Hydrodynamic Stage Research Articles

A spectral-domain wave-to-wire model of wave energy converters

Wave-to-Wire models play an important role in the development of wave energy converters. They could provide insight into the complete operating process of wave energy converters, from the power absorption stage to the power conversion stage. In order to cover a set of relevant nonlinear effects, wave-to-wire models are predominately established in the time domain. However, the low computational efficiency of time-domain modeling is hindering the extensive application of wave-to-wire models, especially in early-stage design and optimization where a large number of iterations are required. To address this issue, a spectral-domain wave-to-wire model is proposed, and the nonlinear effects are incorporated by stochastic linearization. This model can significantly reduce the computational load and maintain good accuracy. The reference concept studied in this paper is defined as a heaving point absorber coupled with a linear permanent-magnet generator. Four representative nonlinear effects involved in both the hydrodynamic stage and the electrical stage of the concept are considered. The proposed model is verified against a corresponding nonlinear time-domain wave-to-wire model, and a good agreement is observed. The relative error of the proposed spectral-domain wave-to-wire model is around 2 % in typical operational regions and is still within 7 % for wave states with large significant wave heights, regarding the estimate of the power conversion efficiency. Meanwhile, the computational load of the spectral-domain wave-to-wire model is reduced by 2 to 3 orders of magnitudes compared with the conventional time-domain approach. Finally, a case study of tuning the PTO damping to maximize power production is conducted to demonstrate the performance of the proposed spectral-domain wave-to-wire model.

Shock-induced aerobreakup of a polymeric droplet

Droplet atomization through aerobreakup is omnipresent in various natural and industrial processes. Atomization of Newtonian droplets is a well-studied area; however, non-Newtonian droplets have received less attention despite their being frequently encountered. By subjecting polymeric droplets of different concentrations to the induced airflow behind a moving shock wave, we explore the role of elasticity in modulating the aerobreakup of viscoelastic droplets. Three distinct modes of aerobreakup are identified for a wide range of Weber number $({\sim }10^2\unicode{x2013}10^4)$ and elasticity number $({\sim }10^{-4}\unicode{x2013}10^2)$ variation: these modes are vibrational, shear-induced entrainment and catastrophic breakup modes. Each mode is described as a three-stage process. Stage I is droplet deformation, stage II is the appearance and growth of hydrodynamic instabilities and stage III is the evolution of liquid mass morphology. It is observed that elasticity plays an insignificant role in the first two stages but a dominant role in the final stage. The results are described with the support of adequate mathematical analysis.

Event-by-event antideuteron multiplicity fluctuation in Pb+Pb collisions at [formula omitted] TeV

Using the nucleon coalescence model based on kinetic freeze-out nucleons from the hybrid model of MUSIC hydrodynamics and UrQMD hadronic transport model, we study the production of antideuteron and its event-by-event fluctuation in Pb+Pb collisions at sNN=5.02 TeV. We find a clear suppression of the antideuteron to antiproton yield ratio in peripheral collisions, which is in accordance with the measurements from the ALICE Collaboration. Also found is a Poissonian event-by-event fluctuation of the antideuteron multiplicity in all collision centralities, which is different from the prediction of a simple coalescence model calculation which assumes that all antiproton and antineutron pairs have the same probability to form an antideuteron. However, due to the lack of baryon number conservation at the particlization when the viscous fluid in the hydrodynamic stage of MUSIC is converted to a hadronic matter, our model fails to describe the net-proton number fluctuation and the negative correlation between the antiproton and antideuteron multiplicities at large pseudorapidity acceptance observed in ALICE experiments. Both can nevertheless be well reproduced after selecting a suitable subset of events to fit the measured net-proton number fluctuation.

