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This report summarizes the research work conducted during the period funded by the AFOSR grant. The PI has conducted a series of research projects on (a). development of hydrodynamic theories for inhomogeneous nematic liquid crystal polymers, cholesteric liquid crystals, blends of liquid crystal polymers and flexible polymer solutions or melts, biaxial liquid crystal polymers or suspension flows of biaxial nano-particles; (b). studies of nematodynamics as well as morphology of inhomogeneous nematic liquid crystal flows as well as relevant temporal chaotic and spatial chaotic behavior in the fascinating high performance material; (c). development of an effective theory to characterize the effective material properties for the nano-suspension and/or liquid crystal polymer; (d). studies of coupled flow and magnetic and electric field assisted processing for liquid crystal polymers as well as suspension flows. These subprojects have revealed a great deal of the flow-orientation couple dynamic in the flowing materials leading to some potential applications in the military and industries.

Understanding the dynamics of flows, mixing and turbulence in estuaries with large tidal range and complex bathymetry. This includes making the connections between Lagrangian and Eulerian mean flow quantities as well as the role of fronts in determining overall estuarine structure. Of particular interest are (a) the dynamics of stratified turbulence in flows that are both strongly sheared and strongly stratified and (b) the effects of spatially varying bottom roughness on drag including directional sensitivity of bottom drag. This work is important to modeling flows in complex estuaries found worldwide, e.g. on the Korean peninsula. By understanding the dynamics of these flows, necessarily limited observations can be integrated most effectively with numerical models in order to make predictions of environmental conditions likely to be encountered in naval operations.

Understanding the dynamics of flows, mixing and turbulence in estuaries with large tidal range and complex bathymetry. This includes making the connections between Lagrangian and Eulerian mean flow quantities as well as the role of fronts in determining overall estuarine structure. Of particular interest are (a) the dynamics of stratified turbulence in flows that are both strongly sheared and strongly stratified and (b) the effects of spatially varying bottom roughness on drag including directional sensitivity of bottom drag. This work is important to modeling flows in complex estuaries found worldwide, e.g. on the Korean peninsula. By understanding the dynamics of these flows, necessarily limited observations can be integrated most effectively with numerical models in order to make predictions of environmental conditions likely to be encountered in naval operations.

In hydrodynamical modeling of the ultrarelativistic heavy-ion collisions the freeze-out is typically performed at a constant temperature or density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate. Recently many calculations have been done using event-by-event hydrodynamics where the initial density profile fluctuates from event to event. In these event-by-event calculations the expansion rate fluctuates strongly as well, and thus it is interesting to check how the dynamical freeze-out changes hadron distributions with respect to the constant temperature freeze-out. We present hadron spectra and elliptic flow calculated using (2+1)-dimensional ideal hydrodynamics, and show the differences between constant temperature and dynamical freeze-out criteria. We find that the differences caused by different freeze-out criteria are small in all studied cases.

A new family of simple, analytic solutions of self-similarly expanding fireballs is found for systems with ellipsoidal symmetry and a direction dependent, generalized Hubble flow. Gaussian, shell like or oscillating density profiles emerge for simple choices of an arbitrary scaling function. New, cylindrically or spherically symmetric as well as approximately one dimensional hydrodynamical solutions are obtained for various special choices of the initial conditions.

The method of many-particle quantum hydrodynamics has been recently developed, particularly this method has been used for an electrically polarized Bose-Einstein condensate. In this paper, we present the development of this method for an electrically polarized three dimensional Fermi gas. We derive corresponding dynamical equations: equation polarization and equation of polarization current evolution as well as the Euler and continuity equations. We study dispersion dependencies of collective excitations in a polarized Fermi gas and consider interference of an equilibrium polarization on dispersion properties.

Effect of flow confinement on the hydrodynamics of circular impinging jets: Implications for erosion assessment (2014). This paper is a copy of ahead of print. The final and original copy is available at: http://link.springer.com/article/10.1007/s10652-014-9354-3

We use hydrodynamic simulations to provide quantitative estimates of the effects of the impact of the accretion stream on disks in interacting binaries. For low accretion rates, efficient radiative cooling of the hotspot region can occur, and the primary consequence of the stream impact is stream overflow toward smaller disk radii. The stream is well described by a ballistic trajectory, but larger masses of gas are swept up and overflow at smaller, but still highly supersonic, velocities. If cooling is inefficient, overflow still occurs, but there is no coherent stream inward of the disk rim. Qualitatively, the resulting structure appears as a bulge extending downstream along the disk rim. We calculate the mass fraction and velocity of the overflowing component as a function of the important system parameters, and discuss the implications of the results for X-ray observations and doppler tomography of cataclysmic variables, low-mass X-ray binaries and supersoft X-ray sources.

