Hydrodynamic Solution Research Articles

Small deformation theory for a magnetic droplet in a rotating field

A three-dimensional small deformation theory is developed to examine the motion of a magnetic droplet in a uniform rotating magnetic field. The equations describing the droplet's shape evolution are derived using two different approaches—a phenomenological equation for the tensor describing the anisotropy of the droplet and the hydrodynamic solution using the perturbation theory. We get a system of ordinary differential equations for the parameters describing the droplet's shape, which we further analyze for the particular case when the droplet's elongation is in the plane of the rotating field. The qualitative behavior of this system is governed by a single dimensionless quantity τω—the product of the characteristic relaxation time of small perturbations and the angular frequency of the rotating magnetic field. Values of τω determine whether the droplet's equilibrium will be closer to an oblate or a prolate shape, as well as whether its shape will undergo oscillations as it settles to this equilibrium. We show that for small deformations, the droplet pseudo-rotates in the rotating magnetic field—its long axis follows the field, which is reminiscent of a rotation; nevertheless, the torque exerted on the surrounding fluid is zero. We compare the analytic results with boundary element simulation to determine their accuracy and the limits of the small deformation theory.

New, Spherical Solutions of Non-Relativistic, Dissipative Hydrodynamics.

We present a new family of exact solutions of dissipative fireball hydrodynamics for arbitrary bulk and shear viscosities. The main property of these solutions is a spherically symmetric, Hubble flow field. The motivation of this paper is mostly academic: we apply non-relativistic kinematics for simplicity and clarity. In this limiting case, the theory is particularly clear: the non-relativistic Navier–Stokes equations describe the dissipation in a well-understood manner. From the asymptotic analysis of our new exact solutions of dissipative fireball hydrodynamics, we can draw a surprising conclusion: this new class of exact solutions of non-relativistic dissipative hydrodynamics is asymptotically perfect.

A Vortex Lattice Method for the Hydrodynamic Solution of Lifting Bodies Traveling Close and Across a Free Surface

The hydrodynamics performance of submerged and surface-piercing lifting bodies is analyzed by a potential flow model based on a Vortex Lattice Method (VLM). Such a numerical scheme, widely applied in aerodynamics, is particularly suitable to model the lifting effects thanks to the vortex distribution used to discretize the boundaries of the lifting bodies. The method has been developed with specific boundary conditions to account for the development of steady free surface wave patterns. Both submerged bodies, such as flat plates and hydrofoils, as well as planing hulls can be studied. The method is validated by comparison against available experimental data and other Computational Fluid Dynamic (CFD) results from Reynolds Averaged Navier Stokes (RANS) approaches. In all the analyzed cases, namely 2D and 3D flat plates, a NACA hydrofoil, planning flat plates and prismatic planing hulls, results have been found to be consistent with those taken as reference. The obtained hydrodynamic predictionsare discussed highlighting the advantages and the possible improvements of the developed approach.

Bitensorial formulation of the singularity method for Stokes flows

<abstract><p>This paper develops the bitensorial formulation of the system of singularities associated with unbounded and bounded Stokes flows. The motivation for this extension is that Stokesian singularities and hydrodynamic fundamental solutions are multi-point functions, and bitensor calculus provides either the proper geometrical setting, in order to avoid inconsistencies and misunderstandings on the role of the different tensorial indices, or a way for compactly deriving hydrodynamic properties. A first relevant result is to provide a clear definition of the singularities (both bounded and unbounded) in Stokes flow, specifying the associated differential equations and boundary conditions. Using this formalism for bounded flows, we show the existence of an integro-differential operator providing the whole system of hydrodynamic singularities by acting on the unbounded Green function (Stokeslet) at its pole and we derive its explicit representation in terms of moments. In the case of an immersed body in a unbounded fluid, we show that, the operator furnishing the disturbance field of a purely $ n $-th order <italic>ambient</italic> flow, is a generalized $ n $-th order Faxén operator, i.e., it yields the $ n $-th moment on the body if applied to a generic <italic>ambient</italic> flow, and that a generic disturbance field can be expressed by a summation of the generalized $ n $-th order Faxén operators. Furthermore, we find that the operator providing the disturbance of an ambient flow coincides with the reflection operator for the Stokes solutions in the same flow geometry. We apply this result to the paradigmatic case of fundamental singularities for the Stokes flow bounded by a plane. In this way, we obtain in an alternative and easy way the image system for the Sourcelet and the Rotlet (already derived in the literature) and for the Source Doublet and the Strainlet (presented here for the first time).</p></abstract>

