Fluid Equations Research Articles

Global classical solutions for three-dimensional compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in bounded domains

In this paper, we study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a finite number of two-dimensional connected components. We derive the global existence and uniqueness of classical solutions provided that the initial total energy is suitably small. Our result generalizes the Cauchy problems of compressible Navier–Stokes equations with Coulomb force [S. Liu, X. Xu and J. Zhang, Global well-posedness of strong solutions with large oscillations and vacuum to the compressible Navier–Stokes–Poisson equations subject to large oscillations and non-flat doping profile, J. Differ. Equ. 269 (2020) 8468–8508] and compressible MHD equations [H. Li, X. Xu and J. Zhang, Global classical solutions to 3D compressible magnetohydrodynamic equations with large oscillations and vacuum, SIAM J. Math. Anal. 45 (2013) 1356–1387] to the case of bounded domains although tackling many surface integrals caused by the slip boundary condition are complex. The main ingredient of this paper is to overcome the strong nonlinearity caused by Coulomb force, magnetic field, and rotation effect of micro-particles by applying piecewise-estimate method and delicate analysis based on the effective viscous fluxes involving velocity and micro-rotational velocity.

An ANN-PSO approach for mixed convection flow in an inclined tube with ciliary motion of Jeffrey six constant fluid

This study examines how boundary conditions affect the modeling of mixed convection flow in an inclined tube for ciliary motion of a non-Newtonian fluid. Understanding mixed convection flow from this study can be useful for environmental engineering tasks like contaminant dispersion in soil or water bodies. The governing equations for non-newtonian fluid and heat are simplified by assuming low Reynolds numbers and long wavelengths. To solve the momentum problem for velocity and temperature equations, Particle Swarm Optimization (PSO) is employed using an unsupervised artificial neural network method. The proposed approach achieves promising results with up to one hundred (100) independent algorithm evaluation runs to predict the non-Newtonian flow behavior of liquids under different temperature conditions. An efficient way for finding approximations of solutions was the ANN-PSO method with optimized weights and fitness function. The fitness function value decreases when the right weights are chosen, showing that the approximation is becoming more accurate. The temperature is an increasing function of the cilia length factor and inversely proportional to the heat absorption factor near the middle of the channel.

Effect of vertical porous baffle on sloshing mitigation of two-layered liquid in a swaying tank

The sloshing behavior of two-layered liquid in a rectangular sloshing tank with a vertical porous baffle under sway excitation has been investigated using both analytical and numerical methods. The analytical model is developed using the matched eigenfunction expansion method in conjunction with linear potential flow theory. The existence of vertical porous baffle results in energy dissipation by applying the boundary condition that pressure drop across the baffle is proportional only to the quadratic drag term. For comparison, numerical simulations are conducted using computational fluid dynamics (CFD) with unsteady, implicit, and incompressible fluid equations. The study explores the effects of the liquid density ratio, the baffle's porosity, and its submergence depth, on various parameters including the free surface and interfacial elevations, hydrodynamic force on the tank surface, and horizontal force on the baffle. The trends observed in the analytical model align well with the CFD results and experiments. It is found that a fully submerged vertical porous baffle with a porosity close to P = 0.1 leads to stable and less dynamically active sloshing behavior in a two-layered liquid tank.

Nearly Toroidal, Periodic and Quasi-periodic Motions of Fluid Particles Driven by the Gavrilov Solutions of the Euler Equations

We consider the smooth, compactly supported solutions of the steady 3D Euler equations of incompressible fluids constructed by Gavrilov (Geom Funct Anal (GAFA) 29(1):190–197, 2019), and we study the corresponding fluid particle dynamics. This is an ode analysis, which contributes to the description of Gavrilov’s vector field.

