Toroidal Channel Research Articles

The effect of oscillations on the flow patterns near a simulated bed

This work investigates the effect of oscillations on the flow near a simulated bed and their impact on erosion. Those oscillations were generated by using wavy lids at the top of a small toroidal channel. Particular attention is dedicated to their influence on the velocity field and turbulence near the bed. The experiments were made in a mini circular flume using a 2D LDA system. It was concluded that such oscillations induce non negligible shear stresses in the flow main stream, becoming more important to the dispersion of entrained matter into the flow than to the initiation of the erosion process.

Dynamics of a turbulent spin-down flow inside a torus

A turbulent screw flow (with Reynolds number exceeding 106) is generated by the sudden stop of a toroidal channel. The working fluid is a gallium alloy and velocity measurements are performed using a dual-axis potential probe. We describe the onset of motion, the development of strongly anisotropic fluctuations, and the final homogenization and decay of turbulence. Our observations are relevant for the relaxation of anisotropic turbulence; they are also in agreement with measurements of magnetohydrodynamic induction processes in this type of flow.

A new cooling scheme for the HCLL TBM

The Helium Cooled Lithium Lead (HCLL) blanket is one of the two blanket concepts selected by the European Union to be tested in ITER. It is based on the use of Eurofer as structural material, helium as coolant and eutectic lithium–lead as breeder/neutron multiplier material. The design of the corresponding Test Blanket Module (TBM) for ITER has undergone several revisions in the last years. This paper presents an alternative cooling scheme for the HCLL-TBM, where the First Wall (FW) is cooled by vertical (poloidal) instead of horizontal (toroidal) channels. New Finite Element models have been developed and thermal and thermo-hydraulical analyses of the new design have been performed. Results show that the new cooling scheme presents several advantages with respect to the previous one: (i) the total number of cooling channels in the FW can be reduced; (ii) the overall pressure drops in one cooling channel are lower; (iii) the temperature profile in the breeding zone is more uniform.

Measurements of turbulent magnetic diffusivity in a liquid-gallium flow

Direct measurements of the effective conductivity (magnetic diffusivity) in the turbulent flow of a liquid metal have been performed. An nonstationary turbulent flow of a gallium alloy has been excited in a closed toroidal channel with dielectric walls. The Reynolds number reaches a maximum value of Re ≈ 106, which corresponds to the magnetic Reynolds number Rm ≈ 1. The conductivity of the metal in the channel has been determined from the phase shift of forced harmonic oscillations in a series RLC circuit whose inductance is a toroidal coil wound around the channel. The maximum deviation of the effective conductivity of the turbulent medium from the ohmic conductivity of the metal is about 1%.

Direct measurement of effective electro conductivity of turbulent liquid metal

AbstractDirect measurement of effective electro conductivity are performed in a nonstationary turbulent flow of liquid gallium, generated in a closed toroidal channel. The peak level of the Reynolds number reached Re ≈ 106, what corresponds to the magnetic Reynolds number Rm ≈ 1. The conductivity of the liquid metal was determined measuring the phase shift between sinusoidal voltage and current in the RLC‐circuit, the inductance of which was made by the toroidal coil embracing the channel. The maximal deviation of electrical conductivity from its ohmic value reaches about 1%. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Full perturbation solution for the flow in a rotating torus

We present a perturbation solution for a pressure-driven fluid flow in a rotating toroidal channel. The analysis shows the difference between the solutions of full and simplified equations studied earlier. The result is found to be reliable for low Reynolds number (Re), as was the case for a previously studied solution for high Re. The convergence conditions are defined for the whole range of governing parameters. The viscous flow exhibits some interesting features in flow pattern and hydrodynamic characteristics.

