Fluid Equations Research Articles

Numerical study of irreversibility analysis on pulsatile flow of blood through a ω-shaped stenotic artery

The mathematical modeling of blood flow in a stenotic blood vessel is very important for understanding the effects of various geometric and rheological parameters on the normal flow of blood. The present study is concerned with the heat and mass transfer in the blood flow of a non-Newtonian fluid through a ω-shaped stenotic arterial segment. The non-Newtonian behavior of blood is described mathematically by employing the constitutive equation of the Herschel-Bulkley fluid. The wall of the artery is considered to be rigid having ω-shaped constriction in its lumen. The mild stenosis assumption is used to simplify the fully coupled momentum, energy, and concentration equations as well as the constitutive equation of the Herschel-Bulkley fluid. Numerical solutions for fluid velocity, temperature, mass concentration, and entropy generation are evaluated by using the explicit finite difference scheme. The effects of various emerging parameters on the velocity, wall shear stress, flow rate, temperature, concentration, and entropy distributions have been analyzed in detail. A comparison between different fluid models has also been presented. It is found that the temperature in the Herschel-Bulkley fluid is marginally lower than that of the Newtonian, Power law, and Bingham fluids whereas an opposite trend is noticed in the case of mass concentration.

Research on two-phase thermo-hydrodynamic lubrication performance considering bubble dynamics

Gas-liquid two-phase fluid in the lubrication gap exist in many important engineering tribo-pairs. Based on the Reynolds equation, the bubble dynamics equation, and the full energy equation for two-phase fluids, the thermo-hydrodynamic lubrication problem in the lubrication gap is investigated. The evolution of the fluid phase composition with operating time and its impact on the thermodynamic properties are studied using the developed model. The mechanisms by which sliding velocity, clearance, surface dilatational viscosity, surface tension, and initial gas volume fraction affect two-phase fluid lubrication behavior are evaluated. The results show that hydrodynamic pressure-driven bubbles eventually condense in the dispersion area and have a major impact on the temperature distribution. Velocity and clearance affect the gas-phase expansion region and initial formation location in the steady state, respectively. The pressure amplitude, bubble expansion, and horizontal and vertical gas phase expansion in the dispersion zone were affected differently by surface dilatational viscosity and surface tension. It becomes difficult to preserve the initial gas-phase composition inside the pressure convergence zone when bubble migration is taken into account, which may be crucial for establishing gas-liquid two-phase lubrication.

FEM-BEM modeling dynamic responses of saturated soil around a fluid-filled lined tunnel subjected to water hammer

Dynamic stress responses of saturated soil around a fluid-filled lined tunnel caused by a water hammer are investigated by a frequency-domain FEM-BEM coupled model. The fluid is modeled as an inviscid and compressible fluid, the lining is modeled by elastic medium and conceptualized as a hollow cylinder of finite length, and the saturated poroelastic medium is adopted to model the soil. Initially, governing equations of fluid and those of lining are solved by FEM in the frequency domain, while those of soil are solved by BEM in the same domain. In the following, fluid, lining, and soil are coupled based on the conditions of deformation compatibility and force balance on their interfaces. Water pressure (inside the tunnel), the distribution of lining displacement and dynamic stress responses of saturated soil generated by the water hammer are presented. It is concluded that the dynamic stresses and the pore pressure change periodically in saturated soil under a water hammer. Modeling soil as an elastic medium inaccurately evaluates the distribution of lining displacement. The soil permeability has a significant influence on the normal stresses of soil and pore pressure but has a slight effect on the shear stresses of soil.

Pressure Based Compressible Solver for Electric Arc-plasma Simulation

The electric arc discharge in a liquid medium is used in several applications such as the sterilization of the liquid by UV radiation, the fracturing of rocks by shock wave, the circuit breakers in oil bath or the forming of mechanical parts. Thus, describing the physics of the arc in a liquid and in particular its interaction with a liquid interface is an important issue to better characterize this type of configuration. However, such a challenging task requires to couple high-fidelity solver for compressible two-phase flows with liquid phase change and a plasma solver to describe the plasma and its interaction with the bubble. To study this type of medium, we use a compressible formulation of the fluid equations. For this purpose, a pressure based solver has been developed for the computation of the energy conservation equation. Moreover, our numerical model uses the immersed boundary method to simulate the solid electrodes. The numerical model is briefly described in this paper and the first results of the electric arc discharge in steam water are presented. To our knowledge this pressure based model has never been used to describe plasmas and electric arc discharge.

