Characterization of chaotic dynamic behavior in the gas–liquid slug flow using directed weighted complex network analysis

Understanding the nonlinear and complex dynamics underlying the gas–liquid slug flow is a significant but challenging problem. We systematically carried out gas–liquid two-phase flow experiments for measuring the time series of flow signals, which is studied in terms of the mapping from time series to complex networks. In particular, we construct directed weighted complex networks (DWCN) from time series and then associate different aspects of chaotic dynamics with the topological indices of the DWCN and further demonstrate that the DWCN can be exploited to detect unstable periodic orbits of low periods. Examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach. We construct and analyze numbers of DWCNs for different gas–liquid flow patterns and find that our approach can quantitatively distinguish different experimental gas–liquid flow patterns. Furthermore, the DWCN analysis indicates that slug flow shows obvious chaotic behavior and its unstable periodic orbits reflect the intermittent quasi-periodic oscillation behavior between liquid slug and large gas slug. These interesting and significant findings suggest that the directed weighted complex network can potentially be a powerful tool for uncovering the underlying dynamics leading to the formation of the gas–liquid slug flow.     

Interaction between phases in the liquid–gas system

This work analyzes the equilibrium between a liquid and a gas over this liquid separated by an interface. Various gas forms exist inside the liquid: dissolved gas molecules attached to solvent molecules, free gas molecules, and gaseous bubbles. Thermodynamic equilibrium is maintained between two phases; the first phase is the liquid containing dissolved and free molecules, and the second phase is the gas over the liquid and bubbles inside it. Kinetics of gas transition between the internal and external gas proceeds through bubbles and includes the processes of bubbles floating up and bubble growth as a result of association due to the Smoluchowski mechanism. Evolution of a gas in the liquid is considered using the example of oxygen in water, and numerical parameters of this system are given. In the regime under consideration for an oxygen–water system, transport of oxygen into the surrounding air proceeds through micron-size bubbles with lifetimes of hours. This regime is realized if the total number of oxygen molecules in water is small compared with the numbers of solvated and free molecules in the liquid.     

Analysis of the interface configuration and flow characteristics in tanks in a multiphase liquid–gas system using numerical simulation

A multiphase study was conducted using a turbulence model of large eddy simulation to investigate the interaction between the gaseous phase and the interface and its respective behaviour until the liquid phase movement was established, first in the near interface, as well as the presence of turbulent structures in the study of transport between phases. The results are shown for three surface configurations: a surface with waves in which the Reynolds number and friction velocity of the gaseous phase are, respectively, 210 and 0.25 m/s; a surface with small undulations, 86 and 0.10 m/s; and a flat surface, 43 and 0.05 m/s. Coherent structures are detected on both sides of the interface; these are intensified and less elongated for larger Reynolds numbers. Additionally, the interface exhibits distinct behaviour with regard to the examined phases. For the gaseous phase, it behaves like a no-slip surface.     

Effect of tilted electrostatic field on the Kelvin–Helmholtz instability in a liquid dielectric and gas flow

The effect of surface ponderomotive forces on the Kelvin–Helmholtz instability is studied in the linear formulation based on the equations and boundary conditions of the electrostatics and fluid dynamics of an ideal incompressible fluid. Conditions to be satisfied by the values of determining parameters of the problem for the transition of an unstable flow in zero electric field into a stable regime after the application of a horizontal electric field have been written in the form of inequalities. It has been shown that, at the stability bound, the wavelength of the most instable mode is independent of the ponderomotive forces. In case of a liquid with large permittivity a stable flow regime exists for which the stability condition only differs in small dimensionless values from the stability condition for the charged surface of a quiescent liquid conductor in contact with a gas at rest.     

Modeling the liquid–gas interface using self-assembled monolayers

Stochastic classical trajectory simulations were used to study the efficiency of the energy exchange at the gas–liquid interface. Self-assembled monolayers (SAM) of long-chain functionalized molecules were used to mimic the liquid surface. Since the molecules in the monolayers are anchored by only one end, they retain some of the mobility that they have in the liquid but lose all their fluidity. The corrugation of the surface and the stiffness of the interface were tuned by varying the length of the molecules in the monolayers. The use of longer molecules leads to increased corrugation of the surface and provides additional dissipation channels that promote more efficient momentum and energy accommodation, increase the translational–rotational energy interconversion and enhance trapping. However, this “length effect” appears to saturate, as no further significant changes are observed in those properties when the monolayer's molecules's length is elongated from six to nine carbons. This saturation effect suggests that, even though monolayers can provide some of the mobility observed in liquid surfaces, they lack the energy dissipation channel provided by the fluidity of the liquid.     