Dynamical magnetic fields in heavy-ion collisions

The magnetic fields in heavy-ion collisions are important ingredients for many interesting phenomena, such as the Chiral Magnetic Effect, Chiral Magnetic Wave, the directed flow $v_1$ of $D^0$ mesons and the splitting of the spin polarization of the $\Lambda$/$\bar{\Lambda}$. Quantitative studies of these phenomena however suffer from limited understanding on the dynamical evolution of these fields in the medium created by the collisions, which remains a critical and challenging problem. The initial magnetic fields from the colliding nuclei decay very fast in the vacuum but their lifetime could be extended through medium response due to electrically conducting quarks and antiquarks. Here we perform a detailed analysis of such medium effect on the dynamical magnetic fields by numerically solving the Maxwell's equations concurrently with the expanding medium described by viscous hydrodynamics, under the assumption of negligible back reaction of the fields on the fluid evolution. Our results suggest a considerable enhancement of late time magnetic fields, the magnitude of which depends sensitively on the fireball expansion as well as the medium electric conductivity both before and during hydrodynamic stage.

On hydrodynamics in the presense of strong external potential field

On the base of the Boltzmann kinetic equation, hydrodynamics of a dilute gas in the presence of the strong external potential field is investigated. First of all, a gravitational field is meant, because the consistent development of hydrodynamics in this environment is of great practical importance. In the present paper it is assumed that it is possible to neglect the influence of the field on the particle collisions. The study is based on the Chapman–Enskog method in a Bogolyubov’s formulation, which uses the idea of the functional hypothesis. Consideration is limited to steady gas states, which are subjected to a simpler experimental study. Chemical potential μ0 of the gas at the point where the external field has zero value and its temperature T are selected as the reduced description parameters of the system. In equilibrium, in the presence of the field, these values do not depend on the coordinates. It is assumed that in thehydrodynamic states T and μ0 are weakly dependent on the coordinates and therefore their gradients, considered on the scale of the free path length of the gas, are small. The kinetic equation, accounting for the functional hypothesis, gives an integro-differential equation for a gas distribution function at the hydrodynamic stage of evolution. This equation is solved in perturbation theory in gradients of T and μ0. The main approximation is analyzed for possibility of the system to be in a local equilibrium by means of comparing it with an equilibrium distribution function. Next, the distribution function is calculated in the first approximation in gradients and it is expressed in terms of solutions Ap , Bp of some first kind integral Fredholm equations. An approach to the approximate solution of these equations is discussed. The found distribution function is used to calculate the fluxes of the number of gas particles and their energy in the first order in gradients T and μ0 . Kinetic coefficients, which describe the structure of these fluxes, are introduced. Matrix elements of the operator of the linearized collision integral (integral brackets) are used for their research. It is a question of validity of the principle of symmetry of kinetic coefficients and definition of their signs.

Bayesian analysis of heavy ion collisions with the heavy ion computational framework Trajectum

We introduce a model for heavy ion collisions named Trajectum, which includes an expanded initial stage with a variable free streaming velocity $v_{\rm fs}$ and a hydrodynamic stage with three varying second order transport coefficients. We describe how to obtain a Gaussian Emulator for this 20-parameter model and show results for key observables. This emulator can be used to obtain Bayesian posterior estimates on the parameters, which we test by an elaborate closure test as well as a convergence study. Lastly, we employ the optimal values of the parameters found in [1] to perform a detailed comparison to experimental data from PbPb and $p$Pb collisions. This includes both observables that have been used to obtain these values as well as wider transverse momentum ranges and new observables such as correlations of event-plane angles.

MODELING OF EXTRACTION PROCESS IN THE SYSTEM SOLID BODY–LIQUID

The paper reports the basic principles of modeling of extraction process through the cell walls. A solid body is assumed to be an aggregate of deformable particles, inside of which there is an extractable substance. Two stages of the process are considered: diffusion and hydrodynamic ones. The mass exchange stage inside the solid is diffusive because it has not fluidity. As far as the diffusion stage is concerned, we propose to consider the process of internal transfer as a set of pseudocatalytic reactions between the solvent molecules and the extractable substance. Based on this approach, the relationship between the diffusion coefficient and the particles structure has been derived under the condition of a cellular structure of the particles. The equations for describing the time change of the mean concentrations of a substance are given, taking into account the effect of the external mass discharge condition at interphase boundaries. It has been proved that the applied approach makes it possible to find a sufficient number of parameters for describing the different effects of extraction and gives physical meaning to interpretations of kinetic curves of extraction. As regards the hydrodynamic stage, a proper frame model of the pore space was formulated, which is deterministic and two-scale. It takes into account possible shear and volume deformations of the particles. Such two-phase medium was considered as a collection of variable intensity sources. The equations for calculating the mass transfer coefficient for the system are solid particles – liquid, taking into account the rheology of the liquid phase as a mixture of extractant and extractable substance. It has been proved that the proposed models have sufficient universality to withstand adaptation to different specific situations.

