Hydrodynamic Solution Research Articles

Ship underwater noise assessment by the Acoustic Analogy part II: hydroacoustic analysis of a ship scaled model

In this paper the Acoustic Analogy is used to predict the underwater noise from a complete scaled ship model in a steady course. The numerical investigation is performed by coupling an incompressible RANS code, equipped with a level-set approach to account for the fundamental time evolution of the free surface, to a FWH-based hydroacoustic solver, here suitably designed to manage the huge set of data coming from a full-unsteady hydrodynamic simulation. The results reveal the overall limited contribution from the propeller thickness and loading noise components and the fundamental one from the nonlinear quadrupole sources. The comparison between the hydrodynamic and hydroacoustic solutions point out the noticeable scattering effects due to the hull surface, the possible influence of sound refractions at the free surface and, above all, the leading role played by the turbulent fluctuating component of the velocity field. Finally, by computing the pressure time histories at a prescribed set of virtual hydrophones and turning them into the frequency domain, the ship noise footprint in dB is traced out, thus showing how the Acoustic Analogy can be effectively used to analyze the ship hydroacoustic behavior, both in terms of amplitude and directivity.

Supercriticality to subcriticality in dynamo transitions

Evidence from numerical simulations suggests that the nature of dynamo transition changes from supercritical to subcritical as the magnetic Prandtl number is decreased. To explore this interesting crossover, we first use direct numerical simulations to investigate the hysteresis zone of a subcritical Taylor-Green dynamo. We establish that a well defined boundary exists in this hysteresis region which separates dynamo states from the purely hydrodynamic solution. We then propose simple dynamo models which show similar crossover from supercritical to subcritical dynamo transition as a function of the magnetic Prandtl number. Our models show that the change in the nature of dynamo transition is connected to the stabilizing or de-stabilizing influence of governing non-linearities.

Low-dimensional chaos in RR Lyrae models

The recent precise photometric observations and successes of the modelling efforts transformed our picture of the pulsation of RR Lyrae stars. The discovery of additional frequencies and the period doubling phenomenon revealed that a significant interaction may occur between pulsational modes. The signs of irregularities were detected both in observed light curves and hydrodynamic calculations. In this paper we present the analysis of four peculiar hydrodynamic model solutions. All four solutions were found to be chaotic. The fractal (Lyapunov) dimensions of their attractors were calculated to be ~2.2. We also investigated possible resonances between the fundamental mode and the first overtone in the dynamical neighbourhood of these models. The most important is the 6:8 resonance that was also detected in the Kepler observations of RR Lyrae itself. These results reveal that the investigation of chaotic models is important in discovering and understanding resonances in RR Lyrae stars.

Electron-Energy Loss Study of Nonlocal Effects in Connected Plasmonic Nanoprisms

We investigate the emergence of nonlocal effects in plasmonic nanostructures through electron-energy loss spectroscopy. To theoretically describe the spatial dispersion in the metal permittivity, we develop a full three-dimensional nonlocal hydrodynamic solution of Maxwell's equations in frequency domain that implements the electron beam as a line current source. We use our numerical approach to perform an exhaustive analysis of the impact of nonlocality in the plasmonic response of single triangular prisms and connected bowtie dimers. Our results demonstrate the complexity of the interplay between nonlocal and geometric effects taking place in these structures. We show the different sensitivities to both effects of the various plasmonic modes supported by these systems. Finally, we present an experimental electron-energy loss study on gold nanoprisms connected by bridges as narrow as 1.6 nm. The comparison with our theoretical predictions enables us to reveal in a phenomenological fashion the enhancement of absorption damping that occurs in these atomistic junctions due to quantum confinement and grain boundary electron scattering.

Convective Mass Transfer From Submerged Superhydrophobic Surfaces

Longevity of entrapped air is an outstanding problem for using superhydrophobic coatings in submersible applications. Under pressure and flowing water, the air micropockets eventually dissolve into the ambient water or burst and diminish. Herein, we analyze from first principles a simple mass transfer problem. We introduce an effective slip to a Blasius boundary layer, and solve the hydrodynamic equations. A slowly evolving, non-similar solution is found. We then introduce the hydrodynamic solution to the two-dimensional problem of alternating solid-water and air-water interfaces to determine the convective mass transfer of air's dissolution into water. This situation simulates spanwise microridges, which is one of the geometries used for producing superhydrophobic surfaces. The mass-transfer problem has no similarity solution but is solvable using approximate integral methods. A mass-transfer solution is achieved as a function of the surface geometry (or gas area fraction), Reynolds number, and Schmidt n...