Structure of multi-component/multi-Yukawa mixtures

Recent small angle scattering experiments reveal new peaks in the structure functionS(k) of colloidal systems (Liu et al 2005 J. Chem. Phys. 122 044507), in a region that wasinaccessible with older instruments. It has been increasingly evident that a single (ordouble) Yukawa MSA-closure cannot account for these observations, and three or moreterms are needed. On the other hand the MSA is not sufficiently accurate (Broccio et al 2005 Preprint); more accurate theories such as the HNC have been tried. But while theMSA is asymptotically exact at high densities (Rosenfield and Blum 1986 J. Chem. Phys. 851556), it does not satisfy the low density asymptotics. This has been corrected in the softMSA (Blum et al 1972 J. Chem. Phys. 56 5197, Narten et al 1974 J. Chem. Phys. 60 3378) byadding exponential type terms. The results compared to experiment and simulation forliquid sodium by Rahman and Paskin (as shown in Blum et al 1972 J. Chem. Phys. 565197) are remarkably good. We use here a general closure of the Ornstein–Zernikeequation, which is not necessarily the MSA closure (Blum and Hernando 2001Condensed Matter Theories vol 16 ed Hernandez and Clark (New York: Nova) p 411). with the boundary condition forgij(r) = 0 for r≤σij. This general closure of the Ornstein–Zernike equation will go well beyond the MSA sinceit has been tested by Monte Carlo simulation for tetrahedral water (Blum et al 1999Physica A 265 396), toroidal ion channels (Enriquez and Blum 2005 Mol. Phys. 103 3201)and polyelectrolytes (Blum and Bernard 2004 Proc. Int. School of Physics Enrico Fermi,Course CLV vol 155, ed Mallamace and Stanley (Amsterdam: IOS Press) p 335). For thisclosure we get for the Laplace transform of the pair correlation function an explicitlysymmetric result This function is also easily transformed intoS(k) by replacing . For low density situations (dilute colloids) and S(k) isa sum of M Lorentzians. For hard sphere PY mixtures we get the simple (compare Lebowitz 1964 Phys.Rev. 133 A895 and Blum and Stell 1979 J. Chem. Phys. 71 42) where Dτ(s) is a scalar function. For polydisperse electrolytes in the MSA a simpler expression is alsoobtained (compare Blum and Hoye 1977 J. Phys. Chem. 81 1311). An explicitcontinued fraction solution of the one component multi-Yukawa case is also given.

Induction, helicity, and alpha effect in a toroidal screw flow of liquid gallium

We investigate experimentally induction mechanisms in a screw flow of gallium in a toroidal channel. The flow is nonstationary and operated in a spin-down regime: the channel (and fluid) are initially set into solid body rotation; as the channel is stopped the fluid is set into strong helical motion by diverters located inside the channel. In this study, we put a particular emphasis on the induction generated by these helical motions, which are expected to develop over the entire range of turbulent scales. We apply an external magnetic field either perpendicular to the channel axis parallel to it. At large scales the nonlinear induction mechanisms are associated with the Parker stretch and twist effect and with the expulsion due to overall rotation. Induction mechanisms can also originate in the small scale helicity as in the alpha induction effect of mean-field magnetohydrodynamics. Our measurements yield an upper bound for the alpha coefficient, significantly lower than estimates based on dimensional analysis. We discuss the consequences of our observations for the engineering of homogeneous dynamos in the laboratory.

Magnetic field rotation in the screw gallium flow

The magnetic field induced by the nonstationary screw flow of gallium in a toroidal channel has been investigated experimentally using a gallium prototype of the sodium apparatus developed in the frame of the experimental dynamo program at the Institute of Continuous Media Mechanics, Perm, Russia. The experimental set-up is a rapidly rotating toroidal channel subjected to abrupt braking. The screw flow is initiated by inertial forces pushing liquid gallium through diverters. The regular structure of the induced magnetic field is generated about 0.1 s after the stop of the channel and persists up to 1 s. The induced field is measured by sensors placed outside the channel. The inductive effects observed are attributed to the mean screw flow. The decay laws of the induced regular magnetic field and turbulent magnetic fluctuations are studied.

The transpiration cooled first wall and blanket concept

To achieve high thermal performance at high power density the EVOLVE concept was investigated under the APEX program. The EVOLVE W-alloy first wall and blanket concept proposes to use transpiration cooling of the first wall and boiling or vaporizing lithium (Li) in the blanket zone. Critical issues of this concept are: the Magnetohydrodynamic (MHD) pressure losses of the Li circuit, the evaporation through a capillary structure and the needed superheating of the Li at the first wall and blanket zones. Application of the transpiration concept to the blanket region results in the integrated transpiration cooling concept (ITCC) with either toroidal or poloidal first wall channels. For both orientations the routing of the liquid Li and the Li vapor has been modeled and the corresponding pressure losses have been calculated by varying the width of the supplying slot and the capillary diameter. The concept works when the sum of the active and passive pumping head is higher than the total system pressure losses and when the temperature at the inner side of the first wall does not override the superheating limit of the coolant. This cooling concept has been extended to the divertor design, and the removal of a surface heat flux of up to 10 MW/m 2 appears to be possible, but this paper will focus on the transpiration cooled first wall and blanket concept assessment.

