On the interaction between bubbles and the free surface with high density ratio 3D lattice Boltzmann method

The bubbles rise up and burst at the free surface is a complex two-phase process.A free energy lattice Boltzmann method(LBM)model is adopted in this paper to study this phenomenon.The interface capturing technique[Zheng et al.,2006]is used to deal with the high density ratio problem.The Laplace law and the air-water interface capturing ability are validated for the multiphase model.The interaction between the single bubble or multiple bubbles and the free surface are studied by the multiphase model.The force acting on the bubble and the evolution of the free surface is studied.Meanwhile,effect of the initial distance between two adjacent bubbles on interaction effects of multiple bubbles is investigated as well.

A Number Theoretic Analysis of the Enthalpy, Enthalpy Energy Density, Thermodynamic Volume, and the Equation of State of a Modified White Hole, and the Implications to the Quantum Vacuum Spacetime, Matter Creation and the Planck Frequency

In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.

Distributions of crystals and gas bubbles in reservoir ice during growth period

In order to understand the dominant factors of the physical properties of ice in ice thermodynamics and mechanics, in-situ observations of ice growth and decay processes were carried out. Two samplings were conducted in the fast and steady ice growth stages. Ice pieces were used to observe ice crystals and gas bubbles in ice, and to measure the ice density. Vertical profiles of the type and size of ice crystals, shape and size of gas bubbles, and gas bubble content, as well as the ice density, were obtained. The results show that the upper layer of the ice pieces is granular ice and the lower layer is columnar ice; the average crystal size increases with the ice depth and remains steady in the fast and steady ice growth stages; the shape of gas bubbles in the upper layer of ice pieces is spherical with higher total content, and the shape in the middle and lower layers is cylinder with lower total content; the gas bubble size and content vary with the ice growth stage; and the ice density decreases with the increase of the gas bubble content.

ESTIMATION OF THE NUMBER OF CORRELATED SOURCES WITH COMMON FREQUENCIES BASED ON POWER SPECTRAL DENSITY

Blind source separation and estimation of the number of sources usually demand that the number of sensors should be greater than or equal to that of the sources, which, however, is very difficult to satisfy for the complex systems. A new estimating method based on power spectral density （PSD） is presented. When the relation between the number of sensors and that of sources is unknown, the PSD matrix is first obtained by the ratio of PSD of the observation signals, and then the bound of the number of correlated sources with common frequencies can be estimated by comparing every column vector of PSD matrix. The effectiveness of the proposed method is verified by theoretical analysis and experiments, and the influence of noise on the estimation of number of source is simulated.

Influence of Gas Density on Hydrodynamics in a Bubble Column

Two kinds of gases were used to investigate the influence of gas density on the hydrodynamic characteristics in a bubble column. It can be found out that higher gas density leads to smaller bubble diameter and the flow patterns are different for the both gases. Energy balance mechanisms are analyzed by considering the gas density difference. Models were developed to predict the average bubble diameter with good accuracy.

Numerical study on hydrodynamic characteristics of spherical bubble contaminated by surfactants under higher Reynolds numbers

It is of significance to investigate deeply the hydrodynamic featu res of the bubble co ntaminated by impurities in view of the fact that the industrial liquid is difficult to keep absolutely pure.On the basis of the finite volume method,the bubble interface contaminated by the surfactant(1-pentanol)is achieved through solving the concentration transport equations in liquid and along the bubble interface,and solving the absorption and desorption equation at the bubble interface.And the three-dimensional momentum equation is solved at the same time.It is investigated in detail on the influence of interfacial contamination degrees(described with the cap angleθ)on hydrodynamic characteristics of the spherical bubble when the bubble Reynolds number(Re)is larger than 200.Theθis realized by changing the surfactant concentration(C_(0)) in liquid.The present results show that the hydrodynamic characteristics,such as interfacial concentration,interfacial shear stress,interfacial velocity and wake flow,are related to both Re and C_(0) for the contaminated bubble.When C_(0) is relatively low in liquid(i.e.,the contamination degree of the bubble interface is relatively slight),the hydrodynamic characteristics of the bubble can still keep the 2 D features even if Re>200.The decrease ofθor the increase of Re can promote the appearance of the unsteady wake flow.For the present investigation,when Re>200 andθ≤60°,the hydrodynamic characteristics of the bubble show the 3D phenomena,which indicates that axisymmetric model is no longer valid.

Experimental determination of distributions of soot particle diameter and number density by emission and scattering techniques

A diagnostics method was presented that uses emission and scattering techniques to simultaneously determine the distributions of soot particle diameter and number density in hydrocarbon flames. Two manta G-504 C cameras were utilized for the scattering measurement, with consideration of the attenuation effect in the flames according to corresponding absorption coefficients. Distributions of soot particle diameter and number density were simultaneously determined using the measured scattering coefficients and absorption coefficients under multiple wavelengths already measured with a SOC701 V hyper-spectral imaging device, according to the Mie scattering theory. A flame was produced using an axisymmetric laminar diffusion flame burner with 194 mL/min ethylene and 284 L/min air, and distributions of particle diameter and number density for the flame were presented. Consequently, the distributions of soot volume fraction were calculated using these two parameters as well, which were in good agreement with the results calculated according to the Rayleigh approximation,demonstrating that the proposed diagnostic method is capable of simultaneous determination of the distributions of soot particle diameter and number density.

