Stability of the magnetic Couette-Taylor flow

In this paper we consider the magnetic Couette-Taylor problem, that is, a conducting fluid between two infinite rotating cylinders, subject to a magnetic field parallel to the rotation axis. This configuration admits an equilibrium solution of the form $ (0,ar + br^{{ - 1}} ,0,0,0,\alpha + \beta \log r). $ (0,ar + br^{{ - 1}} ,0,0,0,\alpha + \beta \log r). It is shown that this equilibrium is Ljapounov stable under small perturbations in $ \mathcal{L}^{2} (\Gamma ), $ \mathcal{L}^{2} (\Gamma ), where $ \Gamma = \{ (r,\varphi ,z)/r_{1} < r < r_{2} ,\varphi \in [0,2\pi ],z \in \mathbb{R}\} , $ \Gamma = \{ (r,\varphi ,z)/r_{1} < r < r_{2} ,\varphi \in [0,2\pi ],z \in \mathbb{R}\} , provided that the parameters a, b, , are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques.     

Stability of the magnetic Couette-Taylor flow

In this paper we consider the magnetic Couette-Taylor problem, that is, a conducting fluid between two infinite rotating cylinders, subject to a magnetic field parallel to the rotation axis. This configuration admits an equilibrium solution of the form It is shown that this equilibrium is Ljapounov stable under small perturbations in where provided that the parameters a, b, , are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques.Received: February 5, 2003; revised: September 29, 2003Dedicated to Prof. H. Amann on the occasion of his 65. birthday     

Numerical and experimental investigation of thermal convection in an inclined narrow gap

The knowledge of the fluid behaviour in inclined cavities is of fundamental importance as far as heat and mass transfer are concerned. The interest in this subject is particularly increasing due to the rapid process in micro technologies. We therefore studied the flow- and temperature field of such flows numerically as well as experimentally using CFD and PIV/T, respectively. We present and discuss the numerical and experimental results of our investigations and explain the applied techniques. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of melting inside concentric and eccentric horizontal annulus

This paper presents numerical investigations on melting of phase change material using N-eicosane inside a cylindrical container. Numerical simulations are performed for symmetric melting of phase change material between two cylinders in concentric and eccentric arrays using the FLUENT software which is sub-cooled initially to 1 °C. Inner cylindrical tube is considered hot wall while outer tube is insulated. Predicted result shows that melting rate is the same approximately for concentric and eccentric array before time of 15 min. After this time, melting rate decreases in concentric array. It is due to the pure conduction between hot tube and cold solid phase change material.     

Numerical prediction of buoyancy driven micropolar fluid flow within uniformly heated eccentric annulus

In this paper, the problem of buoyancy driven micropolar fluid flow within an annulus formed between two circular concentric/eccentric tubes has been numerically investigated using Fourier spectral method. The annulus inner wall is uniformly heated and maintained at constant heat flux while the outer wall is cooled and kept at constant temperature. The full governing equations of linear momentum, angular momentum and energy have been solved to give the details of flow and thermal fields. The heat convection process in the annulus is mainly controlled by modified Rayleigh number Ra, Prandtl number Pr, radius ratio Rr, eccentricity, e and material parameters of Micropolar fluid. The material parameters are dimensionless spin gradient viscosity λ, dimensionless micro-inertia density B and dimensionless vortex viscosity D. The study considered a range of modified Ra up to 10⁵ and is carried out at three values of Pr, namely Pr = 0.1, 1.0 and 7.0, and at three values of parameter D, namely, D = 2, 4, 8 while the eccentricity is varied between −0.65 and +0.65. The radius ratio is fixed at 2.6 while the material parameters B and λ are assigned the value of 1. The effect of the controlling parameters on flow and thermal fields has been investigated with emphasis on the effect of these parameters on local and mean inner wall temperatures. The study has shown that for certain controlling parameters the steady mean temperature of inner wall of the annulus is maximum at a certain eccentricity. The study has also shown that as the parameter D increases the steady mean inner wall temperature increases. Moreover, the study has shown that as the Pr increases the mean inner wall temperature decreases.     

Numerical study of porous channel flow in a rotating system by a homotopy method

Problems in lubrication, transpiration cooling, dialysis, gaseous diffusion processes, subterranean rivers fed by porous bedrock, and flow under the polar icecap are examples of porous channel flow in a rotating system. Using similarity equations the Navier-Stokes equations reduce to a 10th order two-point boundary value problem. For certain parameter ranges this problem is very difficult and is not amenable to simple shooting techniques or classical locally convergent iterative methods. A recently developed globally convergent homotopy algorithm is applied to the boundary value problem, and numerical results are reported for a wide range of parameter values.     

Numerical study of the primitive equations in the small viscosity regime

In this paper we study the flow dynamics governed by the primitive equations in the small viscosity regime. We consider an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain. The generated boundary layer is analyzed in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary. The presence of complex singularities is correlated with the appearance of secondary recirculation regions. Two viscosity regimes, with different qualitative properties, can be distinguished in the flow dynamics.

     

Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. and Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively are considered for the Reynolds number range covering the     

Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method. For comparison with experiments of Nakabayashi et al. and Wimmer, a narrow gap and a medium gap with clearance ratio β=0.06 and 0.18 respectively are considered for the Reynolds number range covering the first Hopf bifurcation point. With adequate initial conditions and temporary imposition of small wave-type perturbation, multiple periodic flow states with three different pair numbers of spiral Taylor-Görtler (TG) vortices have been simulated successfully for β=0.06, of which the 1-pair and 2-pair of spiral TG vortices are newly obtained. Three different periodic flow states with shear waves, Stuart vortices or wavy outflow boundary, have been obtained for β=0.18. Analysis of the numerical results reveals these higher flow modes in terms of fundamental frequency, wave number and spatial structure.     

