Stability of axisymmetric swirl flows of viscous incompressible fluid

A new method of solution to the problem of stability of the swirl flow of viscous incompressible fluid is developed. The method based on expansion of the required function into power series of radial coordinate allows an avoidance of difficulties related to numerical integration of the system of differential equations with a singular point. Stability of the Poiseuille flow in a rotating pipe is considered as an example.     

Stability of flow between rotating cylinders with axial buoyancy effect

The linear stability of a fluid confined between two coaxial cylinders rotating independently with axial buoyancy induced flow is examined. Buoyancy is included through the Boussinesq approximation. The numerical investigation is restricted to radius ratio 0.5 at Prandtl number 0.709 with co-rotation situation. The outer rotating cylinder’s Couette flow Reynolds number is restricted to 200. Zeroth-order discontinuities are found in the critical surface, which are explained as the result of the competition between the centrifugal and axial buoyancy induced shear instability mechanisms. Due to the competition, the neutral stability curves develop islands of instability, which considerably lower the instability threshold. Specific and robust numerical methods to handle these geometrical complexities are developed.     

Angular momentum transport in turbulent flow between independently rotating cylinders

We present measurements of the angular momentum flux (torque) in Taylor-Couette flow of water between independently rotating cylinders for all regions of the (Ω1, Ω2) parameter space at high Reynolds numbers, where Ω1 (Ω2) is the inner (outer) cylinder angular velocity. We find that the Rossby number Ro = (Ω1 - Ω2)/Ω2 fully determines the state and torque G as compared to G(Ro = ∞) ≡ G∞. The ratio G/G∞ is a linear function of Ro(-1) in four sections of the parameter space. For flows with radially increasing angular momentum, our measured torques greatly exceed those of previous experiments [Ji et al., Nature (London), 444, 343 (2006)], but agree with the analysis of Richard and Zahn [Astron. Astrophys. 347, 734 (1999)].     

Entrance-channel angular-momentum dependence of mass transfer between heavy ions

The dependence of the number of transferred nucleons on the entrance-channel angular momentum is discussed on the basis of a simple geometrical model. Excitation functions of different heavy-ion induced reactions on²⁰⁹Bi are calculated and found to be in good agreement with experimental data. Mean entrance-channel angular momenta calculated using this model almost coincide with the values obtained from the analysis of the correlation of charged particles withγ-multiplicities for the interaction of¹⁶O with¹⁵⁴Sm.     

Junction conditions and static fluid cylinders in Lyra's geometry

Junction conditions for Sen's theory in Lyra's geometry are considered. It is proposed that for any gauge function the standard O'Brien-Synge and Lichnerowicz junction conditions should be supplemented by demanding continuity of the displacement vector across the interface. A class of internal solutions of the Sen equations with a source term given by the energy-momentum tensor of a one-component perfect fluid with the ultrarelativistic equation of state that is expressible in terms of Bessel functions is proposed. The internal solution is regularly matched by means of the junction conditions to the exterior solution. The resulting two-parameter solution is globally non-Euclidean.     

Stability of transport

It is shown that the stability criterion derived by Schlögl from statistical theory leads in the case of hydrodynamical transport states to a global stability criterion for a steady nonequilibrium state which leads under assumption of locality and for infinitesimal deviations from the steady state to the stability criterion of Glansdorff and Prigogine.     

Visualization of thermal cutting fluid flows

Outside of the fields where flow visualization is traditionally applied, there exist many processes where fluid phenomena are critical. Here, we survey flow visualization work with a focus on two thermal metal cutting processes. These two processes – plasma-arc cutting and gas assisted laser cutting – account for a large fraction of the means by which steel is cut in our world. Plasma-arc cutting utilizes an electric arc transferred between a cathode and the steel being cut to produce a high temperature gas jet that melts and removes metal. In gas assisted laser cutting, the assist jet is often high-pressure supersonic nitrogen for stainless steel, or near-atmospheric pressure, low-speed oxygen for carbon steel. Visualization of these millimeter-range diameter jets helps to understand the different roles that the assist gas has in these cutting processes, particularly with how the jets interact with the metal being cut. We describe experimental techniques for visualization of the arc jet and gas assist jet, as well as the liquid metal flows being removed from the cut and the gas flow in the torch itself. These visualizations overcome the small physical scales of the process, the bright illumination from the arc itself, and harsh high-temperature environment. The results lend perspective and understanding of the physical phenomena important to process control.     

Stability of magnetohydrodynamic stratified shear flows

Summary The linear stability of a stratified shear flow of a perfectly conducting bounded fluid in the presence of a magnetic field aligned with the flow and buoyancy forces has been studied under Boussinesq approximation. A new upper bound has been obtained for the range of real and imaginary parts of the complex wave velocity for growing perturbations. The upper bound depends on minimum Richardson number, wave number, Alfvén velocity and basic flow velocity. H?iland's necessary criterion for instability of hydrodynamic stratified homogeneous shear flow is modified and its analog for nonhomogeneous magnetohydrodynamic cases is derived. Finally the upper bound for the growth rate ofKC _i and its variants, whereK is the wave number andC _i the imaginary part of complex wave velocity, is derived as the necessary condition of instability. All estimates remain valid even when the minimum richardson numberJ ₁, for some practical problems, exceeds 1/4 for growing perturbations. The authors of this paper have agreed to not receive the proofs for correction.     

