Hydrodynamic Solution Research Articles

NEW SOLUTION TO THE DROPLET KERNEL MODEL

The droplet model of the nucleus is revived, for which an exact solution for an incompressible fluid is obtained using the hydrodynamic potential solution obtained from the Schrödinger equation. Moreover, for an incompressible fluid, there are formulas for the pressure or potential. There is the main part of the hydrodynamic potential, which is obtained by replacing the modulus of the inverse difference of vectors by the difference in moduli of the values of the vectors. The bulk of the potential is expressed in a finite formula with singularities. A formula is obtained for the integral containing the modulus of the difference between the exact values of the vectors minus the main part of the potential. This difference defines a continuous correction with the features taken into account. The main part of the potential at the boundary of the nucleus turned out to be infinitely large with an imaginary part, locking particles in the nucleus. In this case, the real part of the main potential decreases with decreasing radius, becomes negative, and determines the bound state. At half the radius of the nucleus, there is a linear term along the radius. At the zero radius, there is an infinite negative potential with an imaginary part. An expression for the quantum of the emitted energy is obtained. Note that the added mass was not used due to the rotational regime of the nucleus. An algorithm for calculating the spectrum of the kernel is proposed, and each state of the action of the kernel sn corresponds to n calculated frequencies, determined by n angles in the configuration space. The main space is n + 1 dimensional, and each dimension of space has its own energy. But without special means, the potential of the nucleus tends to infinity. It is necessary to introduce the imaginary degree of roughness of the corners, in expressions containing singularities, then the infinities disappear.

Design and optimization investigation on hydraulic transmission and energy storage system for a floating-array-buoys wave energy converter

The energy density of wave power in China is relatively low compared with that of the wave power in Europe. Simply improving the shape or size of the energy-capturing mechanism for a wave energy converter (WEC) cannot directly result in a larger energy output. Instead, a solution of array-type energy-capturing mechanism integrating marine structure bares practical application potential to increase the power take-off (PTO) productivity. To exploit the conditions in China, a WEC system integrating oscillating-array-buoys with a floating platform is proposed and sea trials of a 10 kW prototype confirmed the feasibility of the floating-array-buoys WEC (FABWEC) system for wave energy conversion. However, sea trials data indicated that the energy conversion performance of the mechanical transmission design in the FABWEC system was relatively poor under the low wave energy density, suggesting the urgency of improving energy conversion and storage system to the increase of system performance. Herein, a hydraulic transmission and accumulator system (HTAS) is designed to replace the original mechanical transmission and flywheel system (MTFS), aiming to enhance the total energy conversion performance of the FABWEC system. The hydrodynamic simulation and numerical solution of the wave energy capture mechanism in the FABWEC system are carried out to facilitate the design and main components selection of the HTAS. And then the simulation and optimization of the designed HTAS are performed by the hydraulic simulation software. It is worth noting that there have been few reports on the operating performance of the HTAS with respect to buoys. In the hydraulic optimization process, the final optimization parameters of the HTAS are obtained by comparing the dynamic characteristics of the system, including system pressure, flow rate, motor torque and angular velocity, under the conditions with or without accumulator, with different buoy numbers and with different buoy phase differences. The simulated results show that the accumulator could effectively damp out the fluctuations in output power to turn the wave energy into a dispatchable power source; The energy conversion and output performances of the HTAS behave better with the increase of the buoys number and buoys phase difference, but the space and cost factors need to be taken into consideration in the actual operation; Within the research scope of this paper, the HTAS has an optimal performance for energy conversion and output when the number of buoys on one side of the floating platform is 5 and the phase difference between the buoys is 60°; Under the optimized conditions, the average output power of the hydraulic motor after stable operation of the HTAS can reach 5.8 kW. Significantly, the optimized HTAS could deliver the required electricity power steadily under the low wave energy density and has been practically applied to the next generation FABWEC prototype.

