Numerical solution of an extended White–Metzner model for eccentric Taylor–Couette flow

In this study, we have developed a new numerical approach to solve differential-type viscoelastic fluid models for a commonly used benchmark problem, namely, the steady Taylor—Couette flow between eccentric cylinders. The proposed numerical approach is special in that the nonlinear system of discretized algebraic flow equations is solved iteratively using a Newton–Krylov method along with an inverse-based incomplete lower-upper preconditioner. The numerical approach has been validated by solving the benchmark problem for the upper-convected Maxwell model at a large Deborah number. Excellent agreement with the numerical data reported in the literature has been found. In addition, a parameter study was performed for an extended White–Metzner model. A large eccentricity ratio was chosen for the cylinder system in order to allow flow recirculation to occur. We detected several interesting phenomena caused by the large eccentricity ratio of the cylinder system and by the viscoelastic nature of the fluid. Encouraged by the results of this study, we intend to investigate other polymeric fluids having a more complex microstructure in an eccentric annular flow field.     

Resistance law for a turbulent Taylor–Couette flow at very large Taylor numbers

Based on the semi-empirical model of the transport of the specific rate of turbulence energy dissipation, it has been concluded that the resistance laws are observed for a turbulent Taylor–Couette flow between independently rotating coaxial cylinders for very large Taylor numbers.     

Numerically stable fluid–structure interactions between compressible flow and solid structures

We propose a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semi-implicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tⁿ⁺¹ using an implicit pressure, obtained by solving a modified Poisson system. Similar to previous fluid–structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to [17], which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positive-definite by following the methodology of [16]. Because our method handles the fluid–structure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high density-to-mass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluid–structure interactions are not considered) at the fluid–structure interface, and hence naturally handle highly non-linear phenomenon such as shocks, contacts and rarefactions.     

Turbulent flame and the darrieus–landau instability in a three-dimensional flow

The velocity of a weakly turbulent flame influenced by the Darrieus–Landau (DL) instability in a three-dimensional geometry is investigated on the basis of a model nonlinear equation. The equation takes into account realistically large thermal expansion of burning matter, external turbulence and thermal conduction related to small, but finite flame thickness. An external turbulent flow is imitated by a model obeying the Kolmogorov law. The effects of the DL instability and external turbulence are studied, first separately and then as they influence the flame dynamics together for different values of the turbulent intensity, different thermal expansion of the burning matter and different length scales of the hydrodynamic motion controlled by the width of a hypothetic tube with ideally adiabatic walls. The velocity increase obtained is in a good agreement with experimental results in the case of relatively weak turbulent intensity.     

Scattering characteristics of structures of lossy metamaterial–semiconductor cylinders

Here, we present for the first time the rigorous boundary problem solution of the Maxwell’s equations for the determination of scattering characteristics of a structure. The structure consists of a finite set of infinite parallel circular cylinders that can be made of different lossy isotropic materials. We numerically analyzed two structures that differ only in the symmetrical arrangement of semiconductor cylinders in relation to a central metamaterial cylinder. The electrical radii of cylinders can be arbitrary. Both polarizations of the incident microwave are considered in this work. The Poynting vector of the plane microwave that reflected from and transmitted through the structures analyzed here. We investigated dependency on the radius of an arc where are placed the semiconductor cylinders, the semiconductor-specific resistivity, the operating frequency at two radii of the metamaterial cylinder. We discovered that the structure can have features of a band gap photonic crystal dependent on the topology and the polarization of the incident microwave. We have found that the structure can operate as a microwave reflector at the certain radius of the arc on which are located thirteen n-Si cylinders. The Poynting vector is very sensitive to the change of semiconductor-specific resistivity when the incident microwave has the parallel polarization.     

Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method

We present an application of the residual-based variational multiscale turbulence modeling (RBVMS) methodology to the computation of turbulent Taylor–Couette flow at high Reynolds number. We show that the RBVMS formulation globally conserves angular momentum, a feature that is felt to be important for flows dominated by rotation, and that is not shared by standard stabilized formulations of fluid flow. Weak imposition of Dirichlet boundary conditions is employed to enhance the accuracy of the RBVMS framework in the presence of thin turbulent boundary layers near solid walls. Calculation of conservative boundary forces and torques is also presented for the case of weakly enforced boundary conditions. NURBS-based isogeometric analysis is employed for the spatial discretization, and mesh refinement is performed to assess the convergence characteristics of the proposed methodology. Numerical tests show that very accurate results are obtained on relatively coarse grids. To the best of the authors’ knowledge, this paper is the first to report large eddy simulation computations of this challenging test case.     

Ginzburg–Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow

Plane Couette flow, the flow between two parallel planes moving in opposite directions, is an example of wall-bounded flow experiencing a transition to turbulence with an ordered coexistence of turbulent and laminar domains in some range of Reynolds numbers [R _g, R _t] . When the aspect-ratio is sufficiently large, this coexistence occurs in the form of alternately turbulent and laminar oblique bands. As R goes up trough the upper threshold R _t, the bands disappear progressively to leave room to a uniform regime of featureless turbulence. This continuous transition is studied here by means of under-resolved numerical simulations understood as a modelling approach adapted to the long time, large aspect-ratio limit. The state of the system is quantitatively characterised using standard observables (turbulent fraction and turbulence intensity inside the bands). A pair of complex order parameters is defined for the pattern which is further analysed within a standard Ginzburg–Landau formalism. Coefficients of the model turn out to be comparable to those experimentally determined for cylindrical Couette flow.     

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability

Rayleigh–Taylor instability(RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.     

Simulation of laminar–turbulent transition in compressible Taylor–Green flow basing on quasi-gas dynamic equations

We report the results of numerical simulation of laminar–turbulent transition in the Taylor–Green vortex for viscous compressible gas flow basing on quasi-gas-dynamic (QGD) equations. Here the QGD system is obtained by a temporal averaging of the Navier–Stokes equations. The additional dissipative terms in QGD system serve to model the effects of the unresolved subgrid scales. Comparison with direct numerical simulation and large eddy simulation reference data demonstrates that QGD numerical algorithm provides a uniform and adequate simulation of both laminar and turbulent evolution of the vortex for Reynolds numbers from 100 up to 5000, including transition.     

Pulsed Gradient Spin Echo Nuclear Magnetic Resonance Measurement and Simulation of Two-Fluid Taylor Vortex Flow in a Vertically Oriented Taylor–Couette Device

Magnetic resonance microscopy and Ansys Fluent^? computational fluid dynamics simulation have been used to classify Taylor vortex flows (TVF) for several single fluid and axially stratified two-fluid systems in a vertically oriented Taylor–Couette device. A Rheo-NMR (nuclear magnetic resonance) Couette system (Magritek Ltd, New Zealand) with a 1.05-mm gap was used to evaluate the transition from Couette flow to TVF in 1.65 cSt silicone oil, 1 cSt deionized water, and 0.65 cSt silicone oil. The rotation rate at which instability onset occurred agreed between experiment and simulation, as did the critical wavelength. Velocities were mapped for axially stratified two-fluid systems. The vortex containing the two-fluid interface was found to form with a significantly longer wavelength than that observed in the pure fluids. For experiments and simulations in the TVF regime, a region with no secondary flows was found at the interface, indicating interface stabilization by surface tension forces.     

Saffman–Taylor problem in filtration combustion

In the hydrodynamic approximation, postulating the combustion zone thickness to be much smaller than the channel width, the problem of filtration combustion (FC) has the same spectrum of solutions as the well-known Saffaman-Taylor (ST) problem of the displacement of a high-viscosity liquid by a low-viscosity one. In both cases, the spectrum of solutions includes families of symmetrical and asymmetrical fingers. In the ST problem, asymmetrical fingers are considered unrealizable because of the effect of surface tension at the interface between the liquids, which suppresses the formation of asymmetrical fingers. For FC, there is no exclusion of asymmetrical solutions, since the interphase boundary is a reaction front with zero surface tension. In the present work, it is experimentally demonstrated that an increase in the channel width above a critical value, a planar FC wave loses its stability and the combustion front propagates along one of the channel walls in the form of an asymmetrical finger.     

