystem. A detailed bifurcation analysis is carried out through numerical simulations, and we observe that theoretically it is possible to control the dynamics of the system by manipulating the consumption rate of the super predator.     

Simultaneous particle image velocimetry and chemiluminescence visualization of millisecond-pulsed current�Cvoltage-induced perturbations of a premixed propane/air flame

The effects of millisecond-wide, pulsed current?Cvoltage-induced behavior in premixed laminar flames have been investigated through the simultaneous collection of particle image velocimetry (PIV) and chemiluminescence data with particular attention paid to the onset mechanisms. Disturbances caused by applied voltages of 2?kV over a 30-mm gap to a downward propagating, atmospheric pressure, premixed propane/air flame with a flow speed near 2?m/s and an equivalence ratio of 1.06 are investigated. The combined PIV and chemiluminescence-based experimental data show the observed disturbance originates only in or near the cathode fall region very close to the burner base. The data also suggest that the coupling mechanism responsible for the flame disturbance behavior is fluidic in nature, developing from the radial positive chemi-ion distribution and an ion-drift current-induced net body force that acts along the annular space discharge distribution in the reaction zone in or near the cathode fall. This net body force causes a reduction in flow speed above these near cathodic regions causing the base of the flame to laterally spread. Also, this effect seems to produce a velocity gradient leading to the transition of a laminar flame to turbulent combustion for higher applied current?Cvoltage conditions as shown in previous work (Marcum and Ganguly in Combust Flame 143:27?C36, 2005; Schmidt and Ganguly in 48th AIAA aerospace sciences meeting. Orlando, 2010).     

Two and three dimensional modeling of fluidized bed with multiple jets in a DEM–CFD framework

Fluidized beds with multiple jets have widespread industrial applications. The objective of this paper is to investigate the jet interactions and hydrodynamics of a fluidized bed with multiple jets. Discrete element modeling coupled with in-house CFD code GenIDLEST has been used to simulate a bed with nine jets. The results are compared with published experiments. Mono dispersed particles of size 550 μm are used with 1.4 times the minimum fluidization velocity of the particles. Both two and three dimensional computations have been performed. To the best of our knowledge, the results presented in this paper are the first full 3D simulations of a fluidized bed performed with multiple jets. Discrepancies between the experiment and simulations are discussed in the context of the dimensionality of the simulations. The 2D solid fraction profile compares well with the experiment close to the distributor plate. At higher heights, the 2D simulation over-predicts the solid fraction profiles near the walls. The 3D simulation on the other hand is better able to capture the solid fraction profile higher up in the bed compared to that near the distributor plate. Similarly, the normalized particle velocities and the particle fluxes compare well with the experiment closer to the distributor plate for the 2D simulation and the freeboard for the 3D simulation, respectively. A lower expanded bed height is predicted in the 2D simulation compared to the 3D simulation and the experiment. The results obtained from DEM computations show that a 2D simulation can be used to capture essential jetting trends near the distributor plate regions, whereas a full scale 3D simulation is needed to capture the bubbles near the freeboard regions. These serve as validations for the experiment and help us understand the complex jet interaction and solid circulation patterns in a multiple jet fluidized bed system.     

Plane acoustic wave propagation through a composite of elastic and Kelvin–Voigt viscoelastic material layers

The problem of plane wave propagation through a plane composite layer of thickness h is considered. The composite consists of periodically repeated elastic and Kelvin–Voigt viscoelastic material layers, and all layers are either parallel or perpendicular to the incident wave front. Moreover, it is assumed that the thickness of each separate layer of the composite is much less than the acoustic wave length and the thickness h of the entire composite. We study the problem by using a homogenized model of the composite, which allows us to find the reflection and transmission factors and the variation in the sound intensity level as it propagates though the composite layer of thickness h.     

Flow of elasto-viscoplastic liquids through a planar expansion–contraction

The steady flow of incompressible elasto-viscoplastic liquids through a planar expansion–contraction is investigated. A novel constitutive model is employed to describe the mechanical behavior of the flowing liquids. Numerical solutions of the constitutive and conservation equations were obtained via a finite element method to investigate the role of elasticity, yield stress, and inertia. The fields of velocity, stress, elastic strain, and rate of strain were obtained for different combinations of the governing parameters. It was observed that these fields, as well as the shape and position of the yield surface, are all strong functions of elasticity, yield stress, and inertia. The trends observed agree well with previous numerical and visualization results available in the literature. The present work offers a detailed study on the effects of elasticity, presenting, in particular, the fields of elastic strain.     