This paper investigates different Poisson structures that have been proposed to give a Hamiltonian formulation to evolution equations issued from fluid mechanics. Our aim is to explore the main brackets which have been proposed and to discuss the difficulties which arise when one tries to give a rigorous meaning to these brackets. Our main interest is in the definition of a valid and usable bracket to study rotational fluid flows with a free boundary. We discuss some results which have emerged in the literature to solve some of the difficulties that arise. It appears to the author that the main problems are still open.

The expansion of the strongly interacting quark gluon plasma (sQGP) created in Au+Au collisions at RHIC can be described by hydrodynamical models. Hadrons are created after a freeze-out, thus their distribution describes the final state of the evolution. The earlier stages can be analyzed via penetrating probes like photon observables. These were measured in 2010 and 2011 by the PHENIX experiment. Here we analyze an analytic, 1+3 dimensional perfect relativistic hydrodynamic solution and calculate hadron and photon observables, such as transverse momentum spectra, elliptic flow and correlation (HBT) radii. We find that our model is not incompatible with the data, not even with the direct photon elliptic flow. From fitting the data, we find that early temperatures of the sQGP were well above the quark-hadron transition temperature, in the hottest point, the center of the fireball the temperature may have reached 507+-12 MeV. The equation of state of this quark matter can be described by an average sound speed of 0.36+-0.02. We also predict a photon source that is significantly larger in the out direction than in the side direction.

One of the largest sources of uncertainty in the computation of globular cluster isochrones and hence in the age determination of globular clusters is the lack of a rigorous description of convection. Therefore, we calibrated the superadiabatic temperature gradient in the envelope of metal-poor low-mass stars according to the results from a new grid of 2D hydrodynamical models, which cover the Main Sequence and the lower Red Giant Branch of globular cluster stars. In practice, we still use for computing the evolutionary stellar models the traditional mixing length formalism, but we fix the mixing length parameter in order to reproduce the run of the entropy of the deeper adiabatic region of the stellar envelopes with effective temperature and gravity as obtained from the hydro-models. The detailed behaviour of the calibrated mixing length depends in a non-trivial way on the effective temperature, gravity and metallicity of the star. Nevertheless, the resulting isochrones for the relevant age range of galactic globular clusters have only small differences with respect to isochrones computed adopting a constant solar calibrated value of the mixing length. Accordingly, the age of globular clusters is reduced by 0.2 Gyr at most.

The artificial viscosity is reconsidered in smoothed particle hydrodynamics to prevent inter-particle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan's standard artificial viscosity are considered as time variable, and a restriction on them is proposed such that avoiding the undesired effects in the subsonic regions. The shock formation in adiabatic and isothermal cases are used to study the ability of this modified artificial viscosity recipe. The computer experiments show that the proposal appears to work and the accuracy of this restriction is acceptable.

The artificial viscosity is reconsidered in smoothed particle hydrodynamics to prevent inter-particle penetration, unwanted heating, and unphysical solutions. The coefficients in the Monaghan's standard artificial viscosity are considered as time variable, and a restriction on them is proposed such that avoiding the undesired effects in the subsonic regions. The shock formation in adiabatic and isothermal cases are used to study the ability of this modified artificial viscosity recipe. The computer experiments show that the proposal appears to work and the accuracy of this restriction is acceptable.

The velocities of the same fluid particle observed in two different reference systems are two different quantities and they are not equal when the two reference systems have translational and rotational movements relative to each other. Thus, the velocity is variant. But, we prove that the divergences of the two different velocities are always equal, which implies that the divergence of velocity is invariant. Additionally, the strain rate tensor and the gradient of temperature are invariant but, the vorticity and gradient of velocity are variant. Only the invariant quantities are employed to construct the constitutive equations used to calculate the stress tensor and heat flux density, which are objective quantities and thus independent of the reference system. Consequently, the forms of constitutive equations keep unchanged when the corresponding governing equations are transformed between different reference systems. Additionally, we prove that the stress is a second-order tensor since its components in different reference systems satisfy the transformation relationship.