Numerical treatment of a magnetized electron fluid model in a 3D simulator of plasma thruster plumes

Simulations of energetic plumes from plasma thrusters are of great interest for estimating performances and interactions with the spacecraft. Both in fully fluid and hybrid (particle/fluid) models, the electron population is described by a set of fluid equations whose resolution by different numerical schemes can be strongly affected by convergence and accuracy issues. The case of magnetized plumes is more critical. Here, the numerical discretization of the electron fluid model of a 3D hybrid simulator of plasma plumes was upgraded from a finite-differences (FD) formulation in a collocated grid to a finite-volumes (FV) approach in a staggered grid. Both approaches make use of structured meshes of different resolutions and are compared in two scenarios of interest: 1) an unmagnetized plasma plume around a spacecraft and 2) a magnetized plume expansion in free space. In both physical scenarios, the FD scheme exhibits a global continuity error related to truncation errors that can be reduced only by refining the mesh. The origin of this error is further investigated and explained here. The FV scheme instead can save much computational time using coarser meshes since it is unaffected by these errors due to the conservativeness of its formulation. The physical advantage of the FV scheme over the FD approach is more evident for magnetized plumes with high Hall parameters since it allows us to reach higher anisotropy conditions, here assessed in order to gain insights into the plume magnetization effects, finding that the already foreseen saturation of circulating electric current occurs for Hall parameters of several hundreds.

Large Time Behavior and Stability for Two-Dimensional Magneto-Micropolar Equations with Partial Dissipation

This paper is devoted to the stability and decay estimates of solutions to the two-dimensional magneto-micropolar fluid equations with partial dissipation. Firstly, focus on the 2D magneto-micropolar equation with only velocity dissipation and partial magnetic diffusion, we obtain the global existence of solutions with small initial in H^s({mathbb {R}}^2)(s>1), and by fully exploiting the special structure of the system and using the Fourier splitting methods, we establish the large time decay rates of solutions. Secondly, when the magnetic field has partial dissipation, we show the global existence of solutions with small initial data in dot{B}^0_{2,1}({mathbb {R}}^2). In addition, we explore the decay rates of these global solutions are correspondingly established in dot{B}^m_{2,1}({mathbb {R}}^2) with 0 le m le s, when the initial data belongs to the negative Sobolev space dot{H}^{-l}({mathbb {R}}^2) (for each 0 le l <1).

First Principles Description of Plasma Expansion Using the Expanding Box Model

Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time, we develop a first principles description of radially expanding plasmas in the EB frame. From this approach, we aim to fill the gap between simulations and theory at microscopic scales to model plasma expansion at the kinetic level. Our results show that expansion introduces non-trivial changes in the Vlasov equation (in the EB frame), especially affecting its conservative form through non-inertial forces purely related to the expansion. In order to test the consistency of the equations, we also provide integral moments of the modified Vlasov equation, obtaining the related expanding moments (i.e., continuity, momentum, and energy equations). Comparing our results with the literature, we obtain the same fluids equations (ideal-MHD), but starting from a first principles approach. We also obtained the tensorial form of the energy/pressure equation in the EB frame. These results show the consistency between the kinetic and MHD descriptions. Thus, the expanding Vlasov kinetic theory provides a novel framework to explore plasma physics at both micro and macroscopic scales in complex astrophysical scenarios.