Numerical study of a transverse streamlined flow of an infinite series of cylinders

The problem of transverse streamlined flow of an infinite series of cylinders by a flow of viscous incompressible liquid is considered. The problem is solved numerically by using the method of difference approximation of the Navier-Stokes equations with use of Arakawa scheme of the second degree of accuracy. Computations were given for a series of cylinders with the step L=2.2, 2.8, 3.2, 3.6 and with Reynolds numbers Re equal to 40, 100, 200, 400. Relations between the hydrodynamic characteristics of the series and the distance between the axes of the cylinders are obtained for different Reynolds numbers.Translated from Dinamicheskie Sistemy, No. 7, pp. 53–57, 1988.     

Numerical study of turbulent diesel flow in a pipe with sudden expansion

Three two-equation models and a second-moment closure are implemented in the case of turbulent diesel flow in a pipe with sudden expansion. The chosen two-equation closures are: the standard k–ε, the RNG k–ε and the two-scale k–ε models. The performance of the models is investigated with regard to the non-equilibrium parameter η and the mean strain of the flow, S. Velocity and turbulence kinetic energy predictions of the different models are compared among themselves and with experimental data and are interpreted on the basis of the aforementioned quantities. The effect of more accurate near-wall modeling to the two-equation models is also investigated. The results of the study demonstrate the superiority of the second-moment closure in predicting the flow characteristics over the entire domain. From the two-equation models the RNG derived k–ε model also gave very good predictions, especially when non-equilibrium wall-functions were implemented. As far as η and S are concerned, only the closures with greater physical consistency, such as the two-scale k–ε model, give satisfactory results.     

Numerical and experimental study of mitigation of welding distortion

Welding stresses and deformations are closely related phenomena. During the heating and cooling cycles thermal strains may occur in the weld and adjacent area. The strains produced during the heating stage of welding are always accompanied by plastic deformation of the metal. The stresses resulting from these strains combine and react to produce internal forces that cause a variety of welding distortions. Welding deformation needs to be minimized and also the designer should know before hand the extent of deformation so that it can be accounted for in the design as well as in the construction stages.In this paper, heat sinking as a method of distortion mitigation has been studied. Heat sinking has been affected by circulating water through channel clamped at the bottom surface of the plates undergoing welding. The pseudolinear equivalent constant rigidity concept has been used in this investigation for thermo-mechanical analysis of plates undergoing welding with simultaneous heat sinking. The initial nonlinear problem with varying modulus dependent on temperature is transformed into a pseudolinear equivalent system of constant rigidity that is solved by linear analysis.The numerical results compared very well with those of the experimental ones. The proposed concept is found to be computationally more efficient and simpler to model compared to FEM for solving similar thermo-elasto-plastic nonlinear problems. The procedure presented in this work and the results thus obtained, holds a great promise for determining the heat sinking parameters for effectively controlling welding distortion.     

Numerical study of the flow in a three-dimensional thermally driven cavity

Solutions for the fully compressible Navier–Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied.     

Numerical study of transition in a cylindrical pipe flow

We present numerical results of transition in a smooth cylindrical pipe by small periodical suction and blowing (PSB) at the inlet of a laminar pipe flow at Reynolds number 3000 based on the maximum velocity of the laminar flow and radius of the pipe. The spatial development of the PSB disturbance is simulated by means of pseudo-spectrum element method. The transitional process is described in the paper that the disturbances are growing rapidly in a short part of the pipe after they develop gradually in sufficient long distance. When the rapid growth of disturbances occurs the time step of integration should be decreased and then the flow transits to turbulent.     

Numerical and experimental investigation of the turbulent flow through a low-pressure turbine cascade in the endwall region

In the present work, direct numerical simulations (DNS) of the flow through a low-pressure linear turbine cascade T106 with parallel endwalls were conducted to investigate the effects of unsteady passing wakes of the upstream blade row on the secondary flow in the endwall region of the passage. The impact of the wakes on the secondary flow is discussed by means of the time-averaged values. Furthermore, the results of DNS are compared with experimental data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study of pressure distribution in entrance pipe flow

This article describes the computation of pipe flow in the entrance region. The pressure distribution and flow characteristics, particularly the effect of vorticity in the vicinity of the wall, were analyzed for moderate Reynolds numbers (Re) ranging from 500 to 10,000. It was found, for the first time, that a large pressure gradient in the radial direction exists near the pipe inlet. The pressure gradient is caused by the radial component of the curl of vorticity, which decreases as Re increases. The pressure at the wall is lower than that at the central core for Re ≤$\le$ 5000. This result is beyond the scope of the boundary-layer assumption for pressure, although it applies to flows at high Reynolds numbers.     

Numerical stabilization of the Lorenz system by a small external perturbation

The Lorenz system perturbed by noise and its invariant measure whose density obeys the stationary Fokker-Planck equation are analyzed numerically. A linear functional of the invariant measure is considered, and its variation caused by a variation in the right-hand side of the Lorenz system is calculated. A small (in modulus) external perturbation is calculated under which the strange attractor of the Lorenz system degenerates into a stable fixed point.     

Numerical study of the flow of a polymer solution in a pipe

An approximation is suggested for the length of displacement path with flow of a polymer solution of different concentration in a pipe. The velocity profile and hydrodynamic resistance factor are calculated over a wide range of Reynolds numbers. Comparisons are given with experimental data.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 121–124, 1988.