Hydrodynamic Equations Research Articles

Mathematical Model and Theoretical Investigation of the Performance of Journal Bearing using a discretized Reynolds Lubrication Equation with Finite Width

Hydrodynamic journal bearings are widely used for a large number of applications such as rotating turbo machinery, axial flow compressors, axial flow turbines, and internal combustion engines. These types of journals are used to support high loads high speed rotating turbo machinery elements mainly shafts and attached components and also for enhancing the quality of these machines. In this work, the importance of journal bearing and an overview of the Reynolds hydrodynamic equation in three dimensions have been studied using the Boundary Value finite-difference method. The second-order nonlinear partial differential equation has been solved using numerical iterations approach with MATLAB software. The numerical solution of the transient Reynolds equation has been studied to investigate the Pressure distribution, pressure gradient as well film lubricant thickness on journal bearings. A numerical solution using ANSYS FLUENT has been applied to investigate the main parameters that have the main influence on the performance of the journal bearing and bearing performance.

Theoretically modeling oscillations and waves (EEG and MEG signals) of the brain neuronal fluids and extracellular fluids, using plasma hydrodynamics

Introduction: Ionic oscillations and waves of the brain neurons are mostly analyzed and recorded by EEG (electroencephalography) and (or) MEG (magnetoencephalography). In principle EEG and MEG signals arise from the same neuronal sources. The traditional models of EEG and MEG do not involve natural excitations and attenuations, encodings (decodings), displacement currents of the brain neuronal electromagnetic signals, nor active pumps and passive channels of biological ions. Besides, we have not found any published research at an ionic level to theoretically describe the mechanisms how oscillations and waves of the brain neuronal fluids and extracellular fluids are excited, attenuated and maintained in the both natural and forced modes. Methods and Results: We introduce the plasma physics into brain theory; based on plasma hydrodynamic equations and published data of the brain or neuron sciences and molecular biology, at an ionic level, we model the mechanisms of the complete procedures of excitations, attenuations, propagations (oscillations and waves) of the brain neuronal fluids and extracellular fluids in the both natural and forced modes; our models include active pumps and passive channels of biological ions. Moreover, we also elucidate frequency and amplitude modulations (encodings), displacement currents, as well as effective values of the alternating electric current densities, electric and magnetic fields and voltages, based on the modeling results of the brain neuronal and extracellular plasma waves (oscillations). Conclusion: Our modeling results are qualitatively consistent with the published data of brain neuroscience as well as EEG and MEG.

Simulation of a new process of mixing liquid metal in CCM mold with rotating cooling jacket with vertical ribs

The article proposes a new technology of filling the CCM mold with liquid metal and mixing it. The original patented device consists of a closed bottom nozzle and a rotating jacket. Experimental studies of liquid metal flow in a mold are long, complex and time-consuming, therefore, in the work was used mathematical modeling by numerical method. The objects of research are the hydrodynamic and thermal flows of liquid metal during the new process of steel casting into a CCM mold of rectangular cross-section, and the result is a spatial mathematical model that describes the flows and temperatures of liquid metal in the mold. To simulate the processes occurring during the metal flow in the mold, the authors used a specially crea­ted software package. The theoretical calculations are based on the fundamental equations of hydrodynamics, the equations of mathematical physics (equation of thermal conductivity taking into account mass transfer) and a proven numerical method. The area under study is divided into elements of finite dimensions, for each element a formulated system of equations is written in a difference form. The result is the velocity and temperature fields of the metal flow in the mold volume. According to the developed numerical schemes and algorithms, a calculation program was compiled. The paper considers an example of calculating the steel casting into a mold of rectangular cross-section and flow diagrams of liquid metal over various mold sections. Vector flows of liquid metal in various mold sections are clearly presented for different rotary speed of the rotating jacket. The authors identified the areas of intense turbulence and presented the results of the problem numerical solution in graphical form by diagrams of the velocity fields of liquid metal flows and their temperature over various mold sections.

