Hydrodynamic Solution Research Articles

Fouling of reverse osmosis and nanofiltration membranes by humic acid—Effects of solution composition and hydrodynamic conditions

Fouling of reverse osmosis (RO) and nanofiltration (NF) membranes by humic acid, a recalcitrant natural organic matter (NOM), was systematically investigated. The membrane flux performance depended on both hydrodynamic conditions (flux and cross-flow velocity) and solution composition (humic acid concentration, pH, ionic strength, and calcium concentration), and was largely independent of virgin membrane properties. While increasing humic acid concentration and ionic strength, and lowering cross-flow velocity affected flux performance moderately, severe flux reduction occurred at high initial flux, low pH, and high calcium concentration. At a calcium concentration of 1 mM, all the membranes exhibited an identical stable flux, independent of their respective intrinsic membrane permeabilities. The effect of solution composition was more significant at higher fluxes. Improved salt rejection was observed as a result of humic acid fouling, which was likely due to Donnan exclusion by humic material close to membrane surfaces. Greater rejection improvement was observed for membranes with rougher surfaces.

Fast hadron freeze-out generator

We have developed a fast Monte Carlo procedure of hadron generation that allows one to study and analyze various observables for stable hadrons and hadron resonances produced in ultrarelativistic heavy ion collisions. Particle multiplicities are determined based on the concept of chemical freeze-out. Particles can be generated on the chemical or thermal freeze-out hypersurface represented by a parametrization or a numerical solution of relativistic hydrodynamics with given initial conditions and equation of state. Besides standard spacelike sectors associated with the volume decay, the hypersurface may also include nonspacelike sectors related to the emission from the surface of expanding system. For comparison with other models and experimental data, we demonstrate the results based on the standard parametrizations of the hadron freeze-out hypersurface and flow velocity profile under the assumption of a common chemical and thermal freeze-out. The C++ generator code is written under the ROOT framework and is available for public use at http://uhkm.jinr.ru/.

Modelling the global ocean tides: modern insights from FES2004

During the 1990s, a large number of new tidal atlases were developed, primarily to provide accurate tidal corrections for satellite altimetry applications. During this decade, the French tidal group (FTG), led by C. Le Provost, produced a series of finite element solutions (FES) tidal atlases, among which FES2004 is the latest release, computed from the tidal hydrodynamic equations and data assimilation. The aim of this paper is to review the state of the art of tidal modelling and the progress achieved during this past decade. The first sections summarise the general FTG approach to modelling the global tides. In the following sections, we introduce the FES2004 tidal atlas and validate the model against in situ and satellite data. We demonstrate the higher accuracy of the FES2004 release compared to earlier FES tidal atlases, and we recommend its use in tidal applications. The final section focuses on the new dissipation term added to the equations, which aims to account for the conversion of barotropic energy into internal tidal energy. There is a huge improvement in the hydrodynamic tidal solution and energy budget obtained when this term is taken into account.

On the structure of giant HII regions and HII galaxies

AbstractWe review the structural properties of giant extragalactic HII regions and HII galaxies based on two dimensional hydrodynamic calculations, and propose an evolutionary sequence that accounts for their observed detailed structure. The model assumes a massive and young stellar cluster surrounded by a large collection of clouds. These are thus exposed to the most important star-formation feedback mechanisms: photoionization and the cluster wind. The models show how the two feedback mechanisms compete with each other in the disruption of clouds and lead to two different hydrodynamic solutions: The storage of clouds into a long lasting ragged shell that inhibits the expansion of the thermalized wind, and the steady filtering of the shocked wind gas through channels carved within the cloud stratum that results into the creation of large-scale superbubbles. Both solutions are here claimed to be concurrently at work in giant HII regions and HII galaxies, causing their detailed inner structure.

Universal scaling of the rapidity dependent elliptic flow and the perfect fluid at RHIC

The pseudo-rapidity dependence of the elliptic flow at various excitation energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is one of the surprising results that has not been explained before in terms of hydrodynamical models. Here we show that these data are in agreement with theoretical predictions based on perfect fluid hydrodynamics. We also show that these PHOBOS data satisfy the universal scaling relation predicted by the Buda-Lund hydrodynamical model, based on exact solutions of perfect fluid hydrodynamics.

Conjugate heat transfer study of backward-facing step flow – A benchmark problem

The conjugate heat transfer characteristics are studied for backward-facing step flow problem. Alternating direction implicit (ADI) method is used to find the steady state results for hydrodynamic solution using stream function–vorticity formulation. The energy equation in the fluid region and in the solid region are solved simultaneously. The conjugate effects are studied in connection with four parameters viz. Re, Pr, k and b. Effect of four parameters on local Nusselt number, interface temperature and average Nusselt number are presented in detail. The results are compared with non-conjugate case.

