Numerical simulation of thermal problems coupled with magnetohydrodynamic effects in aluminium cell

A system of partial differential equations describing the thermal behavior of aluminium cell coupled with magnetohydrodynamic effects is numerically solved. The thermal model is considered as a two-phases Stefan problem which consists of a non-linear convection–diffusion heat equation with Joule effect as a source. The magnetohydrodynamic fields are governed by Navier–Stokes and by static Maxwell equations. A pseudo-evolutionary scheme (Chernoff) is used to obtain the stationary solution giving the temperature and the frozen layer profile for the simulation of the ledges in the cell. A numerical approximation using a finite element method is formulated to obtain the fluid velocity, electrical potential, magnetic induction and temperature. An iterative algorithm and 3-D numerical results are presented.     

Optimal control asymptotics of a magnetohydrodynamic flow

An optimal multiplicative control problem is considered for a one-dimensional magnetohydrodynamic flow between parallel planes (Hartman flow). The external magnetic field is used as a control function. An optimality system is derived, and the asymptotics of an optimal control with respect to a regularization parameter and the Reynolds number are constructed.     

Numerical simulation of the endolymph flow in a semicircular canal

We present a concept for the simulation of the fluid flow in the semicircular canals of the inner ear. Based on the temporal dynamics of an idealized model configuration we formulate the governing equations and devise a strategy for their numerical solution. We analyze the proposed method and find a numerical instability. This instability is characterized by an error bound which can serve as a guideline for tuning the numerical method to the specific boundary conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of magnetohydrodynamic pulsatile flow in a constricted channel

The present work reports the study of steady and pulsatile flows of an electrically conducting fluid in a differently shaped locally constricted channel in presence of an external transverse uniform magnetic field. The governing nonlinear magnetohydrodynamic equations simplified for low conducting fluids are solved numerically by finite difference method using stream function-vorticity formulation. The analysis reveals that the flow separation region is diminished with increasing values of magnetic parameter. It is noticed that the increase in the magnetic field strength results in the progressive flattening of axial velocity. The variations of wall shear stress with increasing values of the magnetic parameter are shown for both steady and pulsatile flow conditions. The streamline and vorticity distributions in magnetohydrodynamic flow are also shown graphically and discussed.     

Slow magnetohydrodynamic flow past a circular cylinder

Oseen’ approximations are used to study the slow motion of a viscous, incompressible, electrically conducting fluid past a circular cylinder in the presence of a uniform aligned magnetic field. Using series truncation method, the analytical solutions for the first three terms in the Fourier sine series expansion of the stream function are obtained. Numerical values of the tangential drag for different values of magnetic interaction parameter and viscous Reynolds number are calculated.     

Numerical simulation of laminar flow past a circular cylinder

The present paper focuses on the analysis of two- and three-dimensional flow past a circular cylinder in different laminar flow regimes. In this simulation, an implicit pressure-based finite volume method is used for time-accurate computation of incompressible flow using second order accurate convective flux discretisation schemes. The computation results are validated against measurement data for mean surface pressure, skin friction coefficients, the size and strength of the recirculating wake for the steady flow regime and also for the Strouhal frequency of vortex shedding and the mean and RMS amplitude of the fluctuating aerodynamic coefficients for the unsteady periodic flow regime. The complex three dimensional flow structure of the cylinder wake is also reasonably captured by the present prediction procedure.     

Perturbation analysis of a magnetohydrodynamic boundary layer flow

This paper presents a perturbation analysis study of the flow of an electrically conducting power-law fluid in the presence of a uniform transverse magnetic field over a stretching sheet. The perturbation solutions for small and large values of the mixed convection parameter are explored. The asymptotic behavior of the solutions was examined for different values of the power-law index and the magnetic parameter.     

Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer

Numerical simulation is used to study the Kolmogorov flow in a shear layer of a compressible inviscid medium. A periodic permanent force applied to the flow gives rise to a vortex cascade of instabilities. The influence exerted by the size of the computational domain, the initial conditions, and the amplitude of the force on the formation of an instability cascade and the transition to turbulence is studied. It is shown that the mechanism of the onset of turbulence has an essentially three-dimensional nature. For the turbulent flows computed, the classical Kolmogorov ?5/3 power law holds in the inertial range.     

Heat transfer to magnetohydrodynamic flow in a flat duct

Zusammenfassung Die Untersuchung befasst sich mit der Wärmeübertragung von den Wänden eines flachwandigen Kanals auf eine elektrisch leitende Flüssigkeit bei erzwungener Laminarströmung und in Gegenwart eines quergerichteten Magnetfeldes. Betrachtet wird der Fall konstanter Wandtemperatur mit variierender innerer Wärmeentwicklung durch viskose und elektrische Energiedissipation. Die massgebende Differentialgleichung wird durch eine Differenzengleichung ersetzt und mit der elektronischen Rechenmaschine gelöst. Als Resultat wird die Nusseltzahl angegeben, für die Prandtlzahl 1, die Hartmannzahlen 0, 4, 10 und die Graetzzahlen von 10 bis 10 000, wobei die Kennzahlen für Zähigkeit und elektrische Feldstärke als Parameter auftreten.     

Numerical simulation of a continuum model for bi-directional pedestrian flow

An algorithm for an extended reactive dynamic user equilibrium model of pedestrian counterflow as a continuum is developed. It is based on a cell-centered high-resolution finite volume scheme with a fast sweeping method for an Eikonal-type equation on an orthogonal grid. A high-order total variation diminishing Runge-Kutta method is adopted for the time integration of semi-discrete equations. The numerical results demonstrate the rationality of the model and efficiency of the algorithm. Some crowd pedestrian flow phenomena, such as dynamic lane formation in bi-directional flow, are observed which are helpful for a global comprehension of pedestrian dynamics. Also, the model can be utilized with different potential applications.     

Numerical simulation of flow of viscoelastic fluids

The paper deals with the numerical calculation of highly viscous, non-newtonian fluid flows in apparatus of mechanical engineering. We use a differential constitutive equation to approximate the real behaviour of technical fluids like polymer melts. By means of calculated flow examples in two and three dimensional geometries we demonstrate the influence of the non-newtonian behaviour. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal control of a magnetohydrodynamic viscous heat-conducting gas flow

The control problem for a one-dimensional flow of a polytropic viscous heat-conducting perfect gas through an interval is considered. The density of external currents is taken as the control. The existence of an optimal control function is proved. Necessary optimality conditions are derived. The compactness of the set of solutions is established.     

Laminar magnetohydrodynamic duct flow in the presence of a magnetic dipole

We study magnetohydrodynamic flow of a liquid metal in a straight duct. The magnetic field is produced by an exterior magnetic dipole. This basic configuration is of fundamental interest for Lorentz force velocimetry (LFV), where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The Lorentz force acts in equal strength but opposite direction on the flow as well as on the dipole. We are interested in the dependence of the velocity on the flow rate and on strength of the magnetic field as well as on geometric parameters such as distance and position of the dipole relative to the duct. To this end, we perform numerical simulations with an accurate finite-difference method in the limit of small magnetic Reynolds number, whereby the induced magnetic field is assumed to be small compared with the external applied field. The hydrodynamic Reynolds number is also assumed to be small so that the flow remains laminar. The simulations allow us to quantify the magnetic obstacle effect as a potential complication for local flow measurement with LFV. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of the flow field of a diffused pneumatic silencer

A diffused pneumatic silencer had been widely used in the pneumatic fields due to its small dimensions and high level of performance in noise reduction. A numerical simulation of its interior and exterior flow field was important for studying the gas flow in the silencer and the flow structure outside the silencer, as well as for understanding the mechanism of the silencer’s noise reduction. A porous media model and the Darcy–Forchheimer principle were used as the basic theoretical models in this paper. The unified governing equations were used here to describe the compressible flow in and out of the silencer. A robust numerical scheme was used to discritize the equations, and the TDBC (Time-dependent boundary conditions) was used to treat the non-reflecting boundaries. The detailed structures of the inner and outer flow fields of the diffused pneumatic silencer were obtained. The simulation results displayed the characteristics of the flow in the silencer. The nature of the flow outside the silencer, comparable with the experimental data, was also obtained.     