Pressure–velocity coupling allowing acoustic calculation in low Mach number flow

Low Mach number flow computation in co-located grid arrangement requires pressure–velocity coupling in order to prevent the checkerboard phenomenon. Two broad categories of pressure–velocity coupling methods for unsteady flows can be distinguished based on the time-step dependency of the coupling coefficient in the definition of the transporting velocity on a face of a control volume. As an example of the time-step independent category, the AUSM⁺-up scheme is studied. As an example of the second category, Rhie–Chow momentum interpolation methods are studied. Within the momentum interpolation techniques, again two broad categories can be distinguished based on the time-step dependency of the coupling coefficient used for unsteady flow computations, but when a steady state is reached. Variants of Rhie–Chow interpolation methods in each subcategory are studied on critical test cases. The result of the study is that for a good representation of unsteady flows containing acoustic information, the pressure–velocity coupling coefficient must explicitly depend on the time-step, but that the transporting velocity must become independent of the time-step when a steady state is reached.     

The effect of the negative particle velocity in a soliton gas within Korteweg–de Vries-type equations

The effect of changing the direction of motion of a defect (a soliton of small amplitude) in soliton lattices described by the Korteweg–de Vries and modified Korteweg–de Vries integrable equations (KdV and mKdV) was studied. Manifestation of this effect is possible as a result of the negative phase shift of a small soliton at the moment of nonlinear interaction with large solitons, as noted in [1], within the KdV equation. In the recent paper [2], an expression for the mean soliton velocity in a “cold” KdV-soliton gas has been found using kinetic theory, from which this effect also follows, but this fact has not been mentioned. In the present paper, we will show that the criterion of negative velocity is the same for both the KdV and mKdV equations and it can be obtained using simple kinematic considerations without applying kinetic theory. The averaged dynamics of the “smallest” soliton (defect) in a soliton gas consisting of solitons with random amplitudes has been investigated and the average criterion of changing the sign of the velocity has been derived and confirmed by numerical solutions of the KdV and mKdV equations.     

Depth-resolved temperature measurements of water using the?Brillouin lidar technique

Coupling between the atmosphere and the ocean takes place predominantly in the upper ocean mixed layer. Knowledge of the temperature profile in this region is therefore of particular interest. In this paper we report a successful measurement of a temperature distribution in a water tube based on Brillouin scattering with a fiber amplifier as the light source. It represents an important step towards the practical implementation of a lidar system for field use. Such a system could provide cost-effective on-line data over an extended region of the ocean and has potential impact to studies concerning climate, oceanography, weather forecasting and hurricane movements.     

Application of “POLIS” PIV system for measurement of velocity fields in a supersonic flow of the wind tunnels

Measurement results on the mean velocity fields and fields of velocity pulsations in the supersonic flows obtained by means of the PIV measurement set “POLIS” are presented. Experiments were carried out in the supersonic blow-down and stationary wind tunnels at the Mach numbers of 4.85 and 6. The method of flow velocity estimate in the test section of the blow-down wind tunnel was grounded by direct measurements of stagnation pressure in the setup settling chamber. The size of tracer particles introduced into the supersonic flow by a mist generator was determined; data on the structure of pulsating velocity in a track of an oblique-cut gas-dynamic whistle were obtained under the conditions of self-oscillations.     

Isotopic effect in the solid–liquid phase diagram of quantum clusters

Applying the Fourier path integral formalism to the isothermal-isobaric ensemble, the solid–liquid transition for 13-atom pure Lennard–Jones clusters was characterized. The masses of the clusters were taken as the masses of hydrogen, deuterium and tritium, hence isotopic effects of quantum clusters were considered. The parallel tempering Monte Carlo algorithm was used to solve all multidimensional integral in the FPI method. The volume of the system was defined with respect to the centroids of the quantum particles and a variable constraining potential was used to restrict undesirable thermodynamic events. The maximum value of the constant pressure heat capacity at a given temperature was used to identify the melting temperature. Pressure versus temperature phase diagrams were constructed for these systems with and without the inclusion of quantum effects. A significant difference in the melting temperature was encountered for the different isotopes due to quantum contribution.     

Simultaneous refractive index and temperature measurements by using dual interference in an all-fiber Mach–Zehnder interferometer

A Fourier analysis applied to the Mach–Zehnder interferometer(MZI) transmission spectrum for simultaneous refractive index(RI) and temperature measurements is proposed and experimentally demonstrated in this Letter. In the fast Fourier transform(FFT) spectrum of the MZI transmission spectrum, several frequency components are generally observed, which means that the transmission spectrum of the MZI is formed by the superposition of some dual-mode interference(DMI) spectra, and each frequency component represents different core-cladding interferences. We can select some dominant frequency components in the FFT spectrum of the MZI transmission spectrum to take the inverse FFT(IFFT). Then, the corresponding DMI patterns can be obtained. Due to the shift of the wavelength of these DMI spectra with changes in the environmental parameters,we can use the coefficient matrix of these DMI spectra for multi-parameter sensing. In this Letter, two DMI patterns are separated from the resultant transmission spectrum of the MZI. As the RI and temperature change,the shifts of the two DMI patterns with respect to the RI and temperature will be observed. The sensitivities of the RI and temperature are-137.1806 nm∕RIU(RI unit) and 0.0860 nm∕°C, and-22.9955 nm∕RIU and0.0610 nm∕°C for the two DMIs. Accordingly, it can be used to simultaneously measure RI and temperature changes. The approach can eliminate the influence of multiple interferences and improve the accuracy of the sensor.     