Stationary ‘V’ States for Preferred Motions of Many Particles

We use the discrete kinetic theory with the free-orientation parameter being fixed (\(\pi/4\)) to derive the macroscopic velocity field for many particles flowing through a microdomain. Our results resemble qualitatively other hydrodynamical solutions. The V-shaped velocity field changes as the dominant physical parameter (Knudsen number) varies. We also briefly discuss the possible mechanism due to the entropy production along the boundaries.

On the Feedback from Super Stellar Clusters. I. The Structure of Giant HiiRegions and HiiGalaxies

We review the structural properties of giant extragalactic H II regions and H II galaxies based on two-dimensional hydrodynamic calculations and propose an evolutionary sequence that accounts for their observed detailed structure. The model assumes a massive and young stellar cluster surrounded by a large collection of clouds. These are thus exposed to the most important star formation feedback mechanisms: photoionization and the cluster wind. The models show how the two feedback mechanisms compete with each other in the disruption of clouds and lead to two different hydrodynamic solutions: the storage of clouds into a long-lasting ragged shell that inhibits the expansion of the thermalized wind and the steady filtering of the shocked wind gas through channels carved within the cloud stratum. Both solutions are here claimed to be concurrently at work in giant H II regions and H II galaxies, causing their detailed inner structure. This includes multiple large-scale shells, filled with an X-ray-emitting gas, that evolve to finally merge with each other, giving the appearance of shells within shells. The models also show how the inner filamentary structure of the giant superbubbles is largely enhanced with matter ablated from clouds and how cloud ablation proceeds within the original cloud stratum. The calculations point at the initial contrast density between the cloud and the intercloud media as the factor that defines which of the two feedback mechanisms becomes dominant throughout the evolution. Animated versions of the models presented can be found at http://www.iaa.csic.es/~eperez/ssc/ssc.html.

Ellipsoidal Flows in Relativistic Hydrodynamics of Finite Systems

A new class of 3D anisotropic analytic solutions of relativistic hydrodynamics with constant pressure is found. We analyse, in particular, solutions corresponding to ellipsoidally symmetric expansion of finite systems into vacuum. They can be utilized for relativistic description of the system evolution in thermodynamic region near the softest point and at the final stage of the hydrodynamic expansion in A+A collisions. The solutions can be used also for testing of numerical hydrodynamic codes solving relativistic hydrodynamic equations for anisotropic expansion of finite systems

Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.

Spectral magnetohydrodynamic simulations of the sun and stars

The purpose of this lecture is two fold: first, to describe a powerful numerical technic, namely the spectral method, to solve the compressible (anelastic) magnetohydrodynamic (MHD) equations in spherical geometry and then to discuss some recent numerical applications to study stellar dynamics and magnetism. We thus start by describing the semi-implicit, anelastic spherical harmonic (ASH) code. In this code, the main field variables are projected into spherical harmonics for their horizontal dimensions and into Chebyshev polynomials for their radial direction. We then present, high resolution 3–D MHD simulations of the convective region of A- and G-type stars in spherical shells. We have chosen to model A and G-type stars because they represent good proxies to study and understand stellar dynamics and magnetism given their strikingly different internal “up-side-down” structure and magnetic activity level. In particular, we discuss the nonlinear interactions between turbulent convection, rotation and magnetic fields and the possibility for such flows and fields to lead to dynamo action. We find that both core and envelope turbulent convective zones are efficient at inducing strong mostly non-axisymmetric fields near equipartition but at the expense of damping the differential rotation present in the purely hydrodynamic progenitor solutions.

Numerical method application to the analysis of the hydrodynamic torque converter with a smart working fluid

In this paper the use of smart fluids (magneto rheological or electro rheological fluids) as a hydrodynamic torque converter working fluid was considered from the viewpoint of their applications to control the converter. The main part of the paper presents results of numerical analysis of a mathematical model. The essential conclusion that arises from the numerical calculations is that two factors, the working fluid rheology and the hydrodynamic torque converter design solution, influence the hydrodynamic torque converter performance. This implies that the smart fluid properties should be carefully selected for each type of hydrodynamic torque converter dependent on requirements.