CFD simulation of two-phase flow in a batch-mode electrodialysis of lithium sulphate: Effect of gas evolution

Electrodialysis (ED) of Li2SO4 plays a crucial role in the closed-loop recycling of lithium-ion batteries. The enhanced flexibility and energy efficiency of batch-mode EDs highlight the significance of time-dependent models. The gaseous molecules evolved from electrochemical reactions induce localized turbulence, significantly impacting the velocity, potential, and concentration distributions. This study presents a two-phase model that analyzes the dynamic behaviour of a batch-mode Li2SO4 ED and investigates the bubbles’ impact employing an Euler-Euler model. The finite element method solves time-dependent hydrodynamic, mass conservation, and electrochemical equations. The model shows close agreement with experimental data, and incorporating the two-phase model reduces the concentration error from 20.6% to 10.3%. Bubbles-induced liquid circulation by buoyant and drag forces reduces concentration polarization, increasing transmembrane ionic fluxes and improving ED performance. Although bubbles increase ohmic overpotential, the enhanced ionic concentrations in concentrate channels due to bubble-induced liquid circulation reduce electrolyte resistance. Raising the inlet flowrate reduces the gas fraction and diminishes solution circulation.

A novel methodology in analyzing nonlinear stability of two electrified viscoelastic liquids

The aim of this study is to analyze the nonlinear stability of two viscoelastic electrified superimposed liquids immersed in porous media. Two limitless horizontal semi-infinite electrified fluids make up the present structure. The impacts of an unchanged oblique electric field (EF) and surface tension (ST) are applied. The increasing attraction of atmospheric and oceanic dynamics is fundamental to understanding this issue. The viscous potential flow (VPF) is employed to make mathematical usage easier. The concern mainly relies on combining the essential hydrodynamic equations with Maxwell's equations in an approximately quasi-static style. The linearized controlling equations are addressed to achieve the nonlinear expression under the appropriate boundary conditions (BCs). Subsequently, the influences of viscoelasticity are ignored, while solving the equations of motion. Therefore, the flat axis and the interface disturbance are interacting horizontally. The Rayleigh Helmholtz-Duffing oscillator (RHDO) describes how the two liquids in the interface spread out. He's frequency formula (HFF) converts the traditional nonlinear differential equation (NDE) into a linear one, which is analyzed through the non-perturbative approach (NPA). As shown through a non-dimensional analysis, there are diverse dimensionless physical numerals. Likewise well-known, the non-dimensional physical characteristics could be employed to investigate the fundamental aspects of a liquid structure. Additionally, they applied to degeneration the number of characteristics needed to understand the construction. A brief description of the NPA is likewise provided. The real/complex features of the NDEs are revealed via the stability research. According to the numerical simulations, the entire system is stabilized by different situations of the oblique EF versus the horizontal wavenumber. For both real and complex components, diverse sorts of polar plots are exhibited by graphs to elucidate the impacts of diverse elements and ensure the stability of the solutions. It should be noticed that all circumstances of the EFs are portrayed. It is observed that, when the EF is tangent to the interface, the Darcy and Bond numbers have a stabilized influence on the stability configuration. Supplementary, when the EF is normal to the interface, it is recognized that dynamic viscosity stabilizes the stability distribution. The density parameter has a destabilized effect on the stability zone. Finally, when the EF is inclined to the interface, it is observed that the Bond number and the viscoelastic parameter have a stabilizing influence on the stability region.

Evolution of nanohillocks by fullerene ion-induced localized plasma

Surface nanostructures etch without chemicals; owing to this, their development is a crucial technical process. Surface nanohillocks may be created by irradiating yttrium iron garnet (YIG) with 30-MeV C60 cluster ions. The nanohillock creation mechanism is disputed. In this study, we propose that the formation mechanism is a plasma collective effect of charged particles that depends on localized rogue waves. Rogue waves will explain YIG surface nanohillock creation using a traditional hydrodynamic plasma model. Analytically solving hydrodynamic ion fluid equations and Maxwellian electron distributions yields a non-linear Schrödinger equation. Solving the latter gives us plausible rogue wave domains. Rogue waves concentrate charged ions from the surroundings into a small, confined zone, generating surface nanohillocks. The relevance of different plasma parameters is highlighted in the rogue wave profile.

Generalized Equations in Quantum Mechanics and Brownian Theory

We discuss formal analogies between a nonlinear Schrödinger equation derived by the author from the theory of scale relativity and the equations of Brownian theory. By using the Madelung transformation, the nonlinear Schrödinger equation takes the form of hydrodynamic equations involving a friction force, an effective thermal pressure, a pressure due to the self-interaction, and a quantum potential. These hydrodynamic equations have a form similar to the damped Euler equations obtained for self-interacting Brownian particles in the theory of simple liquids. In that case, the temperature is due to thermal motion and the pressure arises from spatial correlations between the particles. More generally, the correlations can be accounted for by using the dynamical density functional theory. We determine the excess free energy of Brownian particles that reproduces the standard quantum potential. We then consider a more general form of excess free energy functionals and propose a new class of generalized Schrödinger equations. For a certain form of excess free energy, we recover the generalized Schrödinger equation associated with the Tsallis entropy considered in a previous paper.