Hydrodynamic solutions of the generalized Boltzmann-Enskog equation

The properties of a kinetic equation are considered for systems of particles with a binary interaction containing a “hard core” and a far-range component. The solutions that correspond to periodic small perturbations of the distribution function are investigated.

Prediction of Hydrodynamic and Other Solution Properties of Partially Disordered Proteins with a Simple, Coarse-Grained Model.

The possibility of validating structures of intrinsically disordered proteins against solution properties is a goal that would be most helpful in the understanding of their function. We have devised a scheme for the prediction of solution properties of partially disordered proteins that comprise one or more ordered domains, along with flexible tails or linkers. A very simple, coarse-grained, residue-level model, which is easily parametrized using available structural information, along with previously developed tools for the simulation of solution conformation and dynamics, allows the prediction of properties like sedimentation coefficients, relaxation times, and X-ray or neutron scattering. This is demonstrated for a variety of partially disordered proteins, for which well-characterized solution properties are very accurately evaluated, with predictions falling in most cases within experimental errors.

Underwater Gas Tornado and its Possible Occurrence in Nature

An underwater gas tornado is a hydrodynamic phenomenon inverse to the well-known sucking whirlpool. Because it occurs only under special conditions, it has not received sufficient attention for possible applications and has not been studied theo- retically. After demonstrating a simple experiment, we study the hydrodynamic solutions of the gas flow in the tornado core interacting with the surrounding rotating liquid. The main question we try to answer here is whether this phenomenon can oc- cur under natural conditions. We assume that methane-hydrate deposits in the sea bottom are a mighty underwater gas source. There are a few geological examples of bottom traces that seem quite similar to traces of atmospheric tornadoes. These so- called pockmarks are located over methane-hydrate deposits and are possibly traces of underwater tornados. We suggest an experiment to test this hypothesis.

Exact solutions of relativistic perfect fluid hydrodynamics for a QCD Equation of State

We generalize a previously known class of exact analytic solutions of relativistic perfect fluid hydrodynamics for the first time to arbitrary temperature-dependent Equation of State. We investigate special cases of this class of solutions, in particular, we present hydrodynamical solutions with the Equation of State determined from lattice QCD calculations. We discuss the phenomenological relevance of these solutions as well.

Microhydrodynamics Simulation of Single-collector Granular Filtration

Abstract Granular filtration phenomenon is fundamentally investigated using dissipative hydrodynamics with a large collector grain and a non-Brownian sphere. Effects of interparticle forces balanced with hydrodynamic interactions are studied for particle trajectory analysis. In addition to conventional deposition of fine particles on collector surfaces (mostly near front hemispheres), the hydrodynamic trapping of rotating fine particles on the back hemisphere surface is fundamentally investigated using the exact solution of two-body hydrodynamics.

Fluctuations of current in nonstationary diffusive lattice gases

We employ the macroscopic fluctuation theory to study fluctuations of integrated current in one-dimensional lattice gases with a steplike initial density profile. We analytically determine the variance of the current fluctuations for a class of diffusive processes with a density-independent diffusion coefficient. Our calculations rely on a perturbation theory around the noiseless hydrodynamic solution. We consider both quenched and annealed types of averaging (the initial condition is allowed to fluctuate in the latter situation). The general results for the variance are specialized to a few interesting models including the symmetric exclusion process and the Kipnis-Marchioro-Presutti model [Kipnis, Marchioro, and Presutti, J. Stat. Phys. 27, 65 (1982)]. We also probe large deviations of the current for the symmetric exclusion process. This is done by numerically solving the governing equations of the macroscopic fluctuation theory using an efficient iteration algorithm.

