An implicit characteristic-flux-averaging method for the euler equations for real gases

A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.     

Coordination complexes of 3,4-dihydroxyphenylpropionic acid (dihydrocaffeic acid) with copper(II), nickel(II), cobalt(II) and iron(III)

Summary The preparation of complexes of 3,4-dihydroxyphenylpropoionic acid (hydrocaffeic acid): K₂[Cu₂(hydcafH)₂-Cl₂]·2KCl·2MeOH, K₂[Co(hydcafH)₂]·2KCl, K₂[Ni₂(hydcafH)₂Cl₂]·2KCl·2MeOH and Fe₂ (hydcafH)₂Cl₂·2KCl·2H₂O was achieved. Spectroscopic and magnetic studies are commensurate with tetrahedral structures for the prepared complexes in which the catechol-like coordination is present.     

Coordination complexes of l-azetidine-2-carboxylic acid with platinum(II) and palladium(II)

Summary The complexes K[Pt(l-aze)Cl₂, [Pt(l-aze)₂] and [Pd(l-aze)₂] (l-aze = l-azetidine-2-carboxylate) were prepared. X-ray structures show that [Pt(l-aze)₂] and [Pd(l-aze)₂] are isomorphous, having a planar tetragonal geometry with a trans configuration around the Pt and Pd atoms. Slight puckerings of the MN(1)N(11)O(11) chelate ring (M = Pt or Pd) and the azetidine ring were observed. The circular dichroism (c.d.) spectra of the complexes in aqueous solution agree with the structures found in the solid state as far as the hexadecant rule is concerned, giving, for the trans configuration of [M(l-ia)₂] (where ia = imino acid), the profile of the c.d. signs for the three predominant d-d transitions as: +,-,-. I.r., conductivity and n.m.r. measurements are also reported and are in accord with the proposed structures.     

Metal complexes of the diuretic drug furosemide

New complexes of the formulaeM(fur)₂·2H₂O (M = Mn, Cu, Zn),M(fur)₂·3H₂O (M = Co, Ni, Cd), Hg₂(fur)₃Cl₂·2H₂O, Pd(fur)Cl·H₂O and Rh(fur)₃·3H₂O, wherefurH = 4-chloro-N-(2-furfuryl)-5-sulfamoylanthranilic acid, have been prepared and characterized by conductivity measurements, X-ray powder patterns, thermal methods, effective magnetic moments as well as by IR, ligand field,¹H-NMR and ESR spectroscopic studies. The anionfur ^– shows a chelated bidentate O(carboxylato), N(imino)-coordinating behaviour.

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Metallkomplexe der diuretischen Droge Furosemid

Zusammenfassung Neue Komplexe der Verbindungen:M(fur)₂·2H₂O (M = Mn, Cu, Zn),M(fur)₂·3H₂O (M = Co, Ni, Cd), Hg₂(fur)₃Cl₂·2H₂O, Pd(fur)Cl·H₂O und Rh(fur)₃·3H₂O, wobeifurH 4-chlor-N-(2-furfuryl)-5-sulfamoylanthanilsäure ist, wurden dargestellt. Die Komplexe wurden durch Leitfähigkeitsmessungen, Röntgen-Pulver-Aufnahmen, thermogravimetrische Analysen, Messungen des effektiven magnetischen Dipolemomentes sowie durch spektroskopische Untersuchungen (IR,¹H-NMR und ESR) charakterisiert. Das Anionfur ^– zeigt das Verhalten einer Chelat-bidentat-O(carboxylato),N(imino)-Koordination.

     

Primes of the form <Emphasis Type="Italic">x</Emphasis><Superscript>2</Superscript> + (<Emphasis Type="Italic">x</Emphasis> + 1)<Superscript>2</Superscript>. Proper divisors of composites of the same form

The aim of the present paper is to characterize prime numbers of the form n = x ² + (x + 1)² and to obtain certain proper divisors of composite numbers of the same form, i.e. divisors d of n such that 1 < d < n.      

Longitudinal dispersion in a duct with moving walls

The dispersion of a diffusing substance along a channel or pipe is augmented if the channel walls (resp. pipe wall) are moving in the lateral direction. The fluid in the present theoretical investigation is supposed to be inviscid. The longitudinal dispersion enhancement is evaluated analytically and the expressions for various movements of the walls are given in simple formulas.

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Zusammenfassung In der vorliegenden Arbeit wird die Dispersion einer flüssigen Substanz in einem symmetrischen Kanal studiert, dessen ebene Wände sich in der vertikalen Richtung bewegen. Es zeigt sich, daß die longitudinale Dispersion damit vergrößert wird. Die Flüssigkeit wird als reibungsfrei angenommen. Die Lösung wird in analytischer Form dargestellt und an verschiedenen Bewegungen der Kanalwände angewendet. Die Lösung wurde auch für den achsensymmetrischen Fall erweitert.

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In memoriam Prof. Erich Leiter, Technical University of Vienna, Austria     

Development of an artificial compressibility methodology using flux vector splitting

An implicit, upwind arithmetic scheme that is efficient for the solution of laminar, steady, incompressible, two-dimensional flow fields in a generalised co-ordinate system is presented in this paper. The developed algorithm is based on the extended flux-vector-splitting (FVS) method for solving incompressible flow fields. As in the case of compressible flows, the FVS method consists of the decomposition of the convective fluxes into positive and negative parts that transmit information from the upstream and downstream flow field respectively. The extension of this method to the solution of incompressible flows is achieved by the method of artificial compressibility, whereby an artificial time derivative of the pressure is added to the continuity equation. In this way the incompressible equations take on a hyperbolic character with pseudopressure waves propagating with finite speed. In such problems the ‘information’ inside the field is transmitted along its characteristic curves. In this sense, we can use upwind schemes to represent the finite volume scheme of the problem's governing equations. For the representation of the problem variables at the cell faces, upwind schemes up to third order of accuracy are used, while for the development of a time-iterative procedure a first-order-accurate Euler backward-time difference scheme is used and a second-order central differencing for the shear stresses is presented. The discretized Navier–Stokes equations are solved by an implicit unfactored method using Newton iterations and Gauss–Siedel relaxation. To validate the derived arithmetical results against experimental data and other numerical solutions, various laminar flows with known behaviour from the literature are examined. © 1997 John Wiley & Sons, Ltd.     

Fluid flow of incompressible viscous fluid through a non-linear elastic tube

The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung’s (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain–energy density function. The fluid is described through a Navier–Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response.     

Exact solution of the Navier-Stokes equations for the oscillating flow in a duct of a cross-section of right-angled isosceles triangle

The Navier-Stokes equations have been solved in order to obtain an analytical solution of the fully developed laminar flow in a duct having a cross section of a right-angled, isosceles triangle. We obtained a solution for the case of oscillating pressure gradient flow. The pulsating flow is obtained by the superposition of the steady and oscillating pressure gradient solutions.