Течение маслосодержащего материала в канале шнека маслопресса

The paper presents an analysis of the basic operational concepts for the screw channel of the oil press. The channel is chosen by the authors as the object of research. The subject of the study is the the flow velocities distribution for the oil-containing material in the channel of the local auger of the second section of the oil press and the influence of the channel parameters on the performance of the press. The mathematical modeling of the flow of oil-containing material in the channel of the oil press screw is used as a research method. Of the proposed simplifying assumptions for the flow in the auger channel, three assumptions are considered and further developed. The cross section of the channel is assumed to be rectangular. The developed hydrodynamic model, in contrast to previously published works, takes into account the presence of a gap δ between the edge of the screw spiral and the inner surface of the pressing cage, as well as the non-uniformity of the movement velocity for points on the screw. A fundamentally new point in the formulation of the problem is that the velocity is not assumed to be constant on the side walls of the channel. The coordinate dependence of the velocity vz on the rectangular boundaries of the screw is presented. The flow of viscoplastic material is obtained in the form of four components, which are determined by the pressure gradient, the flow of material along the axis of the screw channel, the movement of the side walls of the channel and the viscoplastic material through the gap between the screw spiral and the pressing cage. Simple analytical expressions containing only simple elementary functions are derived for the flow velocity of a viscoplastic material. The found solutions of hydrodynamics use the Newtonian model of fluid flow but can be easily generalized to non-Newtonian Bingham viscoplastic rheology. The results demonstrated can be employed to optimize the parameters of the oil press augers, increase its productivity and oil yield.

Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion

We have studied analytically the longitudinally boost-invariant motion of a relativistic dissipative fluid with spin. We have derived the analytic solutions of spin density and spin chemical potential as a function of proper time $\ensuremath{\tau}$ in the presence of the viscous tensor and the second order relaxation time corrections for spin. Interestingly, analogous to the ordinary particle number density and chemical potential, we find that the spin density and spin chemical potential decay as $\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1}$ and $\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{-}1/3}$, respectively. These solutions can serve both to gain insight on the dynamics of spin polarization in relativistic heavy-ion collisions and as test beds for further numerical codes.

Irradiation-driven escape of primordial planetary atmospheres

Intense X-ray and ultraviolet stellar irradiation can heat and inflate the atmospheres of closely orbiting exoplanets, driving mass outflows that may be significant enough to evaporate a sizable fraction of the planet atmosphere over the system lifetime. The recent surge in the number of known exoplanets, together with the imminent deployment of new ground and space-based facilities for exoplanet discovery and characterization, requires a prompt and efficient assessment of the most promising targets for intensive spectroscopic follow-ups. For this purpose, we developed ATmospheric EScape (ATES), a new hydrodynamics code that is specifically designed to compute the temperature, density, velocity, and ionization fraction profiles of highly irradiated planetary atmospheres, along with the current, steady-state mass loss rate. ATES solves the one-dimensional Euler, mass, and energy conservation equations in radial coordinates through a finite-volume scheme. The hydrodynamics module is paired with a photoionization equilibrium solver that includes cooling via bremsstrahlung, recombination, and collisional excitation and ionization for the case of a primordial atmosphere entirely composed of atomic hydrogen and helium, whilst also accounting for advection of the different ion species. Compared against the results of 14 moderately to highly irradiated planets simulated with The PLUTO-CLOUDY Interface (TPCI), which couples two sophisticated and computationally expensive hydrodynamics and radiation codes of much broader astrophysical applicability, ATES yields remarkably good agreement at a significantly smaller fraction of the time. A convergence study shows that ATES recovers stable, steady-state hydrodynamic solutions for systems with log(−Φp)≲12.9 + 0.17 log FXUV, where Φp and FXUV are the planet gravitational potential and stellar flux (in cgs units). Incidentally, atmospheres of systems above this threshold are generally thought to be undergoing Jeans escape. The code, which also features a user-friendly graphic interface, is available publicly as an online repository.