Charged Multiplicity Density and Number of Participant Nucleons in Relativistic Nuclear Collisions

The energy and centrality dependencies of charged particle pseudorapidity density in relativistic nuclear collisions were studied using a hadron and string cascade model, JPCIAE. Both the relativistic experimental data and the PHOBOS and PHENIX Au+Au data at RHIC energy could be fairly reproduced within the framework of JPCIAE model and without retuning the model parameters. The predictions for collisions at the LHC energy were also given. We computed the participant nucleon distributions using different methods. It was found that the number of participant nucleons is not a well defined variable both experimentally and theoretically. Thus it may be inappropriate to use the charged particle pseudorapidity density per participant pair as a function of the number of participant nucleons for distinguishing various theoretical models.

Pipe Flow of Suspensions Containing Bubbles

The steady laminar pipe flow of a suspension with a gas volume fraction ∅≤0.5 and small or intermediate bubble deformations in long, and straight sections of a circular pipe is calculated. The calculations are based on the constitutive equation that was originally derived for dilute emulsions and further developed for concentrated suspensions containing bubbles. In contrast to the literature, an analytical procedure is used to determine the solution of a pipe flow more accurately. The results are presented and discussed with respect to the Reynolds number Re and capillary number Ca. If Ca 1, a bubble suspension has a parabolic velocity profile indicating a Newtonian rheology. If Ca ≈1, two regimes of flow are observed in agreement with the literature;that is, an inner plug flow where deformation rates are low and an outer flow where deformation rates are high. These results imply that, if Ca ∅?and that, if Ca ≥1, the opposite effect occurs;that is, the Reynolds number Re increases with increasing gas volume fraction.

Numerical Simulation of Shock Bubble Interaction with Different Mach Numbers

The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method （PPM）, in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers （Ma）. The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 （2007） 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.

A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System

Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.

Microsegregation and Rayleigh number variation during the solidification of superalloy Inconel 718

The microstructure and composition of the residual liquid at different temperatures were investigated by scanning electron microscopy （SEM） and energy dispersive X-ray spectrometer （EDX） associated with the Thermo-calc software calculation of the equilibrium phase diagrams of Inconel 718 and segregated liquid. The liquid density difference and Rayleigh number variation during solidification were estimated as well. It is found that the heavy segregation of Nb in liquid prompts the precipitation of δ and Laves phase directly from liquid and the resultant quenched liquid microstructure consists of pro-eutectic γ＋eutectic,or complete eutectic according to the content of Nb from low to high. The liquid density increases with decreasing temperature during the solidification of Inconel 718 and the liquid density difference is positive. The largest relative Rayleigh number occurs at 1320°C when the liquid fraction is about 40vol%.

Modeling Density and Anisotropy of Energetic Electrons Along Magnetic Field Lines

The electromagnetic wave growth or damping depends basically on the number density and anisotropy of energetic particles as the resonant interaction takes place between the particles and waves in the magnetosphere. The variance of both the number density and anisotropy along the magnetic field line is evaluated systematically by modeling four typically prescribed distribution functions. It is shown that in the case of ＂the positive anisotropy＂ （namely, the perpendicular temperature T⊥ exceeds the parallel temperature T｜｜）, the number density of energetic electrons always decreases with the magnetic latitude for a regular increasing magnetic field and the maximum wave growth is therefore generally confined to the equator where the resonant energy is minimum, and the number density is the largest. However, the ＂loss-cone＂ anisotropy of the electrons with a ＂pancake＂ distribution or kappa distribution keeps invariant or nearly invariant, whereas the ＂temperature＂ anisotropy with a pure bi-Maxwellian distribution or Ashour-Abdalla and Kennel＇s distributions decreases with the magnetic latitude. The results may provide a useful approach to evaluating the number density and anisotropy of the energetic electrons at latitudes where the observation information is not available.

The effect of multi-orifice plate configuration on bubble detachment volume

The multi-orifice plate gas sparger, mainly composed of a multi-orifice plate and a gas chamber, is one of the most common sparger facilities.The aeration performance of multi-orifice plate has a close relation with the multiorifice plate configuration.In addition, the weeping phenomenon has a considerable influence on the gas chamber condition which affects the bubble detachment volume directly.This paper conducts a set of visual experiments to study the influence of multi-orifice configuration and gas chamber condition on the aeration performance of gas sparger.For multi-orifice plate, an improved theoretical model is proposed which considers the wave effect of the previous bubbles generated from adjacent orifices and the variance of the number of active bubbling orifice.A parameter is proposed to evaluate the aeration performance in order to overcome the difficulty caused by the randomness of bubble formation process.The experimental results suggest that the gas chamber filled with water is in favor of large bubble formation.The influence of the pitch of orifice on aeration performance can only be observed in high-restricted case.According to the theoretical model and experimental results, the influences of gas flow rate and the number of open orifices on the aeration performance are analyzed and a design criterion for the number of open orifice is proposed.