Dynamics of QCD matter — current status

In this article, there are 18 sections discussing various current topics in the field of relativistic heavy-ion collisions and related phenomena, which will serve as a snapshot of the current state of the art. Section 1 reviews experimental results of some recent light-flavored particle production data from ALICE collaboration. Other sections are mostly theoretical in nature. Very strong but transient magnetic field created in relativistic heavy-ion collisions could have important observational consequences. This has generated a lot of theoretical activity in the last decade. Sections 2, 7, 9, 10 and 11 deal with the effects of the magnetic field on the properties of the QCD matter. More specifically, Sec. 2 discusses mass of [Formula: see text] in the linear sigma model coupled to quarks at zero temperature. In Sec. 7, one-loop calculation of the anisotropic pressure are discussed in the presence of strong magnetic field. In Sec. 9, chiral transition and chiral susceptibility in the NJL model is discussed for a chirally imbalanced plasma in the presence of magnetic field using a Wigner function approach. Sections 10 discusses electrical conductivity and Hall conductivity of hot and dense hadron gas within Boltzmann approach and Sec. 11 deals with electrical resistivity of quark matter in presence of magnetic field. There are several unanswered questions about the QCD phase diagram. Sections 3, 11 and 18 discuss various aspects of the QCD phase diagram and phase transitions. Recent years have witnessed interesting developments in foundational aspects of hydrodynamics and their application to heavy-ion collisions. Sections 12 and 15–17 of this article probe some aspects of this exciting field. In Sec. 12, analytical solutions of viscous Landau hydrodynamics in 1+1D are discussed. Section 15 deals with derivation of hydrodynamics from effective covariant kinetic theory. Sections 16 and 17 discuss hydrodynamics with spin and analytical hydrodynamic attractors, respectively. Transport coefficients together with their temperature- and density-dependence are essential inputs in hydrodynamical calculations. Sections 5, 8 and 14 deal with calculation/estimation of various transport coefficients (shear and bulk viscosity, thermal conductivity, relaxation times, etc.) of quark matter and hadronic matter. Sections 4, 6 and 13 deal with interesting new developments in the field. Section 4 discusses color dipole gluon distribution function at small transverse momentum in the form of a series of Bells polynomials. Section 6 discusses the properties of Higgs boson in the quark–gluon plasma using Higgs–quark interaction and calculate the Higgs decays into quark and anti-quark, which shows a dominant on-shell contribution in the bottom-quark channel. Section 13 discusses modification of coalescence model to incorporate viscous corrections and application of this model to study hadron production from a dissipative quark–gluon plasma.

Navier–Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture

The Navier–Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the Boltzmann equation is obtained via the Chapman–Enskog method for states near the local version of the homogeneous time-dependent state. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. In addition, in contrast to the previous results obtained for low-density granular mixtures, there are also nonzero contributions to the first-order approximations to the partial temperatures Ti(1) and the cooling rate ζ(1). Explicit forms for the diffusion transport coefficients, the shear viscosity coefficient, and the quantities Ti(1) and ζ(1) are obtained by assuming steady state conditions and by considering the leading terms in a Sonine polynomial expansion. The above transport coefficients are given in terms of the coefficients of restitution, concentration, and the masses and diameters of the components of the mixture. The results apply, in principle, for arbitrary degree of inelasticity and are not limited to specific values of concentration, mass, and/or size ratios. As a simple application of these results, the violation of the Onsager reciprocal relations for a confined granular mixture is quantified in terms of the parameter space of the problem.

Numerical simulations of hydrodynamic loads and structural responses of a Pre-Swirl Stator

This paper investigates the effect of different flow models on the Pre-Swirl-Stator structural response from the perspective of a non-existing unified design procedure. Due to viscous effects near the propeller plane, the hydrodynamic solution is calculated by Computational Fluid Dynamics (CFD). Three different models are analysed: without the propeller, with the actuator disk and with the propeller. The main intention of this paper is to clarify the effects of the propeller model on the structural stresses in calm-water and waves which include the ship motion. CFD simulations are performed by means of OpenFOAM, while the structural response is calculated by means of the Finite Element Method (FEM) solver NASTRAN. Calm-water results have shown the inclusion of the propeller necessary from the design perspective, while the wave simulations have shown negligible propeller influence on the resulting stresses arising from the ship motions.