Similarity Solutions for Reactive Shock Hydrodynamics

Similarity Solutions for Reactive Shock Hydrodynamics

Slightly two- or three-dimensional self-similar solutions

Self-similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one-dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find self-similar hydrodynamic solutions that are two- or three-dimensional. Since the deviation from a one-dimensional solution is small, we call these slightly two-dimensional and slightly three-dimensional self-similar solutions, respectively. As an example, we treat strong spherical explosions of the second type. A strong explosion propagates into an ideal gas with negligible temperature and density profile of the form ρ(r, θ, ϕ) = r−ω[1 + σF(θ, ϕ)], where ω > 3 and σ ≪ 1. Analytical solutions are obtained by expanding the arbitrary function F(θ, ϕ) in spherical harmonics. We compare our results with two-dimensional numerical simulations, and find good agreement.

Equation of state and initial temperature of quark gluon plasma at RHIC

Abstract In gold-gold collisions of the Relativistic Heavy Ion Collider a perfect fluid of strongly interacting quark gluon plasma (sQGP) is created. The time evolution of this fluid can be described by hydrodynamical models. After an expansion, hadrons are created during the freeze-out period. Their distribution reveals information about the final state. To investigate the time evolution one needs to analyze penetrating probes: e.g. direct photon observations. In this paper we analyze a 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution, azimuthal asymmetry and momentum correlations of direct photons. Based on earlier fits to hadronic spectra, we compare photon calculations to measurements to determine the equations of state and the initial temperature of sQGP. We find that the initial temperature in the center of the fireball is 507±12 MeV, while for the sound speed we get c s=0.36±0.02. We also estimate a systematic error of these results. We find that the measured azimuthal asymmetry is also compatible with this model. We also predict a photon source that is significantly larger in the out direction than in the side direction.

An asymmetric and slightly dimerized structure for the tetanus toxoid protein used in glycoconjugate vaccines

Tetanus toxoid protein has been characterized with regard oligomeric state and hydrodynamic (low-resolution) shape, important parameters with regard its use in glycoconjugate vaccines. From sedimentation velocity and sedimentation equilibrium analysis in the analytical ultracentrifuge tetanus toxoid protein is shown to be mostly monomeric in solution (∼86%) with approximately 14% dimer. The relative proportions do not appear to change significantly with concentration, suggesting the two components are not in reversible equilibrium. Hydrodynamic solution conformation studies based on high precision viscometry, combined with sedimentation data show the protein to be slightly extended conformation in solution with an aspect ratio ∼3. The asymmetric structure presents a greater surface area for conjugation with polysaccharide than a more globular structure, underpinning its popular choice as a conjugation protein for glycoconjugate vaccines.

Simulation of single mode Rayleigh–Taylor instability by SPH method

A smoothed particle hydrodynamics (SPH) solution to the Rayleigh---Taylor instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with surface tension is presented. The present model is validated by solving Laplace's law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. To further validate the numerical model for the RTI problem, results are quantitatively compared with analytical solutions in a linear regime. It is found that the SPH method slightly overestimates the border of instability. The long time evolution of simulations is presented for investigating changes in the topology of rising bubbles and falling spike in RTI, and the computed Froude numbers are compared with previous works. It is shown that the numerical algorithm used in this work is capable of capturing the interface evolution and growth rate in RTI accurately.

Numerical simulation of mass transport in a filter press type electrochemical reactor FM01-LC: Comparison of predicted and experimental mass transfer coefficient

This paper studies flow characteristics and their effect on local mass transfer rate to a flat plate electrode in a FM01-LC electrochemical reactor. 3D reactor simulations under limiting current and turbulent flow conditions were performed using potassium ferro-ferricyanide electrochemical system with sodium sulfate as supporting electrolyte. The model consists of mass-transport equations coupled to hydrodynamic solution obtained from Reynolds-averaged Navier–Stokes equations using standard k–ɛ turbulence model, where the average velocity field, the turbulence level given by the eddy kinetic energy and the turbulent viscosity of the hydrodynamic calculation were used to evaluate the convection, turbulent diffusion and the concentration wall function. The turbulent mass diffusivity was evaluated by Kays–Crawford equation using heat and mass transfer analogies, while wall functions, for mass transport, were adapted from Launder–Spalding equations. Simulation results describe main flow properties, concentration profiles throughout the entire volume of the reactor and local diffusion flux over the electrode. Overall mass transfer coefficients estimated by simulation, without fitting parameters, agree closely with experimental coefficients determined from limiting current measurements (1.85% average error) for Re between 187 and 1407.