New Hydrodynamic Solutions for Line-driven Winds of Hot Massive Stars Using the Lambert W-function

Abstract Hot massive stars present strong stellar winds that are driven by absorption, scattering, and reemission of photons by the ions of the atmosphere (line-driven winds). A better comprehension of this phenomenon, and a more accurate calculation of hydrodynamics and radiative acceleration, is Required to reduce the number of free parameters in spectral fitting and to determine accurate wind parameters such as mass-loss rates and velocity profiles. We use the non-LTE model-atmosphere code CMFGEN to numerically solve the radiative transfer equation in the stellar atmosphere and to calculate the radiative acceleration g rad(r). Under the assumption that the radiative acceleration depends only on the radial coordinate, we solve analytically the equation of motion by means of the Lambert W-function. An iterative procedure between the solution of the radiative transfer and the equation of motion is executed in order to obtain a final self-consistent velocity field that is no longer based on any β-law. We apply the Lambert-procedure to three O supergiant stars (ζ Puppis, HD 165763, and α Cam) and discuss the Lambert solutions for the velocity profiles. It is found that, even without recalculation of the mass-loss rate, the Lambert-procedure allows the calculation of consistent velocity profiles that reduce the number of free parameters when a spectral fitting using CMFGEN is performed. Synthetic spectra calculated from our Lambert solutions show significant differences compared to the initial β-law CMFGEN models. The results indicate the importance of consistent velocity profile calculation in the CMFGEN code and its use in a fitting procedure and interpretation of observed spectra.

Hydrodynamic attractor in a Hubble expansion

We analytically investigate hydrodynamic attractor solutions in both M\"{u}ller-Israel-Stewart (MIS) and kinetic theories in a viscous fluid system undergoing a Hubble expansion with a fixed expansion rate. We show that the gradient expansion for the MIS theory and the Chapman-Enskog expansion for the Boltzmann equation within the relaxation time approximation are factorially divergent and obtain hydrodynamic attractor solutions by applying the Borel resummation technique to those asymptotic divergent series. In both theories, we find that the hydrodynamic attractor solutions are globally attractive and only the first-order non-hydrodynamic mode exists. We also find that the hydrodynamic attractor solutions in the two theories disagree with each other when gradients become large, and that the speed of the attraction is different. Similarities and differences from hydrodynamic attractors in the Bjorken and Gubser flows are also discussed. Our results push the idea of far-from-equilibrium hydrodynamics in systems undergoing a Hubble expansion.

Non-equilibrium steady state formation in 3+1 dimensions

We present the first holographic simulations of non-equilibrium steady state formation in strongly coupled \mathcal{N}=4𝒩=4 SYM theory in 3+1 dimensions. We initially join together two thermal baths at different temperatures and chemical potentials and compare the subsequent evolution of the combined system to analytical solutions of the corresponding Riemann problem and to numerical solutions of ideal and viscous hydrodynamics. The time evolution of the energy density that we obtain holographically is consistent with the combination of a shock and a rarefaction wave: A shock wave moves towards the cold bath, and a smooth broadening wave towards the hot bath. Between the two waves emerges a steady state with constant temperature and flow velocity, both of which are accurately described by a shock+rarefaction wave solution of the Riemann problem. In the steady state region, a smooth crossover develops between two regions of different charge density. This is reminiscent of a contact discontinuity in the Riemann problem. We also obtain results for the entanglement entropy of regions crossed by shock and rarefaction waves and find both of them to closely follow the evolution of the energy density.

