Non-linear viscoelastodynamic equations of three-dimensional rotating structures in finite displacement and finite element discretization

This paper deals with the non-linear viscoelastodynamics of three-dimensional rotating structure undergoing finite displacement. In addition, the non-linear dynamics is studied with respect to geometrical and mechanical perturbations. On part of the boundary of the structure, a rigid body displacement field is applied which moves the structure in a rotation motion. A time-dependent Dirichlet condition is applied to another part of the boundary. For instance, this corresponds to the cycle step of a helicopter rotor blade. A surface force field is applied to the third part of the boundary and depends on the time history of the structural displacement field. For example, this might corresponds to general unsteady aerodynamics forces applied to the structure. The objective of this paper is to model the non-linear dynamic behavior of such a rotating viscoelastic structure undergoing finite displacements, and to allow small geometrical and mechanical (mass, constitutive equations) perturbations analysis to be performed. The model is constructed by the introduction of a reference configuration which is deduced from the non-linear steady boundary value problem. A constitutive equation deduced from the Coleman and Noll theory concerning the viscoelasticity in finite displacement is used. Thereafter, the weak formulation of the boundary value problem is constructed and discretized using the finite element method. In order to simplify the mathematical study of the equations, multilinear forms are introduced in the algebraic calculation and their mathematical properties are presented.     

Direct on-strip analysis of size- and time-resolved aerosol impactor samples using laser induced fluorescence spectra excited at 263 and 351 nm

We report a novel atmospheric aerosol characterization technique, in which dual wavelength UV laser induced fluorescence (LIF) spectrometry marries an eight-stage rotating drum impactor (RDI), namely UV-LIF-RDI, to achieve size- and time-resolved analysis of aerosol particles on-strip. The UV-LIF-RDI technique measured LIF spectra via direct laser beam illumination onto the particles that were impacted on a RDI strip with a spatial resolution of 1.2 mm, equivalent to an averaged time resolution in the aerosol sampling of 3.6 h. Excited by a 263 nm or 351 nm laser, more than 2000 LIF spectra within a 3-week aerosol collection time period were obtained from the eight individual RDI strips that collected particles in eight different sizes ranging from 0.09 to 10 μm in Djibouti. Based on the known fluorescence database from atmospheric aerosols in the US, the LIF spectra obtained from the Djibouti aerosol samples were found to be dominated by fluorescence clusters 2, 5, and 8 (peaked at 330, 370, and 475 nm) when excited at 263 nm and by fluorescence clusters 1, 2, 5, and 6 (peaked at 390 and 460 nm) when excited at 351 nm. Size- and time-dependent variations of the fluorescence spectra revealed some size and time evolution behavior of organic and biological aerosols from the atmosphere in Djibouti. Moreover, this analytical technique could locate the possible sources and chemical compositions contributing to these fluorescence clusters. Advantages, limitations, and future developments of this new aerosol analysis technique are also discussed.     

Remobilization of pentavalent antimony and vanadium from a granular iron hydroxide material--a comparative study of different leaching systems

The remobilization of antimony and vanadium from previously loaded commercial granular ferric-hydroxide GEH material (intended for water treatment) was examined by using a sequential extraction procedure and three different leaching systems to evaluate their physicochemical mobility and potential availability under different simulated environmental conditions. A classical batch extraction, an extraction cell (EC) and rotating-coiled columns (RCC) were used as extraction systems.For each system it could be shown that the content of ion-exchangeable antimony and vanadium in previously loaded material is negligible (<1.5%). The oxyanions were sorbed strongly and could be predominantly remobilized through reducing agents, which means through dissolution of the iron (hydr)oxide matrix.The major advantages of dynamic systems in comparison to batchwise fractionation technique are the drastically reduced extraction time and the possibility of generating information to the leaching kinetics. It is shown that the efficiency of the three leaching systems is quite different employing Wenzel's sequential fractionation protocol. Only by working with RCC, the iron (hydr)oxide matrix was completely dissolved within four steps resulting in the total mobilization of antimony and vanadium. EC seems to be less suitable for leaching studies of Sb and V sorbed on iron(hydr)oxide. The remobilizable proportion of the several fractions was lower in comparison to batch and RCC and seems to be a result of an agglomeration of the GEH in the EC device.     

Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating-disk flow with Hall current

The focus of the present study is to obtain exact solutions for the flow of a viscous hydromagnetic fluid due to the rotation of an infinite disk in the presence of an axial uniform steady magnetic field with the inclusion of Hall current effect. In place of the traditional von Karman's axisymmetric evolution of the flow, the rotational non-axisymmetric stationary conducting flow is taken into consideration here, whose governing equations allow an exact solution to develop bounded everywhere in the normal direction to the wall.The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions, which differ from those of corresponding to the classical von Karman's conducting flow. Making use of this solution, analytical formulas for the angular velocity components, for the current density field as well as for the wall shear stresses are extracted. The critical peripheral locations at which extrema of the local skin friction occur are also determined. It is proved from the analytical results that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude, approaching their hydrodynamic value in the limit of large Hall numbers.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation function. According to the Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, though it increases by the presence of magnetic field, the increase is slowed down by the Hall effect eventually reaching its hydrodynamic limit.     

Coupled Electron‐Proton Transport in Electropolymerized Methylene Blue and the Influences of Its Protonation Level on the Rate of Electron Exchange with β‐Nicotinamide Adenine Dinucleotide

This paper describes electrochemical characteristics of poly(methylene blue) electrolytically deposited on glassy carbon and examines the electrocatalytic activity of the polymer toward oxidation of the coenzyme NADH. Redox‐active properties of the cationic polyelectrolyte arose from both electron self‐exchange between electroactive sites and a high ionic film‐conductivity. The diffusion coefficient of charge carriers in the film increased with decreasing solution pH, indicating the pH dependence of the electron diffusion coefficient. The electrocatalytic oxidation of NADH at the polymer‐modified electrode proceeded via an intermediate charge‐transfer complex of the reduced polymer with the oxidized coenzyme. The complex dissociated more rapidly into the oxidation products as the reduced polymer protonated. Thus, the rate constant for the cross‐exchange reaction rose with a decrease in pH. For NADH oxidation, the polyelectrolyte exhibited an electrocatalytic activity higher than the monomeric dye because of a stronger oxidizing power of the second oxidized form of the polymer.     

Hamiltonian restriction of Vlasov equations to rotating isopycnic and isentropic two-layer equations

A direct link between a Vlasov equation and the equations of motion of a rotating fluid with an effective pressure depending only on a pseudo-density is illustrated. In this direct link, the resulting fluid equations necessarily appear in flux conservative form when there are no topographical and rotational terms. In contrast, multilayer isopycnic and isentropic equations used in atmosphere and ocean dynamics, in the absence of topographical and rotational terms, cannot be brought into a conservative flux form, and, hence, cannot be derived directly from the Vlasov equations. Another route is explored, therefore: deriving the Hamiltonian formulation of the two-layer isopycnic and isentropic equations as a restriction from a Hamiltonian formulation of two decoupled Vlasov equations. The work is motivated by our search for energy-preserving or even Hamiltonian (kinetic) numerical schemes.     

Numerical analysis of the developing fluid flow in a circular duct rotating steadily about a parallel axis

A numerical analysis of the flow pattern in the inlet region of a circular pipe rotating steadily about an axis parallel to its own is presented. Both finite cell and finite element methods are used to analyse the problem and they give qualitatively similar results which show that a swirling fluid motion is induced in the pipe inlet region. The analyses show that the direction of swirl is opposite to that of the pipe rotation when viewed along the flow axis and that its magnitude depends on the speed of pipe rotation and throughflow Reynolds number. Neither numerical analysis predicts the marked upturn in friction factor (or pressure drop) which has been observed experimentally. However, a dependence on the pipe inlet boundary conditions is demonstrated.     

Numerical studies of slow viscous rotating flow past a sphere. III

The flow of steady incompressible viscous fluid rotating about the z-axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Re_ω. The Navier–Stokes equations governing the axisymmetric flow can be written as three coupled non-linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman–Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’. The results obtained by solving the non-linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Re_ω. Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non-linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Re_ω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.     

Magnetohydrodynamic flow past a porous rotating disk in a circular magnetic field

This paper studies the effects of a circular magnetic field on the flow of a conducting fluid about a porous rotating disk. Using modern quasi-Newton and globally convergent homotopy methods, numerical solutions are obtained for a wide range of magnetic field strengths, suction and injection velocities and Alfven and disk speeds. Results are presented graphically in terms of three non-dimensional parameters. There is excellent agreement with previous work and asymptotic formulae.     

Determination of diffusion coefficients of Cu(I) ions in concentrated perchlorate solutions

The diffusion coefficients of Cu(I) ions in concentrated aqueous Ca(ClO₄)₂ solutions have been determined from the limiting currents of anodic oxidation at the rotating disc electrode.

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Zur Bestimmung der Diffusionskoeffizienten von Cu(I)-Ionen in konzentrierten Perchloratlösungen (Kurze Mitteilung)

Zusammenfassung Diffusionskoeffizienten von Cu(I)-Ionen in konzentrierten wäßrigen Ca(ClO₄)₂-Lösungen wurden durch Messung der anodischen Grenzströme an der rotierenden Scheibenelektrode bestimmt.