Light Curves of Type Ia Supernovae

We have studied the light curves of type Ia supernovae (SNe Ia) and the physical parameters inferred from them. We have constructed both analytical and numerical light curves of SNe Ia. Using an empirical relation between the SN luminosity and light-curve parameters, we have managed to impose constraints on the hydrodynamic solutions obtained by the STELLA code and to produce a sample of models that describe the observational properties of real SNe maximally accurately. With this sample we have established a relationship between the opacity in SN Ia ejecta and the parameters being determined directly from observations. The method has been tested on two classical SNe Ia as an example: 2011fe and 2012fr. The presented approach allows the opacity to be found without resorting to time-consuming computations.

The origin and impact of Wolf-Rayet-type mass loss

AbstractClassical Wolf-Rayet (WR) stars mark an important stage in the late evolution of massive stars. As hydrogen-poor massive stars, these objects have lost their outer layers, while still losing further mass through strong winds indicated by their prominent emission line spectra. Wolf-Rayet stars have been detected in a variety of different galaxies. Their strong winds are a major ingredient of stellar evolution and population synthesis models. Yet, a coherent theoretical picture of their strong mass-loss is only starting to emerge. In particular, the occurrence of WR stars as a function of metallicity (Z) is still far from being understood.To uncover the nature of the complex and dense winds of Wolf-Rayet stars, we employ a new generation of model atmospheres including a consistent solution of the wind hydrodynamics in an expanding non-LTE situation. With this technique, we can dissect the ingredients driving the wind and predict the resulting mass-loss for hydrogen-depleted massive stars. Our modelling efforts reveal a complex picture with strong, non-linear dependencies on the luminosity-to-mass ratio and Z with a steep, but not totally abrupt onset for WR-type winds in helium stars. With our findings, we provide a theoretical motivation for a population of helium stars at low Z, which cannot be detected via WR-type spectral features. Our study of massive He-star atmosphere models yields the very first mass-loss recipe derived from first principles in this regime. Implementing our first findings in stellar evolution models, we demonstrate how traditional approaches tend to overpredict WR-type mass loss in the young Universe.

Numerical investigations of the transient cavitating vortical flow structures over a flexible NACA66 hydrofoil

In this paper, the cavitating flow over a flexible NACA66 hydrofoil is studied numerically by a modified fluid-structure interaction strategy with particular emphasis on understanding the flow-induced vibration and the cavitating vortical flow structures. The modified coupling approaches include (1) the hydrodynamic solution obtained by the large eddy simulation (LES) together with a homogenous cavitation model, (2) the structural deformation solved with a cantilever beam equation, (3) fluid-structural interpolation and volume mesh motion based on the radial basis functions and greedy algorithm. For the flexible hydrofoil, the dominant flow-induced vibration frequency is twice of the cavity shedding frequency. The cavity shedding frequency is same for the rigid and flexible hydrofoils, demonstrating that the structure vibration is not large enough to affect the cavitation evolution. The predicted cavitating behaviors are strongly three-dimensional, that is, the cavity is (a) of a triangular shape near the hydrofoil tip, (b) of a rectangular shape near the hydrofoil root, and (c) with a strong unsteadiness in the middle of the span, including the attached cavity growth, oscillation and shrinkage, break-off and collapse downstream. The unsteady hydroelastic response would strongly affect the cavitation shedding process with small-scale fragments at the cavity rear part. Furthermore, three vortex identification methods (i.e., the vorticity, the Q- criteria and the Ω method) are adopted to investigate the cavitating vortex structures around the flexible hydrofoil. It is indicated that the cavity variation trend is consistent with the vortex evolution. The vortex structures are distributed near the foil trailing edge and in the cavitation region, especially at the cavity-liquid interface. With the transporting downstream the shedding cavities, the vortices gradually increase in the wake flows.