Rapidity decorrelation caused by hydrodynamic fluctuations and initial longitudinal fluctuations

Factorisation breaking of the anisotropic flow coefficients is actively studied to understand the longitudinal dynamics of the quark-gluon plasma produced in high-energy nuclear collisions. Yet no hydrodynamic models have successfully described the centrality dependence of the factorisation breaking in various collisions systems. In this study, we reproduce the centrality dependence of the factorisation ratio in Pb+Pb collisions at LHC by constructing an integrated dynamical model with hydrodynamic fluctuations and initial longitudinal fluctuations. Hydrodynamic fluctuations are thermal fluctuations arising during the hydrodynamic stage of the high-energy nuclear collisions. We include the hydrodynamic fluctuations obeying the fluctuation-dissipation theorem. For the initial longitudinal fluctuations, we run PYTHIA for each binary p+p collision, scale the distribution of the produced particles by the number of participants and assume the distribution to be the entropy density distribution. We switch on and off the hydrodynamic fluctuations to investigate the effects on the longitudinal rapidity decorrelation.

Jet momentum broadening in the pre-equilibrium Glasma

Jets are important probes of heavy ion collisions as they can provide information on the interaction of a highly energetic parton with the medium it traverses. In the hydrodynamic stage of dense, strongly interacting matter, these interactions can be explained in terms of scattering processes, soft gluon emission and collinear parton splittings. However, jets originate even before the hydrodynamic stage. Here we report on the first numerical simulation of transverse momentum broadening of jets stemming from the interaction of partons with boost-invariantly expanding Glasma flux tubes. The Glasma stage is a pre-hydrodynamic stage based on the Color Glass Condensate framework. Our calculation shows strong time-dependence and an intrinsic anisotropy of momentum broadening in the directions transverse to the jet propagation direction.

Cavitating flow structures and corresponding hydrodynamics of a transient pitching hydrofoil in different cavitation regimes

The present paper applied experimental and numerical methods to investigate the cavitating flow structures and corresponding hydrodynamics for a transient pitching Clark-Y hydrofoil. The aims are to (1) improve the understanding of the interplay between the transient cavitating flow structures, motion of the hydrofoil, and hydrodynamic performance, (2) quantify the influence of cavitation on the hydrodynamic load coefficients and flow structures, and (3) analyze the evolution of cavitating flow during different cavitation regime. The pitching motion trajectory is a triangular wave with mean incidence of α0=10° and amplitude of Δα = 5° at a frequency of 2 Hz. The upstream velocity U∞ is fixed at 6.3 m/s, which is corresponding to Re=4.4 × 105. The cavitation patterns for different cavitation numbers are mainly documented by the high-speed photography, and the dynamic characteristics of the hydrofoil are measured by the torque sensor. The numerical investigations were performed by solving the incompressible URANS equations using the mass-transfer cavitation model, the coupled k-ω SST turbulence model and γ-Reθ transition model. The predicted cavity patterns and moment coefficients agree well with the experimental results. Four typical regimes, including sub cavitation, inception cavitation, sheet cavitation and cloud cavitation, are observed. Compared to the sub cavitation case, the hydrodynamic coefficients and flow structures are significantly affected by the incipient cavity. Results show that the leading edge (LE) cavity promotes the formation of the counterclockwise tailing edge vortex (TEV), thus leading to decline of the lift. Moreover, the LE cavity also limits the formation of the clockwise second vortex (SV), which weakens the fluctuation of the hydrodynamic load. For the sheet cavitation case, three cavitating flow patterns(Pattern A/B/C) are observed in the hydrodynamic fluctuation stage, which is corresponding to different characteristic frequency. For the cloud cavitation case, the hydrodynamic curves present four distinct stages. According to the cavity breaking position and characteristic frequency, four different patterns(Pattern I/II/III/IV) of the cavity development and shedding are observed and analyzed.