Effect of Cairns-Tsallis distribution on ion acoustic waves in interstellar medium

Ion acoustic waves (IAWs) in an electron–positron–ion (EPI) plasma are studied as affected by various plasma parameters, e.g., electron density, ion temperature, cold ion cyclotron frequency, nonextensive and nonthermal parameters. Plasma fluid equations have been applied to study the plasma system for which reductive perturbation method (RPM) and small-k expansion method are used to derive the relevant ZK and modified ZK (mZK) equations and the instability growth rate of IAWs, respectively. The effects of nonextensive and nonthermal parameters, external magnetic field, ion–electron temperature ratio and electron density on the dispersion relation, amplitude and width, energy and multi-dimensional instability of IAWs have been shown. It is found that the dispersion relation increases with the increasing nonthermality parameter, but decreases with the increasing nonextensivity parameter. Increasing nonextensive parameter leads to the decreasing soliton energy and the increasing growth rate. Increasing nonthermal parameter leads to the decreasing growth rate. These results will be helpful in the determination of plasma dynamics for electron–positron–ion plasma systems containing Cairns-Tsallis distributed electrons and positrons in interstellar.

Metal-soil interface adhesion in clay clogging during shield tunneling: Theoretical model and experimental validation

Clogging is a major geohazards risk in mechanized tunnelling through cohesive soils. Clay clogging results from the high adhesion between the clay and metal. Based on the water film theory and Reynolds fluid equation, the interfacial adhesion between metal and soil is simplified in this study as viscous hydrodynamic behavior between planes. Considering the influence of capillary force and the viscous force of water film at the interface between metal and soil, a theoretical calculation model of interfacial adhesion between metal and soil is established. The influence of water film thickness and separation rate on the interfacial adhesion between metal and soil is qualitatively analyzed. Then, the adhesion stress between the clay and the metal surface was tested with a pullout test and the influence of moisture content, pullout rates and types of clay minerals on the adhesion stress was analyzed. Finally, the calculation model of adhesion force was compared with the experimental results. The calculation model of soil adhesion stress established in this paper can quantitatively describe the relationship between soil adhesion force and moisture content and can also qualitatively reveal the influence mechanism of soil moisture content on adhesion stress.

Hydrodynamic cumulation mechanism caused by quantum shell effects.

The computational and theoretical analysis carried out in this article demonstrates the existence of a nontrivial mechanism for the compression of a submicron-sized gas bubble formed by a gas of classical ions and a gas of degenerate electrons. This mechanism fundamentally differs from conventional compression mechanisms. It is shown that taking into account the quantum effect of a large spatial scale in the distribution of electrons qualitatively changes the character of cumulative processes. Because of a large-scale electric field caused by quantum shell effects, the compression process is characterized by the formation of multiple shock waves. The values of gas temperature and pressure achieved during compression occur higher by two orders of magnitude as compared with the classical adiabatic regime. The analysis is carried out within the framework of the following model: the dynamics of the electron subsystem is described by equations of a quantum electron fluid, while the hydrodynamic approximation is adopted for the ionic subsystem. The large-scale effect is taken into account by means of effective external field acting on electrons. The theoretical analysis carried out within this approach clarifies the nature of the cumulative process in the system under consideration; some quantitative characteristics obtained with numerical simulation are presented. The possibility of experimental observation of this cumulative mechanism is analyzed. It is suggested that the manifestation of the effect can be observed during laser compression of a system of submicron targets by measuring the neutron yield.

Numerical investigation of wave-cylinder interaction based on a momentum source wave generation method

A momentum source function is constructed for wave generation based on linear wave theory. Based on Navier-Stokes equation and volume of fluid (VOF) method, a three-dimensional numerical wave tank (NWT) is established. Regular and irregular waves can be simulated by applying the momentum source function to NWT, and the expected wave characteristic parameters and wave spectrum are obtained. Furthermore, the load characteristics of two types of cylinders, fully piercing cylinder (FPC) and truncated cylinder (TC), are studied under regular wave field combined with boundary data immersed method (BDIM). Results show that the transverse force exerted on cylinders is dominated by inertial force. And because of the effects of the cylinder on wave profile and drag force, the maximum transverse force occurs soon after the wave node passes through the centerline of the cylinder. Compared with the FPC, the drag force has a greater influence on TC.