On-Chip Integration of a Plasmonic FET Source and a Nano-Patch Antenna for Efficient Terahertz Wave Radiation.

Graphene-based Field-Effect Transistors (FETs) integrated with microstrip patch antennas offer a promising approach for terahertz signal radiation. In this study, a dual-stage simulation methodology is employed to comprehensively investigate the device's performance. The initial stage, executed in MATLAB, delves into charge transport dynamics within a FET under asymmetric boundary conditions, employing hydrodynamic equations for electron transport in the graphene channel. Electromagnetic field interactions are modeled via Finite-Difference Time-Domain (FDTD) techniques. The second stage, conducted in COMSOL Multiphysics, focuses on the microstrip patch antenna's radiative characteristics. Notably, analysis of the S11 curve reveals minimal reflections at the FET's resonant frequency of 1.34672 THz, indicating efficient impedance matching. Examination of the radiation pattern demonstrates the antenna's favorable directional properties. This research underscores the potential of graphene-based FETs for terahertz applications, offering tunable impedance matching and high radiation efficiency for future terahertz devices.

Influence of the centrifugal pump impeller vanes parameters on its energy performance at operating with high-viscosity liquid

BACKGROUND: The currently existing methods for recalculating the operation of centrifugal pumps for viscous fluids cover a sufficiently small range of viscosities. In addition, the considered papers cover the recalculation only, not the search for the optimal geometry of the centrifugal pump for high-viscosity liquids. In this paper, computational fluid dynamics tools were used to test the ability of centrifugal impellers to pump liquids with a viscosity of up to 20,000 sSt, as well as to search for the optimal geometry of the flow path.
 AIM: Determination the dependence pattern of the geometric parameters, including vanes, of the optimal geometry of the centrifugal pump flow path at various values of flow rate and viscosity.
 METHODS: A numerical modeling method based on the solving of discrete analogs of the basic equations of hydrodynamics is used in this paper.
 RESULTS: It was proved that, with the considered viscosities, an impeller with a profiled vane, but with a smaller wrap angle and height, is capable of more efficient operation than a disk impeller. The dependences of the parameters of the optimal flow paths on the characteristics for which their optimization was carried out are given.
 CONCLUSION: Based on the study results, it can be stated that it is advisable to use centrifugal impellers in case of high viscosity of the liquid, taking into account the choice of non-classical values of the geometric parameters of the flow path, including the height and angle of its vanes.

Hydrodynamic Navier-Stokes equations in two-dimensional systems with Rashba spin-orbit coupling

We study a two-dimensional (2D) electron system with a linear spectrum in the presence of Rashba spin-orbit (RSO) coupling in the hydrodynamic regime. We derive a semiclassical Boltzmann equation with a collision integral due to Coulomb interactions on the basis of the eigenstates of the system with RSO coupling. Using the local equilibrium distribution functions, we obtain a generalized hydrodynamic Navier–Stokes equation for electronic systems with RSO coupling. In particular, we discuss the influence of the spin-orbit coupling on the viscosity and the enthalpy of the system and present some of its observable effects in hydrodynamic transport.

Approximate Analytical Solution for Turbulent Flow in Channel

In this work, the approximate analytical solutions of the Generalized Hydrodynamic Equations (GHE) for turbulent flow in channel is presented. The general solution is a superposition of the laminar (parabolic) and turbulent (superexponential) solutions. The analytical solution compares well with the experimental data by Van Doorne (2007) and Nikuradse (1933).It is proposed to explain the nature of turbulence as oscillations between the laminar (parabolic) and turbulent (superexponential) solutions. The suggestion is confirmed by comparing the results for turbulent velocity fluctuations of the analytical formula with the experiment by Van Doorne (2007). The Navier-Stokes equations do not have the superexponential solution.The obtained analytical solution provides a complete structure of the turbulent boundary layer that compares well with the experiments by Wei and Willmarth (1989).