Levy Constrained Search in Fock Space：An Alternative Approach to Noninteger Electron Number

By extending the Levy wavefunction constrained search to Fock Space,one can define a wavefunction constrained search for electron densities in systems having noninteger number of electrons.For pure-state v-representable densities,the results are equivalent to what one would obtain with the zero-temperature grand canonical ensemble.In other cases,the wavefunction constrained search in Fock space presents an upper bound to the grand canonical ensemble functional.One advantage of the Fock-space wavefunction constrained search functional over the zero-temperature grand-canonical ensemble constrained search functional is that certain specific excited states(i.e.,those that are not ground-statev-representable) are the stationary points of the Fock-space functional.However,a potential disadvantage of the Fock-space constrained search functional is that it is not convex.

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.

Study on the Bubble Growth and Departure with A Lattice Boltzmann Method

For the growth and departure of bubbles from an orifice, a free energy lattice Boltzmann model is adopted to deal with this complex multiphase flow phenomenon. A virtual layer is set at the boundary of the flow domain to deal with the no-slip boundary condition. Effects of the viscosity, surface tension, gas inertial force and buoyancy on the characteristics of bubbles when they grow and departure from an orifice in quiescent liquid are studied. The releasing period and departure diameter of the bubble are influenced by the residual gas at the orifice, and the interaction between bubbles is taken into consideration. The relations between the releasing period or departure diameter and the gravity acceleration show fair agreements with previous numerical and theoretical results. And the influence of the gas outflow velocity on bubble formation is discussed as well. For the bubbles growing in cross-flow field, effects of the cross-flow speed and the gas outflow velocity on the bubble formation are discussed, which is related to the application in ship resistance reduction. And optimal choice of the ship speed and gas outflow velocity is studied. Cases in this paper also prove that this high density ratio LBM model has its flexibility and effectiveness on multiphase flow simulations.

Experimental Study of Owl-Like Airfoil Aerodynamics at Low Reynolds Numbers

This study experimentally investigates aerodynamic characteristics and flow fields of a smooth owl-like airfoil without serrations and velvet structures. This biologically inspired airfoil design is intended to serve as the main-wing for low-Reynolds-number aircrafts such as micro air vehicles. Reynolds number dependency on aerodynamics is also evaluated at low Reynolds numbers. The results of the study show that the owl-like airfoil has high lift performance with a nonlinear lift increase due to the presence of a separation bubble on the suction side. A distinctive flow feature of the owl airfoil is a separation bubble on the pressure side at low angles of attack. The separation bubble switches location from the pressure side to the suction side as the angle of attack increases and is continuously present on the surface within a wide range of angles of attack. The Reynolds number dependency on the lift curves is insignificant, although differences in the drag curves are especially pronounced at high angles of attack. Eventually, we obtain the geometric feature of the owl-like airfoil to increase aerodynamic performance at low Reynolds numbers.

Studies of Structural and Thermodynamic Properties for Polychlorinated Thianthrenes by Density Functional Theory

The structural and thermodynamic （PCTAs） in the ideal gas state at 298.15 K and 1.013 properties of 75 polychlorinated thianthrenes ×10^5 Pa have been calculated at the B3LYP/6- 31G＊ level using Gaussian 98 program. Based on the output data of Gaussian, the isodesmic reactions were designed to calculate standard enthalpy of formation （△fH^θ） and standard free energy of formation （△fH^θ） of PCTAs congeners. The relations of these thermodynamic parameters with the number and position of C1 atom substitution （Npcs） were discussed, and it was found that there exists high correlation between thermodynamic parameters （total energy （TE）, zero-point vibrational energy （ZPE）, thermal correction to energy （Eth）, heat capacity at constant volume （Cv^θ）, entropy （S^θ）, enthalpy （H^θ）, free energy （G^θ）, standard enthalpies of formation （△fH^θ） and standard Gibbs energies of formation （△fG^θ）） and Npcs. On the basis of the relative magnitude of their △fG^θ, the order of relative stability of PCTA congeners was theoretically proposed. In addition, the correlations between structural parameters and Npcs were also discussed. The good correlations were found between molecular average polarizability （α）, energy of the highest occupied molecular orbital （EHOMO）, molecular volume （Vm） and Npcs, and all R^2 values are larger than 0.95. Moreover, it was supposed that the isomer groups with higher toxicity should be Tri-CTA and TCTA.