Local strong solutions to the stochastic third grade fluid equations with Navier boundary conditions

Local strong solutions to the stochastic third grade fluid equations with Navier boundary conditions

COCONUT-MF: Two-fluid ion-neutral global coronal modelling

Context. The global coronal model COCONUT (COolfluid COronal uNstrUcTured) was originally developed to replace semi-empirical models such as the Wang-Sheeley-Arge model in space weather forecasting chains in order to improve the physical accuracy of the predictions. This model has, however, several simplifications implemented in its formulation to allow for rapid convergence in an operational setting. These simplifications include the assumptions that the plasma is fully ionised, sufficiently collisional, and that quasi-neutrality holds, so that it can be modelled as a single fluid. This means that all interactions with the low-concentration neutral fluid in the corona, such as collisions or charge exchange, are neglected. Aims. In this paper, we have two goals. Firstly, we aim to introduce a novel multi-fluid global coronal model and validate it with simple cases (like a magnetic dipole) as well as with real data-driven applications. Secondly, we aim to investigate to what extent considering a single-fluid plasma in the global coronal model might affect the resulting plasma dynamics, and thus whether the assumptions on which the single-fluid coronal model is based are justified. Methods. We developed a multi-fluid global coronal model following the ideal magnetohydrodynamics (MHD) COCONUT model, COCONUT-MF, which resolves the ion and neutral fluid equations separately. While this model is still steady-state and thus does not resolve unsteady processes, it can account for resistivity, charge exchange, and chemical (ionisation and recombination) and collisional contributions due to the presence of the neutrals in the fluid equations. Results. We present the results of the ion-neutral COCONUT-MF modelling for a magnetic dipole, a minimum of solar activity case (August 1, 2008), and a solar maximum case (March 9, 2016). Through comparison with the ideal MHD results, we confirm that the resolved multi-fluid solver features are physical and also demonstrate the higher accuracy of the applied upwind numerical flux scheme compared to the one used in the original MHD model. Subsequently, we also repeat the multi-fluid simulations while excluding the charge exchange and the chemical and collisional terms to evaluate the effect these terms have on the resulting plasma dynamics. It is observed in numerical results that, despite the very low concentration of neutrals, they still do affect the flow field to a limited but non-negligible extent (up to 5 to 10% locally), with a higher impact being seen in the case of the solar maximum. It is also demonstrated that the collisional terms are primarily responsible for the neutrals adopting the electromagnetic profiles of the ions, while the charge exchange and chemical terms yield the largest thermal effects of the neutrals on the ion plasma. Despite the fact that the coronal plasma is generally assumed to be collisionless, our results show that there is sufficient collisionality in it to couple the two fluids. Conclusions. We present a novel multi-fluid global coronal model that can separately simulate the behaviour of the ion and neutral fluids. Using this model, we also show that in our set-up, in which the chromosphere is not considered and steady-state solutions are assumed, the presence of the neutrals affects the flow field, though to a limited extent. It is shown that this effect is larger when the flow field is more complex due to a higher magnetic activity. This analysis may change in the future when the global coronal model will be extended to include the lower atmospheric layers as well as terms to model coronal heating, radiation, and thermal conduction. To that end, the current model may need to be further calibrated to better represent the different layers of the atmosphere. We presume that the use of the proposed COCONUT-MF set-up will then be necessary and new numerical experiments will need to be performed in order to confirm this hypothesis.

Large‐Amplitude Shocklets With Trapped Hot‐Electrons in Space Plasmas

AbstractLarge‐amplitude stationary electron‐acoustic (EA) waves are studied, which are developed into the shocklets with the passage of time in an unmagnetized non‐isothermal plasma. The latter comprises two groups of electrons; namely the hot and cool electrons that are distinctly characterized by different electron densities and temperatures. On an EA timescale, the cool electrons behave as fluid, while non‐isothermal hot electrons obey the vortex‐like trapped distribution in the background of immobile ions. The nonlinear fluid equations are solved together both analytically and numerically within the framework of diagonalization matrix technique. Various parameters such as the free hot‐to‐trapped hot electron temperature ratio (β), the cool electron density ratio (α), and the cool‐to‐hot electron temperature ratio (σ) are numerically analyzed for dayside auroral zone plasma, showing a significant modification of solitary and shocklet structures. The plasma model is also applied to the electron diffusion region at the earth magnetopause, revealing the potential excitations depending significantly on the trapping parameter. These findings are important for understanding the nonlinear properties and steepening effects of the EA waves, especially in auroral zone and electron diffusion regions of earth's magnetosphere, where different types of electron populations are observed.