Subhalo abundance matching (SHAM) is a technique for populating simulated dark matter distributions with galaxies, assuming a monotonic relation between a galaxy's stellar mass or luminosity and the mass of its parent dark matter halo or subhalo. We examine the accuracy of SHAM in two cosmological SPH simulations, one of which includes momentum-driven winds. The SPH simulations indeed show a nearly monotonic relation between stellar mass and halo mass provided that, for satellite galaxies, we use the mass of the subhalo at the epoch when it became a satellite. In each simulation, the median relation for central and satellite galaxies is nearly identical, though a somewhat larger fraction of satellites are outliers. SHAM-assigned masses (at z=0-2), luminosities (R-band at z=0), or star formation rates (at z=2) have a 68% scatter of 0.09-0.15 dex relative to the true simulation values. When we apply SHAM to the subhalo population of collisionless N-body simulation with the same initial conditions as the SPH runs, we find generally good agreement for the halo occupation distributions and halo radial profiles of galaxy samples defined by thresholds in stellar mass. However, because a small fraction of SPH galaxies suffer severe stellar mass loss after becoming satellites, SHAM slightly overpopulates high mass halos; this effect is more significant for the wind simulation, which produces galaxies that are less massive and more fragile. SHAM recovers the two-point correlation function of the SPH galaxies in the no-wind simulation to better than 10% at scales 0.1 < r < 10 Mpc/h. For the wind simulation, agreement is better than 15% at r > 2 Mpc/h, but overpopulation of massive halos increases the correlation function by a factor of ~2.5 on small scales.

Firstly, we give a historical overview of attempts to incorporate magnetic fields into the Smoothed Particle Hydrodynamics method by solving the equations of Magnetohydrodynamics (MHD), leading an honest assessment of the current state-of-the-art in terms of the limitations to performing realistic calculations of the star formation process. Secondly, we discuss the results of a recent comparison we have performed on simulations of driven, supersonic turbulence with SPH and Eulerian techniques. Finally we present some new results on the relationship between the density variance and the Mach number in supersonic turbulent flows, finding sigma^2_{ln rho} = ln (1 + b^2 M^2) with b=0.33 up to Mach~20, consistent with other numerical results at lower Mach number (Lemaster and Stone 2008) but inconsistent with observational constraints on sigma_rho and M in Taurus and IC5146.

We obtain the constitutive relations for the stress tensor and gauge current in $(1+1)$ dimensional hydrodynamics in the presence of both gauge and gravitational (conformal as well as diffeomorphism) anomalies. The relations between response parameters and anomaly coefficients are also found. The role of the Israel-Hartle-Hawking vacuum is emphasized. Finally, in the absence of gauge fields, earlier results obtained by a hydrodynamic expansion are reproduced.

A new class of accelerating, exact and explicit solutions of relativistic hydrodynamics is found - more than 50 years after the previous similar result, the Landau-Khalatnikov solution. Surprisingly, the new solutions have a simple form, that generalizes the renowned, but accelerationless, Hwa-Bjorken solution. These new solutions take into account the work done by the fluid elements on each other, and work not only in one temporal and one spatial dimensions, but also in arbitrary number of spatial dimensions. They are applied here for an advanced estimation of initial energy density and life-time of the reaction in ultra-relativistic heavy ion collisions.

I review the AdS/hydrodynamics correspondence, which provides a 1-1 map between large wavelength features of AdS black branes and conformal fluid flows. In this thesis I consider boundaries between nonrelativistic flows, applying the usual boundary conditions for viscous fluids. I find that a naive application of the correspondence to these boundaries yields a surface layer in the gravity theory whose stress tensor is not equal to that given by the Israel matching conditions. In particular, while neither stress tensor satisfies the null energy condition and both have nonvanishing momentum, only Israel's tensor has stress. The disagreement arises entirely from corrections to the metric due to multiple derivatives of the flow velocity, which violate Israel's finiteness assumption in the thin wall limit.