Development of the film-splitting look-up table applicable to mechanistic annular film dryout model in annulus geometry

Annular flow in annulus geometry is characterized as two liquid films flowing along the inner heated rod and outer unheated wall. Critical heat flux (CHF) occurs when the liquid film on the inner heated wall dries out, while there still exists the liquid film on the outer cold wall. In the safety analysis code, film dryout is calculated by a mechanistic model or CHF table look-up method. The mechanistic film dryout is a complex function of film flow rate, applied heat flux and entrainment/deposition rate, etc. and is determined by the hydrodynamic solution. However, both models were not able to distinguish the liquid films on the cold surface from that on the hot surfaces in a calculation cell, that is, the cold wall effect. This resulted in over-estimation of the calculated CHF in the single-channel modeling of annulus geometry, so it needs a new model that could consider the cold wall effect mechanistically in the single-channel modeling. In order to consider the cold wall effect, a mechanistic film-splitting model look-up table was developed, in which the inner and outer liquid film fractions are solved analytically. The new look-up table was assessed using Wurtz experimental data and was assessed indirectly using several annulus geometry CHF test data.

Equation of State and Collective Frequencies of a Trapped Fermi Gas Along the BEC-Unitarity Crossover

We show that the study of the collective oscillations in a harmonic trap provides a very sensitive test of the equation of state of a Fermi gas near a Feshbach resonance. Using a scaling approach, whose high accuracy is proven by comparison with exact hydrodynamic solutions, the frequencies of the lowest compressional modes are calculated at T=0 in terms of a dimensionless parameter characterizing the equation of state. The predictions for the collective frequencies, obtained from the equations of state of mean-field BCS theory and of recent Monte Carlo calculations, are discussed in detail.

Interaction parameter (chi); expansion factor (epsilon); steric hindrance factor (sigma); and shielding function F(xi); for the system PEA-organic solvents by intrinsic viscosity measurements

In this work we present experimental data of the Flory binary interaction parameter, chi, of poly (ethylene adipate) PEA, a plasticizer material. We have used the viscometric method for measuring dilute PEA solutions in good solvents: benzene, chloroform and acetone. A procedure based on the Stockmayer-Fixman, (SF), hydrodynamic solutions theory, allows us to evaluate some thermodynamic parameters via the intrinsic viscosity [eta], measured in several good solvents. This method also estimates the unperturbed parameter, ktheta, and the steric hindrance parameter, (sigma), by viscosity measurements at constant temperature of 30ºC. By correlation of the molecular weight (M) and intrinsic viscosity data, according to the Stockmayer-Fixman (SF) solution theory model, values of Flory binary interaction parameter chi, equal to chi1,2 =0.1544 ± 0.01; chi1,2 =0.1631 ± 0.01; and chi1,2 =0.1922 ± 0.01, for PEA in benzene, chloroform and acetone, respectively, were obtained. In addition we applied the Debye-Bueche theory, in order to estimate values of: expansion factor (epsilon), shielding factor (xi) and depth of shielding (L) for the system PEA-organic solvents, by [eta] and (M) experimental data correlation. The results confirm that values obtained, correspond to "good solvents" for the PEA polymer.

On Tzitzéica Vortex Streets and Their Reciprocals in Subsonic Gas Dynamics

Hydrodynamic vortex street solutions are generated based on an elliptic Tzitzéica model. A multiparameter class of reciprocal transformations is coupled with the action of a Bäcklund transformation to construct compressible vortex solutions of breather type valid in subsonic flow régimes of a generalized Kármán–Tsien gas.

Multistability and Memory Effect in a Highly Turbulent Flow: Experimental Evidence for a Global Bifurcation

We report experimental evidence of a global bifurcation on a highly turbulent von Kármán flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic symmetry of the driving apparatus even at very large Reynolds numbers. The global bifurcation between these states is highly subcritical and the system thus keeps a memory of its history. The transition recalls low-dimension dynamical system transitions and exhibits very peculiar statistics. We discuss the role of turbulence in two ways: the multiplicity of hydrodynamical solutions and the effect of fluctuations on the nature of transitions.

Free percolation and seepage flows from watercourses

Free percolation and seepage flows from natural and artificial watercourses with curvilinear profiles are considered. The rigorous hydrodynamic solution of the problem of free percolation and seepage flow from a watercourse is obtained by representing the watercourse profiles in the plane of the Joukowski variable by means of the equation of a family of lemniscates and using the conformal mapping method. The calculated dependences for determining all the necessary parameters of the seepage flows and constructing the curvilinear watercourse profiles are given. In the case of a circular basis for the shape of the watercourse profile in the plane of the Joukowski variable these dependences coincide with the well-known exact dependences.

Toward a description of contact line motion at higher capillary numbers

The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has already been done for a variety of models, but always assuming the limit of vanishing speed. This excludes phenomena of the greatest current interest, in particular the stability of contact lines. Here we extend perturbation theory to arbitrary order and compute finite speed corrections to existing results. We also investigate the impact of different contact line models on the large-scale shape of the interface.

Simple Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Systems

Simple, self-similar, analytic solutions of 1+1-dimensional relativistic hydrodynamics are presented, generalizing Bjorken’s solution to inhomogeneous rapidity distribution.