Evolution of streamer groups and radical generation in high-voltage multiple-pulse-induced nonthermal plasma

Nonthermal plasmas (NTPs) induced by atmospheric nanosecond multiple-pulse corona discharge have been studied to control pollution generated by combustors, such as boilers, incinerators, and diesel engines. In high-speed short-width high-voltage pulsed corona discharge-induced plasmas, the chemical reactions that occur between multiple pulses and the characteristics of the electron density (denoted by ne) and ozone during the second pulse have not been fully clarified. In this study, we perform quasi-two-dimensional numerical analysis of nonequilibrium NTP induced by a nanosecond positive pulsed corona discharge. The continuum fluid equations for a two-temperature nonequilibrium NTP are used as governing equations. A total of 197 gas phase reactions for 25 chemical species and 21 surface reactions on the inner glass wall surface are considered in an air plasma under atmospheric pressure. We simulate streamer group behavior up to the second pulse and found that ne and the length of streamers change due to chemical reactions between pulses. In addition, we successfully simulated the phenomena of ne reduction and streamer suppression that occur primarily during the second pulse. This is caused by the decrease in potential gradient due to the space and dielectric surface charge build-up. Furthermore, it is confirmed that the ozone formation reaction mainly occurs between pulses. This simulation enables predictions of phenomena in nanosecond positive multiple-pulse plasma systems.

Effect of κ-deformed Kaniadakis distribution on the modulational instability of electron-acoustic waves in a non-Maxwellian plasma

In this paper, the modulational instability (MI) of the high-frequency electron-acoustic waves (EAWs) is reported in a non-Maxwellian plasma composed of two distinct types of electrons and stationary ions. One type of electrons is treated as a cold inertial fluid, whereas the other type is considered as inertialess species following κ-deformed Kaniadakis distribution. The fluid equations to the current model are reduced via a reductive perturbation technique to a nonlinear Schrödinger equation, which is then used to compute the MI and the growth rate of the EAWs. It is instructive to note that the deformation parameter (which develops the Kaniadakis entropy) and the hot-to-cold electron density ratio (hot electron concentration) significantly affect the conditions for MI. The modulated envelope black (dark and gray) solitons are investigated. The current results are beneficial in analyzing the spectrum of the cosmic rays, which violates manifestly the Boltzmann–Gibbs statistics. Moreover, the obtained results can be used to understand the mystery of many observations in stars where the presence of non-Maxwellian particles dominates.

On the shock wave structures in anisotropy magnetoplasmas

In this work, the propagation of nonlinear electrostatic shock wave structures in an anisotropy pressure magnetoplasma composed of warm inertial ions and inertia-less Maxwellian electrons is reported. For this purpose, the technique of reductive perturbation is applied for reducing fluid equations of the current model to the Korteweg–de Vries Burgers (KdVB) equation with a second-order dissipative term and the KdVB–Kuramoto (KBK) equation with both second- and fourth-order dissipative terms. The impact of various plasma parameters, including the parallel ion pressure, perpendicular ion pressure, and dissipation parameter, on the significant characteristics of the shock wave profile is examined and discussed. In addition, a comparison between the profiles of KdVB shocks and KdVB–Kuramoto shocks is reported. We expect that KBK shock wave amplitudes become larger than the KdVB ones by taking the fourth-order dissipative into consideration. Thus, the results of the KBK equation may treat the difference between the theoretical and laboratory results or satellite observations.