On the effect of backscattering of γ quanta and statistics in positron-annihilation lifetime measurements

The contribution of backscattered, 1.27-MeV quanta to the coincidence counts in positron-annihilation lifetime measurements has been investigated. Depending on the energy window settings and geometry, as much as 20% of the coincidence counts was found to arise from backscattered events. Computer analysis of such spectra leads to erroneous results. Analysis of computer-generated lifetime spectra shows that good statistics is more important than good resolution power for the quality of the analysis.On leave of absence at Danfoss, DK-6430 Nordborg, Denmark     

Theoretical study of thermal diffusivity of superlattices in measurements using “mirage” technique

A complete theoretical treatment for the determination of thermal diffusivity of superlattices by the mirage technique has been performed. An effective medium approximation model of the thermal conductivity and thermal diffusivity of both sublayers is presented, which is different from the simple models with the thermal diffusivity or thermal conductivity in series or parallel. The numerical calculation of the transverse component of the probe beam deflection in the mirage effect shows that the results obtained from the complete thermal-wave theory and the medium approximation model, for the optically and thermally thick superlattices, are in good agreement with each other. However, the further study on the thermally thin superlattices shows that either the series or the parallel model of the thermal conductivity should be chosen according to whether the thermal impedance of the superlattice is larger or less than that of substrate, respectively.     

Flame front tracking in turbulent lean premixed flames using?stereo PIV and time-sequenced planar LIF of OH

This paper describes the simultaneous application of time-sequenced laser-induced fluorescence imaging of OH radicals and stereoscopic particle image velocimetry for measurements of the flame front dynamics in lean and premixed LP turbulent flames. The studied flames could be acoustically driven, to simulate phenomena important in LP combustion technologies. In combination with novel image post processing techniques we show how the data obtained can be used to track the flame front contour in a plane defined by the illuminating laser sheets. We consider effects of chemistry and convective fluid motion on the dynamics of the observed displacements and analyse the influence of turbulence and acoustic forcing on the observed contour velocity, a quantity we term as s _d ^2D. We show that this quantity is a valuable and sensitive indicator of flame turbulence interactions, as (a) it is measurable with existing experimental methodologies, and (b) because computational data, e.g. from large eddy simulations, can be post processed in an identical fashion. s _d ^2D is related (to a two-dimensional projection) of the three-dimensional flame displacement speed s _d , but artifacts due to out of plane convective motion of the flame surface and the uncertainty in the angle of the flame surface normal have to be carefully considered. Monte Carlo simulations were performed to estimate such effects for several distributions of flame front angle distributions, and it is shown conclusively that s _d ^2D is a sensitive indicator of a quantity related to s _d in the flames we study. s _d ^2D was shown to increase linearly both with turbulent intensity and with the amplitude of acousting forcing for the range of conditions studied.     

Determination of the low ω cusp in the velocity autocorrelation spectrum of liquid sodium

Recently performed high resolution incoherent neutron scattering experiments on liquid sodium at smallA and low make the precise evaluation of the frequency distribution of the liquid feasible. An appropriate extension of the well known Egelstaff formula for the evaluation of the frequency distribution in a liquid is deduced. The new analysis is shown to be exact in the smallQ low region, removing the singularity of the above formula at 0 andQ0. The easy applicability of the evaluation is demonstrated on neutron scattering data of liquid sodium, where the long discussed low frequency cusp ofz() could be revealed.     

Laminar-turbulent transition in Hagen–Poiseuille flow of a real gas

The effect of gas non-ideality on the laminar-turbulent transition is studied experimentally as the flow in a long circular tube at room temperature. The gases SF₆ and Ar, differing significantly in the value of the second virial coefficient, were chosen for this study. Experiments were carried out by varying the pressure at the tube inlet (the maximum pressure of 10⁵ Pa) and at the tube outlet up to the chock flow (formation of a supersonic flow at the outlet). The difference between the critical Reynolds numbers in the flow of SF₆ and Ar was found. The largest difference was observed for the maximum pressures; with a decrease in pressure, the critical Reynolds numbers become closer. The conclusion is an effect of the non-ideal character of gas exists on the laminar-turbulent transition in Hagen–Poiseuille flow. Some experiments were suggested to confirm this conclusion.     

Solutions of time-fractional Kudryashov–Sinelshchikov equation arising in the pressure waves in the liquid with gas bubbles

In this paper, analytical approximate solutions for time-fractional Kudryashov–Sinelshchikov equation have been obtained. Two different techniques have been implemented to calculate the solutions, namely, homotopy analysis method and residual power series method. The approximate solutions are represented numerically and graphically for different values of fractional order of derivative. The numerical results are expressed in Tables 1, 2, 3 and 4 which show that the approximate solutions are in good agreement with the exact solution. The comparative study of the numerical results reveal that both methods are reliable and effective tools for the solution of time-fractional Kudryashov–Sinelshchikov equation.