We investigate asymptotic convergence in the~$\Delta x \!\rightarrow\! 0$ limit as a tool for determining whether numerical computations involving shocks are accurate. We use one-dimensional operator-split finite-difference schemes for hydrodynamics with a von Neumann artificial viscosity. An internal-energy scheme converges to demonstrably wrong solutions. We associate this failure with the presence of discontinuities in the limiting solution. Our extension of the Lax-Wendroff theorem guarantees that certain conservative, operator-split schemes converge to the correct continuum solution. For such a total-energy scheme applied to the formation of a single shock, convergence of a Cauchy error approaches the expected rate slowly. We relate this slowness to the effect of varying diffusion, due to varying linear artificial-viscous length, on small-amplitude waves. In an appendix we discuss the scaling of shock-transition regions with viscous lengths, and exhibit several difficulties for attempts to make extrapolations.

We investigate hydrodynamic noise in a dilute granular gas during the homogeneous cooling state, by means of a proper application of the Direct Simulation Monte Carlo (DSMC) algorithm. The DSMC includes a source of randomization which is not present in Molecular Dynamics (MD) for inelastic hard disks. Notwithstanding this difference, a fair quantitative agreement is found, including a violation of the fluctuation-dissipation relation for the noise amplitude of the same order observed in MD. This study suggests that deterministic collision dynamics is not an essential ingredient to reproduce, up to a good degree of approximation, hydrodynamic fluctuations in dilute granular gases.

We formulate the stochastic differential equations for non-linear hydrodynamic fluctuations. The equations incorporate the random forces through a random stress tensor and random heat flux as in the Landau and Lifshitz theory. However, the equations are non-linear and the random forces are non-Gaussian. We provide explicit expressions for these random quantities in terms of the well-defined increments of the Wienner process.

By combining the jet quenching Monte Carlo JEWEL with a realistic hydrodynamic model for the background we investigate the sensitivity of jet observables to details of the medium model and quantify the influence of the energy and momentum lost by jets on the background evolution. On the level of event averaged source terms the effects are small and are caused mainly by the momentum transfer.

The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and momentum fluxes are calculated to Navier-Stokes order, and the associated transport coefficients are explicitly determined as functions of the coefficient of normal restitution and the velocity parameter involved in the definition of the model. Also an Euler transport term contributing to the energy transport equation is considered. This term arises from the gradient expansion of the rate of change of the temperature due to the inelasticity of collisions, and vanishes for elastic systems. The hydrodynamic equations are particularized for the relevant case of a system in the homogeneous steady state. The relationship with previous works is analyzed.

We analyse the performance of twelve different implementations of Smoothed Particle Hydrodynamics (SPH) using seven tests designed to isolate key hydrodynamic elements of cosmological simulations which are known to cause the SPH algorithm problems. In order, we consider a shock tube, spherical adiabatic collapse, cooling flow model, drag, a cosmological simulation, rotating cloud-collapse and disc stability. In the implementations special attention is given to the way in which force symmetry is enforced in the equations of motion. We study in detail how the hydrodynamics are affected by different implementations of the artificial viscosity including those with a shear-correction modification. We present an improved first-order smoothing-length update algorithm that is designed to remove instabilities that are present in the Hernquist and Katz (1989) algorithm. For all tests we find that the artificial viscosity is the most important factor distinguishing the results from the various implementations. The second most important factor is the way force symmetry is achieved in the equation of motion. Most results favour a kernel symmetrization approach. The exact method by which SPH pressure forces are included has comparatively little effect on the results. Combining the equation of motion presented in Thomas and Couchman (1992) with a modification of the Monaghan and Gingold (1983) artificial viscosity leads to an SPH scheme that is both fast and reliable.

The Smoothed Particle Hydrodynamics (SPH) is a particle-based, Lagrangian method for fluid-flow simulations. In this work, fundamental concepts of this method are first briefly recalled. Then, the ability to accurately model granular materials using an introduced visco-plastic constitutive rheological model is studied. For this purpose sets of numerical calculations (2D and 3D) of the fundamental problem of the collapse of initially vertical cylinders of granular materials are performed. The results of modeling of columns with different aspect ratios and different angles of internal friction are presented. The numerical outcomes are assessed not only with respect to the reference experimental data but also with respect to other numerical methods, namely the Distinct Element Method and the Finite Element Method. In order to improve the numerical efficiency of the method, the Graphics Processing Units implementation is presented and some related issues are discussed. It is believed that this study corresponds to a new application of SPH approaches for simulations of granular media and results reveal the interest of this method to capture fine details of processes of such complex problems as waves-seabed interactions.