Dispersive Riemann problems for the Benjamin–Bona–Mahony equation

AbstractLong time dynamics of the smoothed step initial value problem or dispersive Riemann problem for the Benjamin‐Bona‐Mahony (BBM) equation are studied using asymptotic methods and numerical simulations. The catalog of solutions of the dispersive Riemann problem for the BBM equation is much richer than for the related, integrable, Korteweg‐de Vries equation . The transition width of the initial smoothed step is found to significantly impact the dynamics. Narrow width gives rise to rarefaction and dispersive shock wave (DSW) solutions that are accompanied by the generation of two‐phase linear wavetrains, solitary wave shedding, and expansion shocks. Both narrow and broad initial widths give rise to two‐phase nonlinear wavetrains or DSW implosion and a new kind of dispersive Lax shock for symmetric data. The dispersive Lax shock is described by an approximate self‐similar solution of the BBM equation whose limit as is a stationary, discontinuous weak solution. By introducing a slight asymmetry in the data for the dispersive Lax shock, the generation of an incoherent solitary wavetrain is observed. Further asymmetry leads to the DSW implosion regime that is effectively described by a pair of coupled nonlinear Schrödinger equations. The complex interplay between nonlocality, nonlinearity, and dispersion in the BBM equation underlies the rich variety of nonclassical dispersive hydrodynamic solutions to the dispersive Riemann problem.

Hydrodynamic solutions of radiation driven wind from hot stars

AbstractWe show the application of the δ- and Ω-slow hydrodynamical solutions to describe the velocity profiles of massive stars. In particular, these solutions can help to unravel some of the problems within the winds of massive stars such as the approximation of the β-law for the velocity profile of B supergiant stars and the slow outflow wind observed in Be stars.

ISOSCELES: Grid of stellar atmosphere and hydrodynamic models of massive stars. The first results

AbstractIn this work we seek to derive simultaneously the stellar and wind parameters of massive stars, mainly A and B type supergiant stars. Our stellar properties encompass the effective temperature, the surface gravity, the micro-turbulence velocity and, silicon abundance. For wind properties we consider the line–force parameters (α, k and δ) obtained from the standard line-driven wind theory. To model the data we use the radiative transport code Fastwind considering the hydrodynamic solutions derived with the stationary code Hydwind. Then, ISOSCELES, a grid of stellar atmosphere and hydrodynamic models of massive stars is created. Together with the observed spectra and a semi-automatic tool the physical properties from these stars are determined through spectral line fittings. This quantitative spectroscopic analysis provide an estimation about the line–force parameters. In addition, we confirm that the hydrodynamic solutions, called δ-slow solutions, describe quite reliable the radiation line-driven winds of B supergiant stars.

Implementation of Direct Acoustic Simulation using ANSYS Fluent

Direct Acoustic Simulation (DAS) is a powerful Computational Aero Acoustics method that obtains hydrodynamic and acoustic solutions simultaneously by solving compressible Navier-Stokes equation together with state equation of ideal gas. Thus, DAS has advantages for cases with flow acoustic coupling and high Mach numbers (). With an increasing demand of massive-scale calculations, a robust numerical solver for DAS is required. ANSYS Fluent is a suitable CFD platform with proven robustness. However, there is no direct implementation of DAS in the current version of ANSYS Fluent. The present study, therefore, aims to investigate an approach for implementing DAS using ANSYS Fluent. Given the acoustic part of fluctuations is much smaller than the hydrodynamic part in amplitude, a DAS solver requires high accuracy and low dissipation. Based on these needs, proper solution methods, spatial discrete methods and boundary conditions are firstly determined through simple calculations of two dimensional propagating plane waves. Afterwards aeroacoustics of a two-dimensional cavity flow at 0.6 is calculated to verify the capability for solving separating flow with the aforementioned set-up. Finally, aeroacoustics of a cylindrical bluff body at a turbulent regime and 0.2 is calculated in three-dimensions to verify the capability for solving turbulent flow using Monotonically Integrated Large Eddy Simulation.

Hydrodynamic disk solutions for Be stars using HDUST

Abstract. In this work, we implemented a hydrodynamical solution for fast rotating stars, which leaves high values of mass-loss rates and low terminal velocities of the wind. This 1D density distribution adopts a viscosity mimicking parameter which simulates a quasi-Keplerian motion. Then, it is converted to a volumetric density considering vertical hydrostatic equilibrium using a power-law scale height, as usual in viscous decretion disk models. We calculate the theoretical hydrogen emission lines and the spectral energy distribution utilizing the radiative transfer code HDUST. Our disk-wind structures are in agreement with viscous decretions disk models.