Photon spectra and anisotropic flow in heavy ion collisions at the top RHIC energy within the integrated hydrokinetic model with photon hadronization emission

The integrated HydroKinetic Model (iHKM) is applied to analyze the results of direct photon spectra as well as elliptic and triangular flow measurements in 200A GeV Au+Au collisions at RHIC for different centrality bins. Experiments detect the strong centrality dependence of photon elliptic and triangular flow as increasing vn(pT)-coefficients towards peripheral collisions. The photon production in the model is accumulated from the different sources along with the process of relativistic heavy ion collision developing. Those include the primary hard photons from the parton collisions at the very early stage of the process, the photons generated at the pre-thermal phase of dense matter evolution, then thermal photons at partially equilibrated hydrodynamic quark-gluon stage, together with radiation displaying a confinement and, finally, from the hadron gas phase. Along the way a hadronic medium evolution is treated in two distinct, in a sense opposite, approaches: chemically equilibrium and chemically non-equilibrium, namely, chemically frozen expansion. We find the description of direct photon spectra, elliptic and triangular flow are significantly improved, similar to that found in iHKM for the LHC energies, if an additional portion of photon radiation associated with the confinement processes, the “hadronization photons”, is included into consideration.

Bulk observables in Pb+Pb collisions at sNN=5.02TeV at the CERN Large Hadron Collider within the integrated hydrokinetic model

The paper is devoted to the description and prediction of various bulk observables in the Pb+Pb collisions at the LHC energy $\sqrt{s_{NN}}=5.02$ TeV within the integrated hydrokinetic model (iHKM). Sensitivity of the results to the choice of the appropriate model parameter values is also investigated. It is found that changing of the relaxation time and the rate of thermalization, which characterize the pre-thermal stage of the matter evolution, as well as switching to another equation of state at the hydrodynamic stage and the corresponding hadronization temperature, does not destroy the results, if simultaneously one provides an appropriate adjusting of the initial time for the superdense matter formation and related maximal initial energy density.

Rapidity decorrelation from hydrodynamic fluctuations

We discuss rapidity decorrelation caused by hydrodynamic fluctuations in high-energy nuclear collisions at the LHC energy. We employ an integrated dynamical model which is a combination of the Monte Carlo version of Glauber model with extension to longitudinal direction for initial conditions, full three-dimensional relativistic fluctuating hydrodynamics for the space-time evolution of created matter in the intermediate stage and a hadronic cascade model in the late stage. We switch on and off the hydrodynamic fluctuations in the hydrodynamic stage to understand the effects of hydrodynamic fluctuations on factorisation ratios rn(ηpa,ηpb). To understand the rapidity gap dependence of the factorisation ratio comprehensively, we analyse Legendre coefficients A2k and B2k.

Viscous hydrodynamics for nonconformal anisotropic fluids

A new formulation of (3+1)-dimensional anisotropic hydrodynamics is presented that accounts nonperturbatively for the large longitudinal-transverse pressure anisotropy and bulk viscous pressure in heavy-ion collisions. The initialization of the anisotropic hydrodynamic stage is discussed, and a comparison to standard viscous hydrodynamics for (0+1)-dimensional Bjorken expansion is presented.

Non-dissipative hydrodynamic equations based on a nonlocal collision integral

We consider a slightly non-uniform one-component gas with weak potential interaction. The basis of the investigation is the known kinetic equation in the case of small interaction which is truncated up to the second order of smallness. This equation contains a nonlocal collision integral of the second order in small interaction. In this paper we consider the hydrodynamic stage of the system evolution, and, in contrast to the standard hydrodynamics, we take into account the non-locality of the collision integral. We propose the following set of the reduced description parameters which are the densities of the conserved quantities: the particle number density, the momentum density, and the total energy density. It should be stressed that in contrast to the standard hydrodynamics, the kinetic energy is not conserved, and only the total system energy is conserved if the nonlocal collision integral is used. Definitions of the system velocity and temperature are proposed; it should be stressed that the proposed temperature definition is based on the total system energy rather than on the kinetic one. The hydrodynamics in the leading order in small gradients is investigated, and it is shown that the system one-particle distribution function in the leading-in-gradients order coincides with the Maxwellian one. Particle number density, velocity and temperature time evolution equations (hydrodynamic equations) are derived in the non-dissipative case. The leading-in-interaction orders of the obtained equations coincide with the corresponding equations in the framework of the standard hydrodynamics. The corrections of the first and second order in small interaction are also obtained.