Flow of oil–water emulsions through a constricted capillary

The flow of oil-in-water emulsions through quartz micro-capillary tubes was analyzed experimentally. The capillaries were used as models of connecting pore-throats between adjacent pore body pairs in high-permeability media. Pressure drop between the inlet and outlet ends of the capillary was recorded as a function of time, for several values of the volumetric flow rate. Several distinct emulsions were prepared using synthetic oils in deionized water, stabilized by a surfactant (Triton X-100). Two oils of different viscosity values were used to prepare the emulsions, while two distinct drop size distributions were obtained by varying the mixing procedure. The average oil drop size varied from smaller to larger than the neck radius. The results are presented in terms of the extra-pressure drop due to the presence of the dispersed phase, i.e. the difference between the measured pressure drop and the one necessary to drive the continuous phase alone at the same flow rate. For emulsions with drops smaller than the capillary throat diameter, the extra-pressure drop does not vary with capillary number and it is a function of the viscosity ratio, dispersed phase concentration and drop size distribution. For emulsions with drops larger than the constriction, the large oil drops may partially block the capillary, leading to a high extra pressure difference at low capillary numbers. Changes in the local fluid mobility by means of pore-throat blockage may help to explain the additional oil recovery observed in laboratory experiments and the sparse data on field trials.     

The hydrodynamics of liquid–liquid upflow through a venturimeter

The present work reports the influence of a venturimeter on liquid–liquid phase distribution during upflow through a vertical pipe. The optical probe technique has been adopted for the characterization of flow. The probability density function and the wavelet multi-resolution analysis of the random probe signals have provided an insight into the details of the flow patterns and the intrinsic differences at the upstream, throat and the downstream sections. The experiments have indicated the flow pattern transitions to occur at lower velocities at the downstream region of the venturi. The pressure drop readings across the venturi have been used to estimate the mass flow rate of the mixture by using suitable models for the different patterns.     

The PELskin project—part III: a homogenized model of flows over and through dense poroelastic media

In the context of the PELskin project, a homogenized model to study flows over and inside poroelastic media has been developed. It allows to simulate the fluid–structure interaction between a fluid and an extremely dense poroelastic medium, without limitations on physical and geometrical parameters such as the density of the elastic material, the porosity or the number of periodic microstructures which constitute the medium. The model is applied to the case of the flow in a channel driven by an oscillating pressure gradient, with half the channel covered by a carpet of flexible, densely packed fibers, connected to each other to allow for the propagation of the deformation field.     

CFD–DEM simulation of the pneumatic conveying of fine particles through a horizontal slit

Fine particles play a significant role in many industrial processes. To study the dynamic behavior of fine particle and their deposition in rock fractures, the pneumatic conveying of fine particles (approximately 100 μm in diameter) through a small-scale horizontal slit (0.41 m × 0.025 m) was studied, which is useful for the sealing technology of underground gas drainage in coal mining production. The CFD–DEM method was adopted to model the gas-particle two-phase flow; the gas phase was treated as a continuum and modeled using computational fluid dynamics (CFD), particle motion and collisions were simulated using the DEM code. Then, the bulk movement of fine particles through a small-scale horizontal slit was explored numerically, and the flow patterns were further investigated by visual inspection. The simulation results indicated that stratified flow or dune flow can be observed at low gas velocities. For intermediate gas velocities, the flow patterns showed pulsation phenomena, and dune flow reappeared in the tail section. Moreover, periodic flow regimes with alternating thick and sparse stream structures were observed at a high gas velocity. The simulation results of the bulk movement of fine particles were in good agreement with the experimental findings, which were obtained by video-imaging experiments. Furthermore, the calculated pressure drop versus gas velocity profile was investigated and compared with relative experimental findings, and the results showed good agreement. Furthermore, the particle velocity vectors and voidage distribution were numerically simulated. Selected stimulation results are presented and provide a reference for the further study of fine particles.     

Influence of steam leakage through vane,gland, and shaft seals on rotordynamics of high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine

A comparative analysis of the influence of steam leakage through vane, gland, and shaft seals on the rotordynamics of the high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine was performed using numerical calculations. The rotordynamic coefficients associated with steam leakage through the three labyrinth seals were calculated using the control-volume method and perturbation analysis. A stability analysis of the rotor system subject to the steam forcing induced by the leakage flow was performed using the finite element method. An analysis of the influence of the labyrinth seal forcing on the rotordynamics was carried out by varying the geometrical parameters pertaining to the tooth number, seal clearance, and inner diameter of the labyrinth seals, along with the thermal parameters with respect to pressures and temperatures. The results demonstrated that the steam forcing with an increase in the length of the blade for the vane seal significantly influences the rotordynamic coefficients. Furthermore, the contribution of steam forcing to the instability of the rotor is decreased and increased with increases in the seal clearance and tooth number, respectively. The comparison of the rotordynamic coefficients associated with steam leakage through the vane seal, gland seal, and shaft seal convincingly disclosed that, although the steam forcing attenuates the stability of the rotor system, the steam turbine is still operating under safe conditions.     