The Effect of the Turbulence Coefficient on the Formation of a Turbulent Process: 2. Existing Scenarios for the Occurrence and Development of Turbulence

Some characteristic features of three scenarios for the occurrence and development of turbulenceare presented: the Landau-Hopf scenario, the scenario of transition to turbulence on a strange attractor, andthe scenario followed by the solutions of the multimoment hydrodynamics equations. The analysis of the presentedcharacteristic features allows us to conclude that these scenarios can be used to interpret turbulence.It is shown that only one of the scenarios satisfactorily interprets the experimental data: the scenario followedby the solutions of the multimoment hydrodynamics equations supplemented with stochastic components.The Landau-Hopf scenario leads to a system that has lost stability in the wrong direction. The scenario of thetransition to turbulence on a strange attractor correctly reproduces only the initial stage of the evolution ofthe liquid layer in the Bénard experiment, namely, heat transfer in the resting layer and convective shafts.Analysis of the behavior of solutions of the Lorentz model leaves no hope for the ability of this scenario tointerpret turbulence

Vectorial active matter on the lattice: polar condensates and nematic filaments

We introduce a novel lattice-gas cellular automaton (LGCA) for compressible vectorial active matter with polar and nematic velocity alignment. Interactions are, by construction, zero-range. For polar alignment, we show the system undergoes a phase transition that promotes aggregation with strong resemblance to the classic zero-range process. We find that above a critical point, the states of a macroscopic fraction of the particles in the system coalesce into the same state, sharing the same position and momentum (polar condensate). For nematic alignment, the system also exhibits condensation, but there exist fundamental differences: a macroscopic fraction of the particles in the system collapses into a filament, where particles possess only two possible momenta. Furthermore, we derive hydrodynamic equations for the active LGCA model to understand the phase transitions and condensation that undergoes the system. We also show that generically the discrete lattice symmetries—e.g. of a square or hexagonal lattice—affect drastically the emergent large-scale properties of on-lattice active systems. The study puts in evidence that aligning active matter on the lattice displays new behavior, including phase transitions to states that share similarities to condensation models.

Schrödinger Symmetry in Gravitational Mini-Superspaces

We prove that the simplest gravitational symmetry-reduced models describing cosmology and black hole mechanics are invariant under the Schrödinger group. We consider the flat FRW cosmology filled with a massless scalar field and the Schwarzschild black hole mechanics and construct their conserved charges using the Eisenhart–Duval (ED) lift method in order to show that they form a Schrödinger algebra. Our method illustrates how the ED lift and the more standard approach analyzing the geometry of the field space are complementary in revealing different sets of symmetries of these systems. We further identify an infinite-dimensional symmetry for those two models, generated by conserved charges organized in two copies of a Witt algebra. These extended charge algebras provide a new algebraic characterization of these homogeneous gravitational sectors. They guide the path to their quantization and open the road to non-linear extensions of quantum cosmology and quantum black hole models in terms of hydrodynamic equations in field space.

Provably convergent Newton–Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics

The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal fluid velocity. However, numerical simulations can violate these constraints, leading to nonphysical results or even simulation failure. Designing genuinely physical-constraint-preserving (PCP) schemes is very difficult, as the primitive variables cannot be explicitly reformulated using conservative variables due to relativistic effects. In this paper, we propose three efficient Newton–Raphson (NR) methods for robustly recovering primitive variables from conservative variables. Importantly, we rigorously prove that these NR methods are always convergent and PCP, meaning they preserve the physical constraints throughout the NR iterations. The discovery of these robust NR methods and their PCP convergence analyses are highly nontrivial and technical. Our NR methods are versatile and can be seamlessly incorporated into any RHD schemes that require the recovery of primitive variables. As an application, we apply them to design PCP finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the RHD equations. Our PCP HWENO schemes incorporate high-order HWENO reconstruction, a PCP limiter, and strong-stability-preserving time discretization. We rigorously prove the PCP property of the fully discrete schemes using convex decomposition techniques. Moreover, we suggest the characteristic decomposition with rescaled eigenvectors and scale-invariant nonlinear weights to enhance the performance of the HWENO schemes in simulating large-scale RHD problems. Several demanding numerical tests are conducted to demonstrate the robustness, accuracy, and high resolution of the proposed PCP HWENO schemes and to validate the efficiency of our NR methods.