Modification of junction flows by altering the section shapes of the cylinders

Through visualization and measurement on the cylinder-plate junction flow, we show the horseshoe vortices can be significantly modified by altering the section shape of the cylinder. Both smoke-wire and Laser-Induced-Fluorescence (LIF) are employed to visualize the vortex structures. Laser Doppler velocimeter is used to measure the velocity field in the symmetry plane upstream of the cylinder. Electrical pressure-scanning valve is applied to acquire the pressure on the plate. It is found that, the sharper the frontal shape of the cylinder, the closer the vortex shedding position and the primary horseshoe vortex location to the cylinder. We quantitatively show the variation of the scale and strength of the primary horseshoe vortex, as well as the maximum wall shear stress, when the section shape of the cylinder is varied. The reduced streamwise adverse pressure gradient explains why the horseshoe vortices are significantly suppressed when the frontal shape of the cylinder becomes sharper. At last, we present a swept thin cylinder installed in front of the primary cylinder can be used to suppress the horseshoe vortices, which is greatly effective and easy to implement.     

Properties of static fluid cylinders and plane layers in general relativity

Exact solutions of field equations representing static perfect fluid cylinders and plane layers, with possible inclusion of electromagnetic or scalar field, are constructed and discussed. For the case of cylindrical symmetry, conditions at a regular axis are formulated and examples of regular solutions are presented. For planar and pseudoplanar configurations some limitations are obtained concerning existence of mirror symmetry in the thickness direction. These limitations make such symmetry rather unprobable, thus giving evidence that realistic models for equilibrium disklike configurations should be nonstatic (rotating). A configuration described by Teixeira, Wolk, and Som, possessing planar plus mirror symmetry (the case of disordered radiation), is shown to be unphysical.     

Lattice Boltzmann simulations of 2D laminar flows past two tandem cylinders

We apply the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model to simulate laminar flows in two-dimensions (2D). In order to simulate flows in an unbounded domain with the LBE method, we need to address two issues: stretched non-uniform mesh and inflow and outflow boundary conditions. We use the interpolated grid stretching method to address the need of non-uniform mesh. We demonstrate that various inflow and outflow boundary conditions can be easily and consistently realized with the MRT-LBE. The MRT-LBE with non-uniform stretched grids is first validated with a number of test cases: the Poiseuille flow, the flow past a cylinder asymmetrically placed in a channel, and the flow past a cylinder in an unbounded domain. We use the LBE method to simulate the flow past two tandem cylinders in an unbounded domain with Re = 100. Our results agree well with existing ones. Through this work we demonstrate the effectiveness of the MRT-LBE method with grid stretching.     

Experimental investigation of dynamical coupling between turbulent transport and parallel flows in the JET plasma-boundary region

The dynamical coupling between turbulent transport and parallel flows has been investigated in the plasma boundary region of the Joint European Torus tokamak. Experimental results show that there is a dynamical relationship between transport and parallel flows. As the size of transport events increases, parallel flows also increase. These results show that turbulent transport can drive parallel flows in the plasma boundary of fusion plasmas. This new type of measurement is an important element to unravel the overall picture connecting radial transport and flows in fusion plasmas.     

Regular and chaotic transport of impurities in steady flows

This paper considers the properties of the transport of impurity particles in steady fluid flows and describes the principal modes of particle motion. An impurity consisting of particles with a lower density than that of the medium is localized at stationary points of the flow, whereas a heavy impurity can perform a spatially unbounded motion. The conditions for the transition from the bounded motion of a heavy impurity to the long-range transport mode, which occurs as a result of a loss of the stability of the heteroclinic trajectory, are obtained for a model two-dimensional flow having an eddy-cell structure. A mode is found in which a particle, after being transported over a long distance, is trapped forever within the confines of one cell. The transition from regular to chaotic particle transport is analyzed. The question of the effect of a small noise (for example, molecular diffusion) on the character of the motion of a heavy impurity is investigated. It is shown that this effect is important at high viscosity and leads to a transition from bounded motion of the impurity particle to diffusion-type chaotic motion. (c) 1994 American Institute of Physics.     

Stability of oscillatory flows past compliant surfaces

The stability of oscillatory flows over compliant surfaces is studied analytically and numerically. The types of compliant surfaces studied are the spring backed wall model, which permits tangential motion of the surface, and the incompressible viscoelastic gel model. The stability is determined using the Floquet analysis, where amplitude of perturbations at time intervals separated by one time period is examined to determine whether perturbations grow or decay. The oscillatory flows past both the spring backed wall model and the viscoelastic gel model exhibit an instability in the limit of zero Reynolds number, and the transition amplitude of the oscillatory velocity increases with the frequency of oscillations. The transition amplitude has a minimum at zero wave number for the spring backed plate model, whereas the minimum occurs at finite wavenumber for the viscoelastic gel model. For the spring backed plate model, it is shown that the instability due to steady mean flow and the purely oscillatory instability reinforce each other, and the regions of instability are mapped in the ( ) plane, where is the steady strain rate and A is the oscillatory strain rate. For the viscoelastic gel model, the instability is found to depend strongly on the gel viscosity , and the effect of oscillations on the continuation of viscous modes at intermediate Reynolds number shows a complicated dependence on the oscillation frequency.Received: 17 March 2004, Published online: 30 September 2004PACS: 47.20.Ft Instability of shear flows - 83.50.-v Deformation and flow - 87.19.Tt Rheology of body fluids