A super-real-time three-dimension computing method of digital twins in space nuclear power

Digital twins (DTs) have attracted widespread attention in academia and industry in recent years. It can accurately reflect the physical world in real-time, enabling online monitoring, control, and prediction operations. Their foundation is super-real-time computing and high data representation capabilities. However, current DTs do not achieve 3D super-real-time computing. This study proposes a novel 3D computational method for solving fluid–solid coupling problems in a super-real-time. The method is based on a mixed solution framework that combines traditional numerical methods with deep learning operators. Specifically, the method employs multi-core CPU parallel acceleration to solve the solid equations while leveraging the computing power of GPU to solve the fluid equations. The fluid–solid coupling is achieved through information exchange between the GPU and the multi-core CPU. In addition, the proposed method introduces a new deep learning operator framework based on the DeepONET. The framework is accompanied by a database structure that facilitates model training and validation and a loss function that guides the training. The space nuclear reactor, an improved TOPAZ-II system, was selected to demonstrate its feasibility. Four non-training transient conditions were simulated to test the generalization performance. The results show that the proposed method achieves an average error between the calculated results and reference values below 2.5%, with the average error of thermodynamic parameters below 1.5%. The average deviation between system parameter peak values during the transient process and the reference value was less than 5 s. The result meets the acceptable error level and satisfies the super-real-time requirements with a time acceleration ratio of approximately 1.17, which is 60 times faster than traditional numerical methods. The results demonstrate the accuracy and efficiency of the proposed method for DT.

Brownian dynamics simulations and Ornstein-Zernike equation for charged fluids using the Wolf potential

From a computational point of view, a promising description for charged-stabilized fluids is the so-called Wolf method, which is faster than the standard Ewald summation technique. Using Monte Carlo computer simulations, it was recently shown that the static correlation functions of strong electrolytes obtained with the Wolf potential satisfy the Stillinger–Lovett sum rules, which are a consequence of perfect screening, and are directly related to the local electroneutrality condition and the electrostatic screening within the Debye–Hückel regime. In this contribution, the Wolf potential is adapted to Brownian dynamics simulations to study both the structural and dynamical properties of charged fluids. In addition, we have solved the Ornstein-Zernike equation with the Wolf potential using the HNC closure relation. The resulting radial distributions agree well with the simulation data and previous results obtained with the Ewald technique. Simulation results using Brownian dynamics for weakly charged colloidal dispersions and asymmetric electrolytes are presented. The results include mean square displacement, self-intermediate scattering, and shear relaxation function, with no consideration of hydrodynamic interactions. Including the Wolf potential in Brownian dynamics simulations opens up the possibility of studying interesting transport phenomena in the low Reynolds and Peclet regime, even in those cases where hydrodynamic interactions become relevant.

Analysis of periodic pulsating blood flow of fractional Maxwell power-law fluid in carotid artery with elastic vessel wall

Hemodynamic analysis reveals a highly significant effect on the prevention, diagnosis, and treatment of human vascular diseases. This article goes deeply into the periodic pulsatile blood flow in the carotid artery with an elastic vessel wall. In view of blood rheological experimental data, the constitutive equation of fractional Maxwell power-law fluid with yield stress, which can describe the four characteristics of yield stress, viscoelasticity, shear thinning, and thixotropy is established. Meanwhile, drawing support from the data of pulsatile flow, the finite Fourier series of pressure gradient with a period of 1 s has been proposed. Leading into Hooke’s law can build the fluid-structure coupling boundary condition of blood flow and elastic vessel wall. The numerical solutions are got hold of finite difference method integrated with the newly developed L1-algorithm, and their convergence and stability of which are verified. The axial velocities of blood under different constitutive relationships are compared. The results throw light that other constitutive relationships underestimate the velocity of blood. Furthermore, the flow rate and wall shear stress on different fluid are calculated. It can be concluded that compared with Bingham fluid, the maximum and minimum flow rate/wall shear stress of fractional Maxwell power-law fluid with yield stress increases by 19% and 32%, respectively. The flow rate lags behind the pressure gradient and has time delay effect, on the contrary, the velocity of blood vessel wall is keeping pace with the pressure gradient. The effects of relevant physical parameters on velocity are discussed. In addition, the spatiotemporal distribution of blood flow in cerebral artery and femoral artery are analyzed.