Temporal evolution of tubular initial conditions and their influence on two-particle correlations in relativistic nuclear collisions

Relativistic nuclear collisions data on two-particle correlations exhibit structures as function of relative azimuthal angle and rapidity. A unified description of these near-side and away-side structures is proposed for low to moderate transverse momentum. It is based on the combined effect of tubular initial conditions and hydrodynamical expansion. Contrary to expectations, the hydrodynamics solution shows that the high-energy density tubes (leftover from the initial particle interactions) give rise to particle emission in two directions and this is what leads to the various structures. This description is sensitive to some of the initial tube parameters and may provide a probe of the strong interaction. This explanation is compared with an alternative one where some triangularity in the initial conditions is assumed. A possible experimental test is suggested.

Heat Transfer in a Short Parallel-Plate Channel in the Transition Regime

Heat transfer in a parallel-plate channel with uniform wall heat flux and refrigerated by water is investigated experimentally for the laminar and transition hydrodynamic regimes. The dimensions of the channel were chosen such that entry effects are relevant for a significant part of the channel length. The influence of the following parameters has been studied: inlet Reynolds number, inlet temperature and wall heat flux. Experimental results are compared with predictions based on different empirical correlations for convection in ducts. This analysis shows that the correlation of Gnielinski provides a good agreement with the experimental results for Reynolds numbers between 5,000 and 10,000 at 20°C and under relatively low heat fluxes. Experiments performed at relatively low heat fluxes show that, in the entry region previous to the laminar-turbulent transition, the behavior of the flow is well described by the combined hydrodynamic and thermal entry solution obtained by Hwang and Fan (Finite Difference Analysis of Forced-Convection Heat Transfer in Inlet Region of a Flat Rectangular Duct, Appl. Sci. Res., vol. 13, pp. 401–422, 1964). The hydrodynamic and thermal entry effects for the experimental conditions in the present work are relevant for most of the test section. The location of the transition point is affected in the first instance by the local bulk Reynolds. On the other hand, the wall heat flux affects the fluid properties, i.e., the fluid viscosity, and therefore, it also affects the transition. It was found that for the transition regime, an increase of the wall heat flux produces lower values of the convection coefficient than the values predicted by the correlation of Gnielinski. This behavior, which seems to be associated to the variation of the fluid properties, is opposite to the increase of the convection coefficient observed for heating in the laminar and turbulent regimes for water and oils. The case of an inlet Reynolds number of 5,000 was studied in detail, and the influence of heat flux on the Nusselt number is addressed.

An offline unstructured biogeochemical model (UBM) for complex estuarine and coastal environments

Due to increased pollutant loads and water use from coastal development and population growth, occurrences of low-dissolved oxygen and “hypoxic zones” have increased. Reports of fish kills and water quality impairment are also becoming more frequent in many coastal waters. Water quality managers and regulatory agencies rely on numerical modeling tools to quantify the relative contributions of anthropogenic and “natural” pollutant loads (nutrients and biochemical oxygen demand) on dissolved oxygen levels and use the results for remedial activities and source control. The ability to conduct season-long simulations with sufficient nearshore resolution is therefore a key requirement. Mesh flexibility and the ability to increase site specific resolution without disturbing the larger domain setup and calibration are critical. The objective of this effort was to develop a robust biogeochemical model suitable for simulation of water quality dynamics including dissolved oxygen in complex coastal environments with multiple tidal channels, tidal flats, and density-driven circulation using unstructured-grid formulation. This paper presents an offline unstructured biogeochemical model that uses the Finite Volume Coastal Ocean Model (FVCOM) discretization of the study domain and the corresponding hydrodynamic solution to drive biogeochemical kinetics based on a water quality model CE-QUAL-ICM. In this paper, the linkage between selected hydrodynamic and water quality models is subjected to several scalar transport and biogeochemical module tests (plume transport and dilution, BOD/DO sag, and phytoplankton/nutrients reaction), and results are compared to their analytical solutions as part of model validation. A preliminary application of the biogeochemical model with a year-long simulation of Hood Canal basin in Puget Sound, USA, is presented as an example and a test of the tool in a real estuary setting. The model reproduced the dynamics and seasonal variations in the biogeochemical state variables and was used to test short-term wind-driven dynamics that could influence dissolved oxygen concentrations in Hood Canal.