Evolution of quark-gluon plasma (QGP) near equilibrium can be described by the second-order relativistic viscous hydrodynamic equations. Consistent and analytically verifiable numerical solutions are critical for phenomenological studies of the collective behavior of QGP in high-energy heavy-ion collisions. A novel analytical solution based on the conformal Gubser flow which is a boost-invariant solution with transverse fluid velocity is presented. Due to the non-linear nature of the equation, the analytical solution is non-perturbative and exhibits features that are rather distinct from solutions to usual linear hydrodynamic equations. It is used to verify with high precision the numerical solution with a newly developed state-of-the-art $(3+1)$-dimensional second-order viscous hydro code (CLVisc). The perfect agreement between the analytical and numerical solutions demonstrates the reliability of the numerical simulations with the second-order viscous corrections. This lays the foundation for future phenomenological studies that allow one to gain access to the second-order transport coefficients.

The paper proposes a second-order accurate direct Eulerian generalized Riemann problem (GRP) scheme for the spherically symmetric general relativistic hydrodynamical (RHD) equations and a second-order accurate discretization for the spherically symmetric Einstein (SSE) equations. The former is directly using the Riemann invariants and the Runkine-Hugoniot jump conditions to analytically resolve the left and right nonlinear waves of the local GRP in the Eulerian formulation together with the local change of the metrics to obtain the limiting values of the time derivatives of the conservative variables along the cell interface and the numerical flux for the GRP scheme. While the latter utilizes the energy-momentum tensor obtained in the GRP solver to evaluate the fluid variables in the SSE equations and keeps the continuity of the metrics at the cell interfaces. Several numerical experiments show that the GRP scheme can achieve second-order accuracy and high resolution, and is effective for spherically symmetric general RHD problems.

We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic energy are conserved quantities. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse grained description (density, momentum and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.

This report describes the testing program conducted to evaluate the impact of enlargement of the Houston-Galveston Navigation Channel on the salinity and hydrodynanuc fields of tidally influenced Galveston Bay. The present channel norninal dimensions are 40 ft deep at mean low water (mlw) and 400 ft wide. The proposed enlargements tested are for a channel 45 ft deep at mlw and 530 ft wide (Phase I) and 50 ft deep and 600 ft wide (Phase II). Current plans do not include the Phase II enlargement. Salinity fields for these channel configurations and the existing channel dimensions are compared. In a separate study the results from these simulations were used to drive an ecosystem model to predict oyster production. Testing conditions included tidal conditions and winds for the year 1984. The freshwater inflows (developed outside this study) were tested for low-, medium-, and high-flow years. Additionally, since water demand in the future is expected to modify freshwater distribution and quantities, future distributions for the test year 1999 (Wallisville Dam in place), 2024. The code used (RMAlO-WES) is a Galerkin-based finite element solution to simulate three-dimensional (3-D) unsteady open-channel flow. The code represents 3-D hydrodynamics using conservation of fluid mass, horizontal momentum, and salinity/temperature transport equations subject to the hydrostatic assumption. (MM)

Spatial and temporal variability of the Black Sea surface circulation with the link to chlorophyll-a concentration and surface winds is investigated using Satellite data from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO), Sea-viewing Wide Field-of-view Sensor (SeaWiFS), and Quick Scatterometer (QuikSCAT) with the Self-Organizing Maps (SOMs). Six spatial patterns with temporal variability were identified for the surface currents Pattern-1 (Sevastopol Cyclonic and Batumi Dipole Eddies, 21%), Pattern-2 (Cyclonic RIM Current and Anti-cyclonic Batumi Eddy, 16%), Pattern-3 (Anti-cyclonic Sevastopol and Batumi Eddies, 17%), Pattern-4 (Cyclonic RIM Current and Cyclonic Batumi Eddy, 21%), Pattern-5 (Anti-cyclonic RIM Current and Batumi Dipole Eddies, 15%), Pattern-6 (Anti-cyclonic RIM Current and Multi Eddies, 10%). It is found the change of the bi-modal characteristics in 2000-2009 with the fall bloom being more significant than the spring bloom. The surface circulation Pattern-4 (cyclonic RIM current and Batumi eddy) is associated with the occurrence of the fall bloom. Evident connection of negative NAO and negative ENSO to the Pattern-4 circulation implies the large-scale atmospheric effect. Possible connection of these patterns to the climatological indices, such as the North Atlantic Oscillation (NAO) and the East Atlantic/West Russian (EAWR), oscillation are also discussed.