Application of Large Eddy Simulation to Predict Underwater Noise of Marine Propulsors. Part 2: Noise Generation

Methods to predict underwater acoustics are gaining increased significance, as the propulsion industry is required to confirm noise spectrum limits, for instance in compliance with classification society rules. Propeller–ship interaction is a main contributing factor to the underwater noise emissions by a vessel, demanding improved methods for both hydrodynamic and high-quality noise prediction. Implicit large eddy simulation applying volume-of-fluid phase modeling with the Schnerr-Sauer cavitation model is confirmed to be a capable tool for propeller cavitation simulation in part 1. In this part, the near field sound pressure of the hydrodynamic solution of the finite volume method is examined. The sound level spectra for free-running propeller test cases and pressure pulses on the hull for propellers under behind ship conditions are compared with the experimental measurements. For a propeller-free running case with priory mesh refinement in regions of high vorticity to improve the tip vortex cavity representation, good agreement is reached with respect to the spectral signature. For behind ship cases without additional refinements, partial agreement was achieved for the incompressible hull pressure fluctuations. Thus, meshing strategies require improvements for this approach to be widely applicable in an industrial environment, especially for non-uniform propeller inflow.

Forecasting Underground Water Dynamics within the Technogenic Environment of a Mine Field. Case Study

The objective is to analyze the dynamics of the underground water of a mine field based on the study of the geofiltration process of the rock mass disturbed by mining to achieve safe extraction operations as well as subsurface territories at the stage of the mining enterprise closure. Numerical modeling, based on a finite difference method under the conditions of multifactority and definite uncertainty of processes of transformation of technogenic environment of a mine field, helps solve a problem concerning underground water dynamics forecasting. A hydrodynamic model of the M.I. Stashkov mine was developed while solving option series of epignosis problems in terms of the chronology of mine field stoping. The abovementioned made it possible to identify regularities of the history of filtration, the capacity parameters of rock mass and the expansion of areas of heightened hydraulic conductivity as well as to evaluate qualitatively the water balance components of a carbonic watered formation and an overlying one. The stage of mining closure helped obtain the forecasting hydrodynamic solutions. The efficiency of measures, concerning reduction of water ingress into mine workings and the mitigation of surface ecological effects of mine flooding was evaluated quantitatively. It was determined that implementation of the water control procedures makes it possible to perform a 10–38% decrease in water ingress. In this context, they may be applied both independently and simultaneously. In terms of mine closure and flooding, a period of complete underground water recovery takes three years; in the process, surface zones of potential waterlogging and swamping are developed within the floodplain of Samara River, located at the territory of Western Donbas (Ukraine). The scientific novelty is to define regularities of hydraulic conductivity transformation of the rock mass of a mine field starting from the mine working roof fall, up to its compaction during the mine operation period. To do that, nonstationary identification problems were solved, using numerical modeling. The abovementioned makes it possible to improve the reliability of hydrodynamic prognoses and develop technological schemes to control water at the state of the mine closure.

MHD thermal boundary layer flow of a Casson fluid over a penetrable stretching wedge in the existence of nonlinear radiation and convective boundary condition

In this paper, we discuss the solution of the magneto hydrodynamics (MHD) thermal boundary layer flow of Casson liquid over a penetrable extending wedge with ohmic heating and convective boundary condition (BC). Important applications of such flows and condition include the MHD pump, radiation therapy, MHD generator, soil mechanics, melt spinning process, thermal insulation and many others. Practical applications of convective BC are often encountered in laser damage or laser processing. The problem is non dimensionalized and computational solutions are achieved for the governing nonlinear coupled ordinary differential equations (PDEs) by using homotopy analysis method (HAM) and influence of various emerging parameters on momentum and temperature field are examined. A table containing computational data for the wall shear stress f′′(0) and local Nusselt -θ′(0) number is also provided. Major findings/objectivesof the present study are: an increasing in Casson fluid parameter δ decreases velocity when wedge stretches faster than free stream velocity for R=2. However, velocity increases for R=0.1 case. Temperature velocity decreases for R=2 or R=0.1 cases for δ escalations. Enhancing Bi for convective heat transfer increases the momentum and thermal boundary layer thickness in the presence of suction C. Computational outcomes for velocity, drag force, temperature velocity and heat transfer rate are discussed through tables numerically. Results are verified with varied choices of suction parameter C. It is noted that the convective parameter magnified the heat transfer rate.