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches.

Velocity autocorrelation functions (VAFs) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have a purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the molecular dynamic data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode theory, the mode coupling theory, and some other theoretical approaches.

Evolution of charge fluctuations and correlations in the hydrodynamic stage of heavy ion collisions

Charge fluctuations for a baryon-neutral quark-gluon plasma have been calculated in lattice gauge theory. These fluctuations provide a well-posed rigorous representation of the quark chemistry of the vacuum for temperatures above T_c >~ 155 MeV. Due to the finite lifetime and spatial extent of the fireball created in relativistic heavy ion collisions, charge-charge correlations can only equilibrate for small volumes due to the finite time required to transport charge. This constraint leads to charge correlations at finite relative position that evolve with time. The source and evolution of such correlations is determined by the evolution of the charge fluctuation and the diffusion constant for light quarks. Here, calculations are presented for the evolution of such correlations superimposed onto hydrodynamic simulations. Results are similar to preliminary measurements from STAR, but significant discrepancies remain.

Broadening of the chiral critical region in a hydrodynamically expanding medium

We investigate higher cumulants of the sigma field as the chiral order parameter at the QCD phase transition. We derive a thermodynamic expression for the skewness and kurtosis from susceptibilities and use these to determine $S\sigma$ and $\kappa\sigma^2$ for the sigma field in equilibrium. In a next step, we study the behavior of these cumulants in both an equilibrated static medium and an expanding medium resembling the hydrodynamic stage of a heavy-ion collision. For the latter one, we find a significant broadening of the critical region.

Quantifying the chiral magnetic effect from anomalous-viscous fluid dynamics**This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, within the framework of the Beam Energy Scan Theory (BEST) Topical Collaboration. The work is also supported in part by the National Science Foundation under Grant No. PHY-1352368 (SS and JL), by

The Chiral Magnetic Effect (CME) is a macroscopic manifestation of fundamental chiral anomaly in a many-body system of chiral fermions, and emerges as an anomalous transport current in the fluid dynamics framework. Experimental observation of the CME is of great interest and has been reported in Dirac and Weyl semimetals. Significant efforts have also been made to look for the CME in heavy ion collisions. Critically needed for such a search is the theoretical prediction for the CME signal. In this paper we report a first quantitative modeling framework, Anomalous Viscous Fluid Dynamics (AVFD), which computes the evolution of fermion currents on top of realistic bulk evolution in heavy ion collisions and simultaneously accounts for both anomalous and normal viscous transport effects. AVFD allows a quantitative understanding of the generation and evolution of CME-induced charge separation during the hydrodynamic stage, as well as its dependence on theoretical ingredients. With reasonable estimates of key parameters, the AVFD simulations provide the first phenomenologically successful explanation of the measured signal in 200 AGeV AuAu collisions.

Anisotropic hydrodynamic modeling of 2.76 TeV Pb-Pb collisions

We compare phenomenological results from 3+1d quasiparticle anisotropic hydrodynamics (aHydroQP) with experimental data collected in LHC 2.76 TeV Pb-Pb collisions. In particular, we present comparisons of particle spectra, average transverse momentum, elliptic flow, and HBT radii. The aHydroQP model relies on the introduction of a single temperature-dependent quasiparticle mass which is fit to lattice QCD data. By taking moments of the resulting Boltzmann equation, we obtain the dynamical equations used in the hydrodynamic stage which include the effects of both shear and bulk viscosities. At freeze-out, we use anisotropic Cooper-Frye freeze-out performed on a fixed-energy-density hypersurface to convert to hadrons. To model the production and decays of the hadrons we use THERMINATOR 2 which is customized to sample from ellipsoidal momentum-space distribution functions. Using smooth Glauber initial conditions, we find very good agreement with many heavy-ion collision observables.