Equations of dynamics of a mixture composed of a gas and hollow selective‐permeable microspheres

Based on the laws of conservation of mass, momentum, and energy, equations of dynamics of multiphase systems, which are gas mixtures with hollow microspheres with selectively permeable shells, are obtained under the assumption of quasisteadiness of the process offilling the microspheres by the gas. Acoustic characteristics of the system composed of a uniform gas and hollow permeable microspheres are studied using a simplified (onevelocity and onetemperature) model. The frequency dependences of velocity and damping coefficient of sound are determined with regard for gas density (pressure) relaxation inside the microspheres.     

Fluid dynamics of horizontal air–water slug flows through a dividing T-junction

Experimental data from horizontal air–water slug flows were obtained in a test facility which was a 34 mm internal diameter, 10 m long Plexiglas pipe connected to the 90° branch arms from a T-junction. The test points were located on the flow pattern map in the proximity of the transition lines which separates different flow patterns. Capacitive probes with helical and concave plate sensors were used to quantify the dynamic liquid holdup in each branch. They were combined with Venturi nozzles + differential pressure transmitters in each outlet branch for measuring the two-phase mass flow rates. The dynamic characteristics of the slug flow splitting in a T-junction were studied from the acquired signals. Diaphragm straight-through type valves were used in the run and in the lateral branch arms to imitate equipments consuming the two-phase flow after the T-junction. This assembly can also be used as a gas–liquid separation system. The results showed different mechanisms acting on the slug flow division phenomenon. Liquid accumulation into the run branch, between the TJ and the control valve, caused more gas to come to the lateral branch.     

Stability and bifurcation periodic solutions in a Lotka–Volterra competition system with multiple delays

This paper is concerned with a Lotka?CVolterra competition system with multiple delays. Firstly, we investigate the existence and stability of the positive equilibrium. In particular, we find that the system has Hopf bifurcation at the positive equilibrium, whereas this singularity does not occur for the corresponding system with two delays when interspecies competition is weaker than intraspecies competition. Secondly, we analyze the stability of the periodic solutions by reducing the original system on the center manifold. Finally, some numerical examples are given to verify our theoretical results.     

Simultaneous velocity and concentration measurements in the near field of a turbulent low-pressure jet by digital particle image velocimetry–planar laser-induced fluorescence

The main purpose of this work is to develop a method for simultaneous measurement of velocity and passive scalar concentration by means of digital particle image velocimetry and planar laser-induced fluorescence. Details of the implementation of the method are given, and the technique is applied to measurements of concentration and velocity in the centre-plane of a liquid jet with a Reynolds number of 6,000. The measurements are compared with large eddy simulations. Mean velocities and concentrations, fluctuating velocities and concentrations, and correlation between fluctuating velocities and concentrations are analysed for the first six diameters downstream of the jet exit. The general agreement between measured and simulated results was found to be good, in particular for mean quantities. Mean profiles are also found to be in good agreement with other experimental work on jets reported in the literature. The “whole-plane” measurement method was found to be very useful for detailed comparisons of turbulent statistics with simulated data. The inadequacy of models for turbulent mass transport based on the standard gradient diffusion concept is demonstrated through the experimental data. Received: 4 October 2000/Accepted: 27 November 2000     

On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity: occurrence of multiple attractors

Nonlinear Dynamics - Chua’s circuit is one of the well-known nonlinear circuits which have been used to study a rich variety of nonlinear dynamic behaviors such as bifurcation, chaos, and...     

Lag synchronization of multiple identical Hindmarsh–Rose neuron models coupled in a ring structure

Lag synchronization of multiple identical Hindmarsh–Rose neuron systems coupled in a ring structure is investigated. In the coupled systems, each neuron receives signals only via synaptic strength from the nearest neighbors. Based on the Lyapunov stability theory, the sufficient conditions for synchronization of the multiple systems with chaotic bursting behavior can be obtained. The synchronization condition about the control parameter g is also obtained by numerical method. Finally, numerical simulations are provided to show the effectiveness of the developed methods.