Thermocapillary migration of a drop with a thermally conducting stagnant cap

Hypothesis The thermocapillary migration of a spherical drop with a stagnant cap in the presence of a constant applied temperature gradient can be strongly affected by the finite thermal conductivity of the stagnant cap.Numerics The heat conduction of the stagnant cap is analytically modeled. The effects of the additional interfacial stresses generated by the disturbances to the local temperature field due to the presence of the cap at the fluid-fluid interface and the corresponding velocity of migration of the drop are evaluated by solving for the temperature and hydrodynamic field equations in and around the drop. An asymptotic model is derived to predict the terminal velocity in the presence of an infinitely conducting stagnant cap.Findings The effects of the surface conductivity and size of the stagnation region alongside the bulk thermal conductivities and viscosities of the drop and surrounding media are evaluated. The terminal velocity of the drop is shown to have a monotonic dependence on the conductivity of the stagnant cap. The bounds to the terminal velocity increment due to the stagnant cap are derived. These bounds can be of significance to multiphysics problems involving particle laden drops, Pickering emulsions and other multi-phase technologies where the conductivity of the surface adsorbents is non-negligible.

Research on the Secondary Motion of Engine Piston Considering the Transport of Lubricating Oil

<div>At present, it is generally considered in the analysis of the secondary motion of engine piston that the piston skirt–cylinder liner friction pair is fully lubricated in an engine operating cycle. However, in practice, when the piston moves upward, the amount of lubricating oil at the inlet may not ensure that the friction pair is fully lubricated. In this article, the secondary motion of piston is studied when the transport of lubricating oil is considered to determine the lubrication condition of piston skirt–cylinder liner friction pair. The secondary motion of piston is solved based on the combined piston motion model, hydrodynamic lubrication model, asperity contact model, and lubricating oil flow model. The secondary motion equation of piston is solved by the Broyden method. The hydrodynamic lubrication equation is solved by the finite difference method. The asperity contact between piston skirt and cylinder liner is calculated by the Greenwood model. The flow of lubricating oil is analyzed based on the theory of fluid mechanics. The results indicate that, when the actual transport of lubricating oil is considered to determine the lubrication condition of piston skirt–cylinder liner friction pair, the secondary motion of piston is remarkably different from that in which the flooded lubrication is assumed in an engine operating cycle. Therefore, it is helpful to improve the accuracy and make the analysis closer to the actual engine operating situation that the transport of lubricating oil is considered in the analysis of the secondary motion of engine piston.</div>

A new result on the fractal dimension estimates of random attractor for non-autonomous random 2D stochastic dynamical type systems

We prove some conditions for bounding the fractal dimension of random invariant sets of non-autonomous random dynamical systems on separable Banach spaces. Then we apply these conditions to prove the finiteness of fractal dimension of random attractor for stochastic 2D hydrodynamical type equations with linear additive white noise in bounded domains or unbounded domains satisfying the Poincaré inequality.

Numerical model of a gaseous inductive discharge in oxygen, taking into account the complete scheme of the vibrational kinetics of O2 molecules

In this work, the two-dimensional model of inductively coupled plasma discharge in oxygen was developed. The model includes hydrodynamic equations in drift-diffusion approximation for describing the kinetics of charged (electrons and ions) and neutral plasma particles, Maxwell’s equations for electromagnetic fields, and equations for the temperature and neutral gas flow as well as a detailed scheme of plasma-chemical reactions. The model was tested against theoretical and experimental data in a simple cylindrical chamber. The electron density and temperature distributions were obtained over a wide range of powers deposited in the plasma (100–500 W) and compared with literature data. Also, the complete scheme of the vibrational kinetics of O2 molecules was included in the model. The vibrational distribution function was calculated in low-pressure inductive discharge as well as spatial distributions of plasma parameters (density and temperature of electrons, excited components, neutral gas temperature, etc.) and flows of charged and active neutral particles at the reactor walls.

Manipulating Nonlinear Photocurrent from Interlayer Coupling in Bilayer Metamaterials for Polarized Terahertz Generation

AbstractPolarized terahertz (THz) wave generation is of great significance for chiral and anisotropic sensing applications. However, how to manipulate amplitude, polarization, and ellipticity of the THz generation is still a fundamental challenge. Herein, polarized THz wave generation is achieved from a bilayer metamaterial consisting of T‐shaped structure (TSS) and split resonator rings (SRRs) by combining Maxwell and hydrodynamic equations. The elliptically polarized THz wave can be synthetized directly from horizontally and vertically polarized THz components due to the orthogonal nonlinear photocurrents along the arm‐directions of TSS and SRRs, respectively. Besides, the ellipticity and the orientation angle of the THz polarization ellipse can be modulated by the twist angle between the SRRs and TSS layers. The maximum ellipticity can reach 0.34 while the orientation angle is tunable from −0.45 to 0.48π by tuning the twist angle. This work proposes an interlayer coupling method for the polarized THz sources based on metamaterials in potential circular dichroism and chiral sensing applications.