Transport of produced water through reactive porous media

During hydraulic fracturing (or fracking) large volumes of wastewater (flow-back and produced water) are generated, which are naturally rich in heavy metals and radionuclides, such as radium. Spills may occur during operations and contaminate the groundwater. Therefore, there is an urgent need to identify a practice that can mitigate the negative impact of accidental leaks on water resources. Here, we present an experimental and modeling work on the transport of alkaline earth elements in produced water, which are congeners of radium, namely, barium (Ba2+), strontium (Sr2+), calcium (Ca2+), and magnesium (Mg2+) in addition to sodium (Na+). Column-flood tests were conducted using produced water from a shale-gas site and reactive porous media made of ubiquitous minerals such as sand, hydrous ferric oxide, activated alumina, and manganese oxide. In all cases, no retardation of the ions was observed at the salinity conditions of the produced water, but strong retardation in the pH front was measured, indicating that adsorption indeed occurred. When using manganese oxide and upon dilution of produced water, the concentration fronts of all major divalent cations were retarded. However, a fast wave of solute, traveling at the average flow velocity, emerged. This phenomenon confirmed that significant adsorption occurred under those conditions. But, pH-dependent adsorption and hydrodynamic dispersion favored fast solute transport.Overall, these results suggest that manganese oxide could be used as a reactive material in the lining of temporary storage tanks and in the well cases in order to retard the migration of the major toxic elements in produced water. However, mixing must be controlled to avoid the emergence of an instability at the concentration fronts favoring the formation of fast waves.

A Semikinetic Model of Plasmasphere Refilling Following Geomagnetic Storms and Comparison With Hydrodynamic Results

AbstractThe objective of this paper is the development of a kinetic model for plasmasphere refilling following geomagnetic storms. The kinetic model is based on the “particle‐in‐cell” method, a method based on the simulation of particle motion and thus well suited to high altitude, low‐density regimes, where the plasma transport equations are not valid. The model was validated with exact, analytical benchmarks, which are provided in this paper. The refilling results obtained from the kinetic model were then compared with results from a recently developed hydrodynamic solution methodology based on the “flux‐corrected transport” method, and the limitations of hydrodynamic modeling for low‐density flow at high altitudes were explored.

Perturbation solutions of relativistic viscous hydrodynamics forlongitudinally expanding fireballs * * This work was in part Supported by the Ministry of Science and Technology of China (MSTC) under the "973" Project No. 2015CB856904(4), NSFC (11735007, 11890711), by the Sino-Hungarian bilateral Cooperation Program (Te'T 12CN-1-2012-0016). D. She is Supported by the China Scholarship Council (CSC) (201906770027)

The solutions of the relativistic viscous hydrodynamics for longitudinally expanding fireballs are investigated with the Navier-Stokes theory and Israel-Stewart theory. The energy and the Euler conservation equations for the viscous fluid are derived in Rindler coordinates, by assuming that the longitudinal expansion effect is small. Under the perturbation assumption, an analytical perturbation solution for the Navier-Stokes approximation and numerical solutions for the Israel-Stewart approximation are presented. The temperature evolution with both shear viscous effect and longitudinal acceleration effect in the longitudinal expanding framework are presented. The specific temperature profile shows symmetric Gaussian shape in the Rindler coordinates. Further, we compare the results from the Israel-Stewart approximation with the results from the Bjorken and the Navier-Stokes approximations, in the presence of the longitudinal acceleration expansion effect. We found that the Israel-Stewart approximation gives a good description of the early stage evolutions than the Navier-Stokes theory.

Dissipative-type theories for Bjorken and Gubser flows

We use the dissipative-type theory (DTT) framework to solve for the evolution of conformal fluids in Bjorken and Gubser flows from isotropic initial conditions. The results compare well with both exact and other hydrodynamic solutions in the literature. At the same time, DTTs enforce the Second Law of thermodynamics as an exact property of the formalism, at any order in deviations from equilibrium, and are easily generalizable to more complex situations.