Low frequency electrostatic nonlinear structures in an inhomogeneous magnetized non-Maxwellian electron–positron–ion plasma

The properties of low frequency (coupled acoustic and drift wave) nonlinear structures including solitary waves and double layers in an inhomogeneous magnetized electron–positron–ion (EPI) nonthermal plasma with density and temperature inhomogeneities are studied in a simplified way. The nonlinear differential equation derived here for the study of double layers in the inhomogeneous EPI plasma resembles with the modified KdV equation in the stationary frame. But the method used for the derivation of nonlinear differential equation is simple and consistent to give both the stationary solitary waves and double layers. Further, the illustrations show that superthermality κ, drift velocity and temperature inhomogeneity have significant effects on the amplitude, width, and existence range of the structures.     

Solving Navier–Stokes equation for flow past cylinders using single-block structured and overset grids

Many complex fluid motions are driven by physical processes of instability, transition and turbulence dependent upon nonlinear mechanisms. Here, we solve the flow past cylinder(s) using single-block structured and overset grids by computing Navier–Stokes equation in two-dimensions. The suitability of a compact scheme in discretizing convection and diffusion terms are investigated first by looking at relevant numerical properties. Also, for the overset grid method, one of the methods is identified that shows the best results in minimizing interpolation error at sub-domain boundaries for an analytical test function. We provide extensive comparisons with experimental and other computational results for flow past a single cylinder, utilizing both single-block structured and Chimera or overset grids. Apart from showing instability of this flow calculated by these methods, we also compare the computed vorticity and velocity data using these two grids by employing the proper orthogonal decomposition (POD). We have analyzed and developed an overset grid method with compact scheme that does not need any filtering to control error. This has been ascertained by performing POD analysis. To show that the developed method is capable of handling complex geometries, we have computed flow past two cylinders in side-by-side arrangement. Results obtained capture the known flow characteristics for this arrangement well using relatively fewer number of grid points.     

Metal–insulator transition in Si–MOS structures

A survey is presented on recent investigations of the metal-to-insulator transition in two-dimensional systems with special emphasis on n-Si–MOS structures. Experimental facts are presented and the currently open questions on the nature of this transition are addressed.     

Electric flow through an ideal ferromagnet–superconductor junction

It is investigated the possibility of controlling the electric flow through a ferromagnet–superconductor junction by spin polarization, within a simple, ideal model of a perfect ferromagnetic–superconductor junction. The ferromagnetic and superconducting properties as well as the Andreev reflection are briefly reviewed and the electrical resistance of the junction is computed both in the diffusive and ballistic regime for the ferromagnetic sample. It is shown that the resistance of the junction increases with increasing magnetization, including both positive or negative jumps on passing from the ballistic to the diffusive regime.     

High magnetic shear gain in a liquid sodium stable Couette flow experiment: a prelude to an α-Ω dynamo

The Ω phase of the liquid sodium α-Ω dynamo experiment at New Mexico Institute of Mining and Technology in cooperation with Los Alamos National Laboratory has demonstrated a high toroidal field B(?) that is ?8×B(r), where B(r) is the radial component of an applied poloidal magnetic field. This enhanced toroidal field is produced by the rotational shear in stable Couette flow within liquid sodium at a magnetic Reynolds number Rm?120. Small turbulence in stable Taylor-Couette flow is caused by Ekman flow at the end walls, which causes an estimated turbulence energy fraction of (δv/v)(2)～10(-3).     

Surface waves in thermocapillary flow–revisited

The European Physical Journal Special Topics - Following theoretical predictions [1,2] thermocapillary layers can exhibit instabilities called “hydrothermal waves” (HTWs) and...