Non-stationary screw flow in a toroidal channel: way to a laboratory dynamo experiment

A possibility to implement a new type of dynamo experiment, namely, a nonstation- ary dynamo in a braked toroidal channel is considered. We suggest that a helical flow with the magnetic Reynolds number sucient for screw dynamo action can develop in a toroidal channel with liquid sodium (about 100 kg) accelerated up to the frequency of 50 RPS and braked abruptly. The growth of the resulting magnetic eld is expected to be sucient to isolate dynamo eect. In this paper we present the results of hydrodynamic experiments with water prototypes. The spatial and temporal proles of the helical flow excited in a braked channel by a diverter are investigated. Numerical simulation of the magnetic eld evolution is performed for a helical flow with a prole extracted from the experimental data and scaled to the parameters of MHD apparatus. The data from the hydrodynamic experiment and the results of MHD numerical simulations are used to optimize the MHD apparatus under development. Introduction. At the very end of the XX century the long-standing experi- mental eorts to implement the self-excitation of magnetic elds by MHD dynamo was crowned with success. The MHD dynamo experiments performed in Riga (1) and Karlsruhe (2) are a real breakthrough in the development of experimental verication of the dynamo theory predictions. This verication seems to be of crucial importance for geophysics and astrophysics because dynamo is thought to be responsible for generation and maintenance of magnetic elds in cosmic bod- ies, e.g., the Sun and the Earth (3, 4). Furthermore, the dynamo experiments allow one to construct geophysical and astrophysical dynamo models not only on the principles basis, but also on the experimental results. The available dynamo experiments reproduce only a part of the aspects encountered in astro- physical dynamos. Therefore, many additional experiments are needed to gain a more penetrating insight into the MHD dynamo phenomenon (5). The realization of MHD dynamo is an extremely complicated and expensive experiment, since this phenomenon is a threshold process requiring high mag- netic Reynolds numbers. The lowest theoretical estimate (6) of the critical value, Rm =1 7 :7, was obtained for the so-called Ponomarenko dynamo (see below), representing a screw motion of a rigidly rotating cylinder in an innite conduc- tive medium. However, even such a relatively low magnetic Reynolds number can be obtained by moving tons of liquid sodium and hundred kilowatts to drive the pumps. The rst attempt to perform the MHD dynamo experiment by pumping liquid sodium through tubes of specic shape was made in Riga in 1987 (7). In this experiment, a decrease in magnetic eld decrement with increasing velocity was observed, but the generation threshold has not been reached yet. The second generation of dynamo experiments based on the same physical idea of pumping liquid sodium is currently undertaken by several scientic teams, and the rst results have been recently obtained. In the Riga experiments the beginning of

Simulation of the Onset of Nonstationarity and Chaos in a Hydrodynamic System Governed by a Small Number of Degrees of Freedom

The hypothesis of the onset of nonstationarity and chaos in a hydrodynamic system as a result of the nonlinear interaction of a small number of degrees of freedom is verified experimentally with reference to fluid convection in a toroidal channel. Regimes of motion of a fluid medium which correspond qualitatively to the Lorenz model are obtained experimentally. These include steady-state regimes, their bifurcations, nonuniqueness and instability, unsteady periodic and stochastic regimes. The spectral and statistical characteristics of the and unsteady processes are investigated, the nature of the onset of chaos is analyzed, and the results are compared with calculations. The mathematical model of the problem is refined.

Unsteady Turbulent Spiral Flows in a Circular Channel

Turbulent spiral flows of water, developing in a rapidly rotating toroidal channel after abrupt braking, are investigated experimentally. The spiral flow structure is created by fixed-blade diverters located in the channel. The Reynolds number may be as high as 106. A simple model for describing the evolution of the longitudinal and azimuthal velocity components averaged over the channel section is proposed.

Brownian Dynamics Study of Ion Transport in the Vestibule of Membrane Channels

Brownian dynamics simulations have been carried out to study the transport of ions in a vestibular geometry, which offers a more realistic shape for membrane channels than cylindrical tubes. Specifically, we consider a torus-shaped channel, for which the analytical solution of Poisson's equation is possible. The system is composed of the toroidal channel, with length and radius of the constricted region of 80 Å and 4 Å, respectively, and two reservoirs containing 50 sodium ions and 50 chloride ions. The positions of each of these ions executing Brownian motion under the influence of a stochastic force and a systematic electric force are determined at discrete time steps of 50 fs for up to 2.5 ns. All of the systematic forces acting on an ion due to the other ions, an external electric field, fixed charges in the channel protein, and the image charges induced at the water-protein boundary are explicitly included in the calculations. We find that the repulsive dielectric force arising from the induced surface charges plays a dominant role in channel dynamics. It expels an ion from the vestibule when it is deliberately put in it. Even in the presence of an applied electric potential of 100 mV, an ion cannot overcome this repulsive force and permeate the channel. Only when dipoles of a favorable orientation are placed along the sides of the transmembrane segment can an ion traverse the channel under the influence of a membrane potential. When the strength of the dipoles is further increased, an ion becomes detained in a potential well, and the driving force provided by the applied field is not sufficient to drive the ion out of the well. The trajectory of an ion navigating across the channel mostly remains close to the central axis of the pore lumen. Finally, we discuss the implications of these findings for the transport of ions across the membrane.