Steady compressible Navier-Stokes flow in a square

We investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain Q∈R². We show existence if a solution that is a small perturbation of a constant flow (, ). We also show that this solution is unique in a class of small perturbations of the constant flow . In order to show the existence of the solution we adapt the techniques known from the theory of weak solutions. We apply the method of elliptic regularization and a fixed point argument.     

The non-steady flow in a magnetohydrodynamic shock-wave generator of finite length

Zusammenfassung Durch geeignete Transformationen der diese Vorgänge beschreibenden Grundgleichungen in differentieller Form, Impulssatz, Kontinuitätsgleichung und Energiesatz, können sogenannte Verträglichkeitsbedingungen erhalten werden. Diese gelten entlang den Charakteristiken beziehungsweise den Lebenslinien. Letzteres System von gewöhnlichen, nichtlinearen Differentialgleichungen darf linearisiert werden, sofern die elektromagnetischen Wechselwirkungen mit der Strömung schwach sind. Elementare Integrationen führen dann zu relativ übersichtlichen und einfachen Resultaten. Insbesondere sind die unbekannten Funktionen an drei ausgezeichneten Stellen des -t-Feldes explizite zu bestimmen und die Funktionswerte im übrigen Strömungsfeld lassen sich leicht graphisch ermitteln. Die stromaufwärts reflektierten Druckschwankungen, verursacht durch die elektromagnetische Wechselwirkung im Generator, können nach einer von den Betriebsbedingungen abhängigen Anlaufstrecke zu einem Stoss auflaufen. Die exakte Bestimmung dieser Anlaufstrecke ist im Rahmen der Linearisierung auch möglich. Es ist erstaunlich, wie rasch, gemessen an der Zeit, die die Stosswelle zum Durchlaufen des Generators braucht, die Strömung im Generator stationär wird.     

Numerical simulation of non-Newtonian blood flow in bypass models

The article presents the numerical investigation of non–Newtonian effects of steady blood flow in complete idealized 3–D bypass models, whose native artery is either coronary or femoral with average physiological parameters. Considering the blood to be a generalized Newtonian fluid, the shear–dependent viscosity is described by two well–known macroscopic non–Newtonian models (the Carreau–Yasuda model and the modified Cross model). The results were obtained by own developed computational software based on the pseudo–compressibility approach and on the cell–centred finite volume method defined on unstructured hexahedral grids. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of glottal flow in surgically changed larynx

According to clinical experience the shape of the larynx seems to have a significant impact on the airflow degree and breathing pattern. In this study we perform a set of numerical experiments simulating the glottal flow in surgically changed larynx, where the vocal folds or false vocal are modified. We are aiming to find an optimal geometry of the larynx in terms of easiness for breathing. To this goal we numerically solve the system for weakly compressible Navier–Stokes equations using the finite element method and we compare the airflow resistance and the volumetric flow rate for the set of geometries for inspiration as well as expiration. We discuss the optimal geometry with respect to the quality of breathing. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of flow past a sphere in vertical motion within a stratified fluid

In the present study we consider a viscous fluid, stratified by a diffusive saline agent and compute numerically the flow produced by a solid sphere moving vertically and uniformly. The governing equations describing this situation are solved on a variational grid. The results show the dependence of the boundary-layer separation point and the vanishing of vortices behind the sphere as the stratification increases at moderate Reynolds number flows. Details of the flow, density and pressure fields near the sphere are also shown. Important quantities for engineering use (drags, pressure and skin coefficients) are also computed and displayed in the Richardson vs. Reynolds number space. Comparison with experimental evidence shows and excellent agreement.