A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows

Compressible flow has intrinsically multiple scale nature due to the large variations of gas density and characteristic scale of flow structure, especially in hypersonic and reentry problems. It is challenging to construct an accurate and efficient numerical algorithm to capture non-equilibrium flow physics across different regimes. In this paper, a unified gas kinetic scheme with adaptive velocity space (AUGKS) for multiscale flow transport will be developed. In near-equilibrium flow region, particle distribution function is close to the Chapman-Enskog expansion and can be formulated analytically, where only macroscopic conservative flow variables are updated. With the emergence of non-equilibrium effect, the AUGKS automatically switches to the original unified gas kinetic scheme (UGKS) with a discrete velocity space to follow the evolution of particle distribution function. A criterion is proposed to quantify the non-equilibrium and is used for the switch between continuous and discrete particle velocity space. Following the scale-dependent local evolving solution, the AUGKS presents the discretized gas dynamic equations directly on the cell size and time step scales, i.e., the so-called direct modeling method. As a result, the scheme is able to capture the cross-scale flow physics from particle transport to hydrodynamic wave propagation, and provides a continuous variation of solutions from the Boltzmann to the Euler equations. Different from conventional DSMC-Fluid hybrid method, the AUGKS does not need a buffer zone to match up kinetic and hydrodynamic solutions. Instead, continuous and discrete particle velocity spaces are automatically and robustly switched, such as translating the continuous Chapman-Enskog distribution function to the discrete grid points in the velocity space. Therefore, the AUGKS is feasible for the numerical simulations with unsteadiness and complex geometries. Compared with the asymptotic preserving (AP) method which solves kinetic equation uniformly over entire computational domain with discretized velocity space, the current velocity-space adaptive unified scheme speeds up the computation, reduces the memory requirement significantly, and maintains the equivalent accuracy for multiscale flow simulations. Many test cases validate the current approach. The AUGKS provides an effective tool for non-equilibrium flow studies.

New Solutions of Viscous Relativistic Hydrodynamics

Relativistic hydrodynamics represents a powerful tool to investigate the time evolution of the strongly interacting quark gluon plasma created in ultrarelativistic heavy ion collisions. The equations are solved often numerically, and numerous analytic solutions also exist. However, the inclusion of viscous effects in exact, analytic solutions has received less attention. Here we utilize Hubble flow to investigate the role of bulk viscosity, and present different classes of exact, analytic solutions valid also in the presence of dissipative effects.

Lifetime Estimations and a Non-Monotonic Initial Energy Density in Heavy Ion Collisions at RHIC and LHC

We highlight some connections between the final state hadronic observables and the initial conditions using a recently found new exact family of solutions of relativistic hydrodynamics. These relations provide explicit examples of the scaling behaviour in relativistic hydrodynamics and may provide an advanced estimate of the lifetime and the initial energy density in $\sqrt{s_{NN}} = 62.4$, $130$, and $200$ GeV Au+Au collisions at RHIC and $\sqrt{s_{NN}} = 5.0$ TeV Pb+Pb and $5.44$ TeV Xe+Xe as well as $\sqrt{s} = 7$, $8$ and $13$ TeV p+p collisions at LHC energies. A surprising result is that these advanced estimates yield a non-monotonic increase of the initial energy density with increasing collision energy at the RHIC energy range.

Analytic Model Studies of Polarized Baryon Production

We investigate known exact solutions of hydrodynamics and derive analytic formulas for the polarization of baryons produced at freeze-out. Such polarization (observed in high energy heavy-ion experiments) carries information on the time evolution of the quark-gluon plasma (sQGP), and our results give first analytic insight into the connection between this type of measurements and dynamical properties of the sQGP (e.g. vorticity). We present results for a rotating and acceleratingly expanding solution and also give hints on how to calculate the polarization using a rotating extension of the Buda--Lund parameterization.