In this paper the problem of consistency of smoothed particle hydrodynamics (SPH) is solved. A novel error analysis is developed in $n$-dimensional space using the Poisson summation formula, which enables the treatment of the kernel and particle approximation errors in combined fashion. New consistency integral relations are derived for the particle approximation which correspond to the cosine Fourier transform of the classically known consistency conditions for the kernel approximation. The functional dependence of the error bounds on the SPH interpolation parameters, namely the smoothing length $h$ and the number of particles within the kernel support ${\cal{N}}$ is demonstrated explicitly from which consistency conditions are seen to follow naturally. As ${\cal{N}}\to\infty$, the particle approximation converges to the kernel approximation independently of $h$ provided that the particle mass scales with $h$ as $m\propto h^{\beta}$, with $\beta >n$. This implies that as $h\to 0$, the joint limit $m\to 0$, ${\cal{N}}\to\infty$, and $N\to\infty$ is necessary for complete convergence to the continuum, where $N$ is the total number of particles. The analysis also reveals the presence of a dominant error term of the form $(\ln {\cal{N}})^{n}/{\cal{N}}$, which tends asymptotically to $1/{\cal{N}}$ when ${\cal{N}}\gg 1$, as it has long been conjectured based on the similarity between the SPH and the quasi-Monte Carlo estimates.

The hydrodynamics and intrinsic properties of galactic-scale gaseous outflows generated by violent starbursts are thoroughly discussed, taking into account the hot gas chemical evolution and radiative cooling. It is shown that the metallicity of superbubbles vary with time and can easily exceed the solar value. Galactic superwinds driven by compact and powerful starbursts undergo catastrophic cooling and establish a temperature distribution radically different to that predicted by adiabatic solution. The observational properties of supergalactic winds in X-rays and visible line regimes derived from our calculations are compared with the standard adiabatic model predictions.

Hydrodynamics in a circulating fluidized bed with annular furnace and six parallel cyclones 作者： Shuai Daping 1,2 Wang Xiaofang 1 Lyu Qinggang 1,2 作者单位： 1. Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China 2. University of Chinese Academy of Sciences, Beijing, 100049, China 提交时间： 2017-06-26 摘要: Systematic measurements were conducted on a cold CFB with annular furnace and six parallel cyclones to study gas-solids flow in the annular furnace and flow non-uniformity among six cyclones. The results show that axial solids holdup in the annular furnace decreases exponentially with height, similar to the conventional rectangular furnace. The uniform transverse distribution of solids holdup suggests a good gas-solids mixing in the annular furnace. The annular furnace presents the core/double-annulus flow structure, and it results in enhanced gas-solids back-mixing than the conventional core/annulus flow structure. The gas-solids flow of the inner wall-layer and the outer wall-layer is very close at most part of the furnace height, and the wall-layer thickness decreases with height. Flow non-uniformity exists among six parallel cyclones in the annular furnace CFB. But non-uniform distribution of solids circulating rates and cyclone pressure drops show no regularity, and the flow non-uniformity is no larger than the CFBs with conventional furnace. Under typical operating conditions, the relative deviation of six solids circulating rates is 8.0%. Circulating fluidized bed annular furnace parallel cyclones flow structure flow non-uniformity square cross-section riser profiles Thermodynamics Engineering 期刊： JOURNAL OF THERMAL SCIENCE 分类： 动力与电气工程 &gt;&gt; 工程热物理学 引用： ChinaXiv:201706.00772 (或此版本 ChinaXiv:201706.00772V1 ) DOI:10.1007/s11630-017-0939-2 CSTR:32003.36.ChinaXiv.201706.00772.V1 推荐引用方式： Shuai Daping,Wang Xiaofang,Lyu Qinggang.(2017).Hydrodynamics in a circulating fluidized bed with annular furnace and six parallel cyclones.JOURNAL OF THERMAL SCIENCE .doi:10.1007/s11630-017-0939-2 版本历史 [V1] 2017-06-26 14:32:51 ChinaXiv:201706.00772V1 下载全文

A numerical experiment is described in which an attempt was made to reduce the calculation time for a two-dimensional, Lagrangian, hydrodynamics code, without loss of accuracy. The reduction was accomplished by utilizing a space-dependent time step; i.e., the frequency with which a point is calculated depends on the rate at which changes are occurring in the vicinity of the point. This system permitted savings to be made by eliminating calculations in regions undergoing relatively slow changes.