IMEX_SfloW2D v2: a depth-averaged numerical flow model for volcanic gas–particle flows over complex topographies and water

Abstract. We present developments to the physical model and the open-source numerical code IMEX_SfloW2D (de' Michieli Vitturi et al., 2019). These developments consist of a generalization of the depth-averaged (shallow-water) fluid equations to describe a polydisperse fluid–solid mixture, including terms for sedimentation and entrainment, transport equations for solid particles of different sizes, transport equations for different components of the carrier phase, and an equation for temperature/energy. Of relevance for the simulation of volcanic mass flows, vaporization and entrainment of water are implemented in the new model. The model can be easily adapted to simulate a wide range of volcanic mass flows (pyroclastic avalanches, lahars, pyroclastic surges), and here we present its application to transient dilute pyroclastic density currents (PDCs). The numerical algorithm and the code have been improved to allow for simulation of sub- to supercritical regimes and to simplify the setting of initial and boundary conditions. The code is open-source. The results of synthetic numerical benchmarks demonstrate the robustness of the numerical code in simulating transcritical flows interacting with the topography. Moreover, they highlight the importance of simulating transient in comparison to steady-state flows and flows in 2D versus 1D. Finally, we demonstrate the model capabilities to simulate a complex natural case involving the propagation of PDCs over the sea surface and across topographic obstacles, through application to Krakatau volcano, showing the relevance, at a large scale, of non-linear fluid dynamic features, such as hydraulic jumps and von Kármán vortices, to flow conditions such as velocity and runout.

Supervised machine learning-based multivariate regression of parallel closures for a high-collisionality deuterium-carbon plasma

Many plasmas of interest in laboratory experiments and space consist of multiple ion species. In tokamak edge plasmas, for instance, ionized impurities expelled from the vessel wall influence plasma transport. When describing multi-species plasmas using fluid equations, we need accurate closure relations to close the set of fluid equations. In this study, we introduce the development of fitting formulas for parallel closures using supervised machine learning, in conjunction with the recent closure theory [J.-Y. Ji, Plasma Phys. Controlled Fusion 65, 075014 (2023)], considering multi-ion collisions and arbitrary ion temperatures. We apply this approach to a high-collisionality deuterium-carbon plasma and demonstrate its effectiveness. The machine learning-based method for developing practical and accurate closures can be extended to a wider range of plasmas.

Global strong solutions of three-dimensional compressible non-isentropic micropolar fluid equations with far field vacuum

We are concerned with the Cauchy problem of three-dimensional (3D) compressible non-isentropic micropolar fluid equations with far field vacuum. With the help of Serrin type blow-up criterion, we show the global existence and uniqueness of strong solutions provided that the initial mass is suitably small. Our work generalizes the result of Huang et al. (2021) [8] to the case that vacuum is allowed at infinity.

Contribution of electromagnetism in lowering entropy in microchannel

The study examined how entropy can be reduced in an asymmetric microchannel with sinusoidal walls by analyzing the flow of an incompressible micropolar fluid that is electrokinetically driven. The study takes into account the effects of Ohmic and viscous dissipation of energy in a magnetohydrodynamic environment. To model electroosmotic phenomena, the Poisson equation and Nernst–Planck equation were used, which were simplified using Debye–Huckel linearization and a small ionic Peclet number. The energy, rotational momentum, mass, and momentum equations for the micropolar fluid were constructed and linearized using a lubrication approach before being solved analytically. The resulting expressions for velocity microrotation and temperature were then used to compute the Bejan number and the formation of entropy number The study also examined the effects of various thermophysical parameters and discussed their potential applications in fields such as biomedical engineering, pharmaceuticals, energy conservation, cancer treatment, and manufacturing. The findings suggest that entropy generation can be reduced by increasing the micropolar coupling number and temperature difference parameter This study provides a theoretical guide for the operation and thermal control of flow actuation systems with asymmetric geometry.

An Evans function for the linearised 2D Euler equations using Hill’s determinant

We study the point spectrum of the linearisation of Euler’s equation for the ideal fluid on the torus about a shear flow. By separation of variables the problem is reduced to the spectral theory of a complex Hill’s equation. Using Hill’s determinant an Evans function of the original Euler equation is constructed. The Evans function allows us to completely characterise the point spectrum of the linearisation, and to count the isolated eigenvalues with non-zero real part. We prove that the number of discrete eigenvalues of the linearised operator for a specific shear flow is exactly twice the number of non-zero integer lattice points inside the so-called unstable disc.

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.