Analytical Solutions of Poisson's Equation for Realistic Geometrical Shapes of Membrane Ion Channels

Analytical solutions of Poisson's equations satisfying the Dirichlet boundary conditions for a toroidal dielectric boundary are presented. The electric potential computed anywhere in the toroidal conduit by the analytical method agrees with the value derived from an iterative numerical method. We show that three different channel geometries, namely, bicone, catenary, and toroid, give similar potential profiles as an ion traverses along their central axis. We then examine the effects of dipoles in the toroidal channel wall on the potential profile of ions passing through the channel. The presence of dipoles eliminates the barrier for one polarity of ion, while raising the barrier for ions of the opposite polarity. We also examine how a uniform electric field from an external source is affected by the protein boundary and a mobile charge. The channel distorts the field, reducing it in the vestibules, and enhancing it in the constricted segment. The presence of an ion in one vestibule effectively excludes ions of the same polarity from that vestibule, but has little effect in the other vestibule. Finally, we discuss how the solutions we provide here may be utilized to simulate a system containing a channel and many interacting ions.

Experimental investigation of fluid convection in a closed toroidal channel

The results of investigating convective fluid motion in a closed toroidal channel are analyzed and compared with the results of calculations based on the Lorenz model. It is shown that this model adequately describes the fluid convection only in the case of a large aspect ratio of the mean radius of the torus to its cross-sectional dimension and small heating power. The measurements and visual observations record substantial deviations from the assumptions underlying the Lorenz model in the domain of problem parameters in which, in accordance with the calculations, bifurcations and instability of steady solutions of the Lorenz model should take place.

Mechanical Design and Fabrication of the U.S. Solid Breeder Blanket for ITER

The solid breeder blanket has been chosen as the first option for ITER, with three of the four participating international groups submitting designs utilizing solid breeding materials. This paper describes the design submitted by the U.S. group. The ITER chamber will have both inboard and outboard blankets. The outboard side is divided into 48 modules, three per TF sector, where one central module fits between TF coils and two side modules fit partially within the coils. The central module is divided into an upper and lower segment leaving space at the midplane for penetrations. These penetrations include spaces for test modules, neutral beams and RF heating units. The two side modules extend the full height of the reactor. The inboard side is divided into 32 modules with each module separated into three electrically insulated front zones. A slab configuration is used within the blanket, where Be zones are interleaved with thin LiO2 solid breeder zones and water coolant panels. In the outboard blanket the first wall and coolant panels have toroidal channels while the inboard blanket has poloidal channels. The first wall has to be designed to be capable of withstanding the pressure generated by plasma disruptions. An independent coolant loop is used for the first wall while the blanket and shield are integrated into another loop.

Effect of initial conditions on the characteristics of free jets exiting from curvilinear channels

Results are presented from an experimental study of the effect of centrifugal forces in a toroidal channel on the characteristics of a jet escaping therefrom.

Numerical calculation of the coefficient of capture of aerosol particles in toroidal channels of circular section

The flow of a liquid (or gas) with aerosol particles suspended in it in channels of different configurations is of great interest in the solution of many practical problems. The aim of the present paper is to develop a method for calculating the hydrodynamics and the heat and concentration transfer of aerosol particles for steady flow of an incompressible fluid in toroidal channels of circular section. The paper uses an implicit difference scheme with different approximations of the convective terms on a nonuniform grid (directed differences, central differences, and the monotonic approximation of Samarskii), which makes it possible to reduce the solution of the system of the original nonlinear partial differential equations to the successive solution of one-dimensional systems [1]. The method proposed by Polezhaev and Gryaznov [2] is used to calculate the boundary conditions for the vorticity. The hydrodynamic equations are solved by means of the difference scheme developed by Khristov [3], and the heat and concentration transfer equations are solved by the difference scheme proposed by Val'tsiferov and Polezhaev [4]. The obtained results make possible a detailed analysis of the dependence of the basic integrated (particle capture coefficient) and local characteristics on the values of the relevant dimensionless numbers, namely, the Dini, Prandtl, and Schmidt numbers, the parameter R/Rk, which characterizes the curvature of the channel, and the dimensionless parameter Wf = fμRG(TO–TW)/(pMν), which characterizes the rate of thermophoresis.

History dependent orbital dissipation in 3HeA

Measurements of the damping and inertia of torsion pendulums containing 3HeA in toroidal flow channels are presented. A highly dissipative state is created if the channel velocity during the normal to A-phase transition, v o(T c), is high. On the other hand a low v o (T c) creates a state of low dissipation; it is then possible to increase the dissipation by a short period of high velocity oscillation. It is possible to interpret these history dependent results in terms of the formation and subsequent motion of surface singularities.