Via the hydrodynamical formulation of quantum mechanics, an approach to the problem of tunneling through sharp-edged potential barriers is developed. Above all, it is shown how more general boundary conditions follow from the continuity of mass, momentum, and energy.

COMPLETE APPROXIMATION IN EUCLIDEAN SPACE OF NEW BOUNDARY VALUE PROBLEM

The nonextensive one-dimensional version of a hydrodynamical model for multiparticle production processes is proposed and discussed. It is based on nonextensive statistics assumed in the form proposed by Tsallis and characterized by a nonextensivity parameter $q$. In this formulation the parameter $q$ characterizes some specific form of local equilibrium which is characteristic for the nonextensive thermodynamics and which replaces the usual local thermal equilibrium assumption of the usual hydrodynamical models. We argue that there is correspondence between the perfect nonextensive hydrodynamics and the usual dissipative hydrodynamics. It leads to simple expression for dissipative entropy current and allows for predictions for the ratio of bulk and shear viscosities to entropy density, $\zeta/s$ and $\eta/s$, to be made.

We present here a classical hydrodynamic model of a two-dimensional fluid which has many properties of Fractional Quantum Hall effect. This model incorporates the FQHE relation between the vorticity and density of the fluid and exhibits the Hall viscosity and Hall conductivity found in FQHE liquids. We describe the relation of the model to the Chern-Simons-Ginzburg-Landau theory of FQHE and show how Laughlin's wave function is annihilated by the quantum velocity operator.

Dissipative Particle Dynamics (DPD) is becoming a popular particle based method to study flow through microchannels due to the ease with which the presence of biological cells or DNA chains can be modeled. Many Lab-On-Chip (LOC) devices require the ability to manipulate the transport of cells or DNA chains in the fluid flow. Microchannel surfaces coated with combinations of hydrophilic and hydrophobic materials have been found useful for this purpose. In this work, we have numerically studied the hydrodynamics of a steady nonuniform developing flow between two infinite parallel plates with hydrophilic and hydrophobic surfaces using DPD for the first time. The hydrophobic and hydrophilic surfaces were modeled using partial-slip and no-slip boundary conditions respectively in the simulations. We also propose a new method to model the inflow and outflow boundaries for the DPD simulations. The simulation results of the developing flow match analytical solutions from continuum theory for no-slip and partial-slip surfaces to good accord. The entrance region constitutes a considerable fraction of the channel length in miniaturized devices. Thus it is desirable for the length of the developing region to be short as most microfluidic devices such as cell or DNA separators and mixers are designed for the developed flow field. We studied the effect of a hydrophilic strip near the inlet of a microchannel on the effective developing length. We find that the presence of the hydrophobic strip significantly reduces the developing length.

Dissipative Particle Dynamics (DPD) is becoming a popular particle based method to study flow through microchannels due to the ease with which the presence of biological cells or DNA chains can be modeled. Many Lab-On-Chip (LOC) devices require the ability to manipulate the transport of cells or DNA chains in the fluid flow. Microchannel surfaces coated with combinations of hydrophilic and hydrophobic materials have been found useful for this purpose. In this work, we have numerically studied the hydrodynamics of a steady nonuniform developing flow between two infinite parallel plates with hydrophilic and hydrophobic surfaces using DPD for the first time. The hydrophobic and hydrophilic surfaces were modeled using partial-slip and no-slip boundary conditions respectively in the simulations. We also propose a new method to model the inflow and outflow boundaries for the DPD simulations. The simulation results of the developing flow match analytical solutions from continuum theory for no-slip and partial-slip surfaces to good accord. The entrance region constitutes a considerable fraction of the channel length in miniaturized devices. Thus it is desirable for the length of the developing region to be short as most microfluidic devices such as cell or DNA separators and mixers are designed for the developed flow field. We studied the effect of a hydrophilic strip near the inlet of a microchannel on the effective developing length. We find that the presence of the hydrophobic strip significantly reduces the developing length.