Improvement of Non-Hydrostatic Hydrodynamic Solution Using a Novel Free-Surface Boundary Condition

Hydrodynamic models based on the RANS equation are well-established tools to simulate three-dimensional free surface flows in large aquatic ecosystems. However, when the ratio of vertical to horizontal motion scales is not small, a non-hydrostatic approximation is needed to represent these processes accurately. Increasing efforts have been made to improve the efficiency of non-hydrostatic hydrodynamic models, but these improvements require higher implementation and computational costs. In this paper, we proposed a novel free-surface boundary condition based on a fictional sublayer at the free-surface (FSFS). We applied the FSFS approach at a finite difference numerical discretization with a fractional step framework, which uses a Neumann type of boundary condition to apply a hydrostatic relation in the top layer. To evaluate the model performance, we compared the Classic Boundary Condition Approach (CBA) and the FSFS approach using two numerical experiments. The experiments tested the model’s phase error, capability in solving wave celerity and simulate non-linear wave propagation under different vertical resolution scenarios. Our results showed that the FSFS approach had a lower phase error (2 to 5 times smaller) than CBA with a little additional computational cost (ca. 7% higher). Moreover, it can better represent wave celerity and frequency dispersion with 2 times fewer layers and low mean computational cost (CBA δ t = 2.62 s and FSFS δ t = 1.22 s).

Non-linear evolutions of magnetized thick discs around black holes: dependence on the initial data

ABSTRACT We build equilibrium solutions of magnetized thick discs around a highly spinning Kerr black hole and evolve these initial data up to a final time of about 100 orbital periods. The numerical simulations reported in this paper solve the general relativistic magnetohydrodynamic equations using the bhac code and are performed in axisymmetry. Our study assumes non-self-gravitating, polytropic, constant angular momentum discs endowed with a purely toroidal magnetic field. In order to build the initial data, we consider three approaches, two of which incorporate the magnetic field in a self-consistent way and a third approach in which the magnetic field is included as a perturbation on to an otherwise purely hydrodynamical solution. To test the dependence of the evolution on the initial data, we explore four representative values of the magnetization parameter spanning from almost hydrodynamical discs to very strongly magnetized tori. The initial data are perturbed to allow for mass and angular momentum accretion on to the black hole. Notable differences are found in the long-term evolutions of the initial data. In particular, our study reveals that highly magnetized discs are unstable, and hence prone to be fully accreted and expelled, unless the magnetic field is incorporated into the initial data in a self-consistent way.

Prediction of flow and heat transfer through a microtube filled with bidisperse porous medium under local thermal nonequilibrium condition

AbstractIn this paper, the thermal and hydrodynamic solutions of a microtube filled with bidisperse porous medium (BDPM) under the local thermal nonequilibrium (LTNE) condition are presented. Considering the LTNE condition, the energy equations have been numerically solved. The rarefaction effects are considered for Knudsen numbers ranging from 0 to 0.1; therefore, first‐order boundary condition is applied on the wall. The temperature distribution of each phase is examined with respect to the involved parameters in the BDPM system. For the first time, the Nusselt number ratio (NRDP) is introduced to study the influence of Darcy number on the Nusselt number more precisely. Also, the effect of different thermophysical parameters on the Nusselt number is studied. The advantage of BDPM system over monodisperse porous medium (MDPM) structure is examined through the heat transfer performance parameter. The findings exhibit a good agreement with the literature. Also, the LTNE condition produces more realistic results in comparison to local thermal equilibrium assumption. On the whole, although implementing the BDPM enhances the heat transfer rate compared with the MDPM, it does not improve the thermal hydrodynamic performance significantly.

Generalization of Bantilan-Ishi-Romatschke flow to magnetohydrodynamics

We present a generalization of the Bantilan-Ishi-Romatschke (BIR) solution of relativistic hydrodynamics to relativistic magnetohydrodynamics (RMHD). Using the symmetries of the boundary of the Kerr-AdS5 black hole, and certain simplifying assumptions we solve the equations of RMHD on this boundary for a highly conductive fluid. We then transform the resulting solution to the flat spacetime. Furthermore, we show that the force-free condition causes the magnetic field to become singular at particular points and propose a regularization process for removing the singularities. The regularization process reveals the importance of non-vanishing electrical current in RMHD.