FES2014 global ocean tide atlas: design and performance

Abstract. Since the mid-1990s, a series of FES (finite element solution) global ocean tidal atlases has been produced and released with the primary objective to provide altimetry missions with tidal de-aliasing correction at the best possible accuracy. We describe the underlying hydrodynamic and data assimilation design and accuracy assessments for the latest FES2014 release (finalized in early 2016), especially for the altimetry de-aliasing purposes. The FES2014 atlas shows extremely significant improvements compared to the standard FES2004 and (intermediary) FES2012 atlases, in all ocean compartments, especially in shelf and coastal seas, thanks to the unstructured grid flexible resolution, recent progress in the (prior to assimilation) hydrodynamic tidal solutions, and use of ensemble data assimilation technique. Compared to earlier releases, the available tidal constituent's spectrum has been significantly extended, the overall resolution has been augmented, and additional scientific byproducts such as loading and self-attraction, energy diagnostics, or lowest astronomical tides have been derived from the atlas and are available. Compared to the other available global ocean tidal atlases, FES2014 clearly shows improved de-aliasing performance in most of the global ocean areas and has consequently been integrated in satellite altimetry geophysical data records (GDRs) and gravimetric data processing and adopted in recently renewed ITRF standards (International Terrestrial Reference System, 2020). It also provides very accurate open-boundary tidal conditions for regional and coastal modelling.

Tsunami Squares modeling of landslide tsunami generation considering the ‘Push Ahead’ effects in slide/water interactions: Theory, experimental validation, and sensitivity analyses

Landslide tsunami generation is a complex physical process that involves solid materials interacting with water bodies and other 3D nonlinear wave effects. Modeling of this process ranks as an urgent task because wave source features are crucial clues for subsequent tsunami motions and hazards threatening coastlines. Herein, we introduce a concept of ‘Push Ahead’ (PA) in landslide/water interactions and propose a PA formulation integrated in a meshless numerical procedure named ‘Tsunami Squares’ (TS) for modeling of landslide tsunami generation. We draw comparisons on the physical significances of PA acceleration versus ‘Drag Along’ (DA) acceleration and conventional aerodynamic and hydrodynamic solutions. We carry out physical experiments of wave generation by block-dragging and gravel flows and corresponding TS simulations to study PA effects in landslide/water interactions. Wave features in TS simulations match the experimental observations in a reasonable range, providing a firm validation of the PA formulation in the TS approach. Sensitivity analysis that compares simulations with various ratios of PA acceleration is carried out both for the block-dragging and gravel flow experiments. The comparisons indicate that PA acceleration plays an important role in landslide wave generation and that larger PA accelerations make greater contributions to the initial wave source. We discuss intrinsic relations between PA formulation and the empirical equations derived from previous experiment studies that support the validity and applicability of the PA solution. We also insist that the complex 3D wave effects such as dispersion, shoaling, refraction, reflection and superposition, occurring in the experiments can be well reproduced in the TS simulations. The newly proposed PA acceleration that works together with our previously presented ‘Drag Along’ and ‘Lift Up’ effects can excellently illustrate the mechanical process of landslide water interactions. We conclude that TS simulations that do not include the ‘Push Ahead’ acceleration can seriously underestimate landslide tsunami size. • Development of a ‘Push Ahead’ acceleration in TS modeling of landslide/water interactions. • Model validation with well-designed experiments of waves generated by block slide and gravel flow. • Sensitivity analysis of the ‘Push Ahead’ acceleration that affects landslide tsunami generation. • Discussion on intrinsic relations between PA formulation and the empirical equations.