A formulation of the governing partial differential equations for fluid flow and reacting chemical species in a tubular combustor is presented. A numerical procedure for the solution of the governing differential equations is described, and models for chemical equilibrium and chemical kinetics calculations are presented. The chemical equilibrium model is used to characterize the hydrocarbon reactions. The chemical kinetics model is used to predict the concentrations of the oxides of nitrogen. The combustor consists of a cylindrical duct of varying cross sections with concentric streams of gaseous fuel and air entering the duct at one end. Four sample cases with specified inlet and boundary conditions are considered, and the results are discussed

We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.

We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.

We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.

We derive system of equations describing fluidity of the medium consisting of non-relativistic particles with finite mass-widths. For that we use expressions for the kinetic Noether 4-current and the Noether energy-momentum tensor being conserved provided one uses self-consistent approximations to the gradient expanded Kadanoff-Baym equations. Kinetic coefficients entering equations of non-ideal hydrodynamics of resonances are obtained in terms of the real and imaginary parts of the self-energies within a relaxation time approximation.

Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic flow of $\Lambda$, $\Xi$, and $\Omega$ in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV. Comparing our model results with the data measurements, we find that the VISHNU model gives general descriptions of the measurements of these strange and multi-strange hadrons at several centrality classes at RHIC and LHC. Mass ordering of elliptic flow $v_{2}$ among $\pi$, $K$, $p$, $\Lambda$, $\Xi$, and $\Omega$ are further investigated and discussed at the two collision systems. We find, at both RHIC and LHC, the $v_{2}$ mass ordering among $\pi$, $K$, $p$, and $\Omega$ are fairly reproduced within the VISHNU hybrid model, and more improvements are needed to implement for well describing the $v_{2}$ mass ordering among $p$, $\Lambda$, and $\Xi$.

Recent years have seen the development of a rich phenomenology beyond the Luttinger Liquid model of one dimensional quantum fluids, arising from interactions between the elementary phonon excitations. It has been known for some time, however, that the straightforward inclusion of these interactions presents technical difficulties that have necessitated approaches based on refermionization or effective impurity models. In this work we show that the nonlinear extensions of the Luttinger model are tractable in the phonon basis. We present a calculation of the singularities present in the zero temperature dynamical structure factor in the semiclassical limit where the phonon dispersion is strong. A unitary transformation decouples interactions between left-- and right--moving phonons, leaving a nonlinear chiral Hamiltonian. At low momenta, this Hamiltonian has a spectrum bounded above and below by thresholds identified with phonon and soliton excitations in the semiclassical limit. The chiral dynamical structure factor therefore has support only in this region, with power law singularities at the thresholds originating in the Anderson orthogonality catastrophe, which we calculate analytically. The dynamical structure factor for the original nonchiral Hamiltonian is a convolution of this chiral correlator with a power law arising from the left--right decoupling.

Compelling evidence associates the nuclei of active galaxies and massive starbursts. The symbiosis between a compact nuclear starburst stellar cluster and a massive black hole can self-consistently explain the properties of active nuclei. The young stellar cluster has a profound effect on the most important observable properties of active galaxies through its gravity, and by mass injection through stellar winds, supernovae and stellar collisions. Mass injection generates a nuclear ISM which flows under gravitational and radiative forces until it leaves the nucleus or is accreted onto the black hole or accretion disc. The radiative force exerted by the black hole--accretion disc radiation field is not spherically symmetric. This results in complex flows in which regions of inflow can coexist with high Mach number outflowing winds and hydrodynamic jets. We present two-dimensional hydrodynamic models of such nISM flows, which are highly complex and time variable. Shocked shells, jets and explosive bubbles are produced, with bipolar winds driving out from the nucleus. Our results graphically illustrate why broad emission line studies have consistently failed to identify any simple, global flow geometry. The real structure of the flows is _inevitably_ yet more complex.

We calculate the squeezed back-to-back correlation (BBC) functions of $\phi \phi$ and $K^+K^-$ for heavy-ion collisions at RHIC and LHC energies, using ($2+1$)-dimensional hydrodynamics with fluctuating initial conditions. The BBC functions averaged over event-by-event calculations for many events for the hydrodynamic sources are smoothed as a function of the particle momentum. For heavy-ion collisions of Au+Au at $\sqrt{s_{NN}}=200$ GeV, the BBC functions are larger than those for collisions of Pb+Pb at $\sqrt{s_{NN}}=2.76$ TeV. The BBC of $\phi\phi$ may possibly be observed in peripheral collisions at the RHIC and LHC energies. It is large for the smaller sources of Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV.