Verdampfen und Kondensieren binärer Gemische als Strömungsproblem

Zusammenfassung Die Grenze zwischen gasförmiger und flüssiger Phase eines binären Gemisches stellt beim Verdampfen oder Kondensieren eine Wärme- und Stoffquelle dar. Phasenumwandlungen von Gemischen führen folglich im allgemeinen auf Strömungsvorgänge mit Wärme- und Stoffübertragung. Die Grundgleichungen dafür werden sowohl in Massen- wie in Moldarstellung hergeleitet. Bei Filmkondensation werden im Falle des Gleichstromes von Dampf und Flüssigkeit neue Erkenntnisse gewonnen, womit ältere Versuchsergebnisse erklärt werden.

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Evaporation and condensation of binary mixtures as a flow problem

The boundary between the gaseous and liquid phases of a binary mixture is a source of both heat and mass, if evaporation or condensation takes place. Thus phase transitions of binary mixtures are related to flow processes with combined heat and mass transfer. The basic equations for this type of processes are derived in terms of mass and mole fractions, respectively. New results, which allow an interpretation of previous experimental data, are obtained for film condensation under cocurrent flow conditions.

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Formelzeichen a Bewegungsgeschwindigkeit vonF in Normalenrichtung - b Spaltbreite des Ringrohres - B Integrationsbereich - C Massenanteil - c _p spez. Wärme bei konst. Druck - D Diffusionskoeffizient - e spez. innere Energie - E Molenergie - F Begrenzungsfläche - g Schwerebeschleunigung - i spez. Enthalpie - I Molenthalpie - j Diffusionsstromdichte - K _Hy hydraulische Kennzahl - L Rohrlänge - Massenstromdichte - M Masse - Massenstrom - n Moldichte - Molstromdichte - n Einheitsvektor der Flächennormalen - N Mohlzahl - Molstrom - p Druck - q Wärmestrom - R Rohrradius - T Temperatur - t Zeit - mittlere Geschwindigkeit - u, v, w Geschwindigkeitskomponenten - v Rücklaufverhältnis - V Volumen - W Geschwindigkeitsvektor - x, y, z Koordinaten - X Molanteil - Filmdicke - Verdampfungswärme bei konst. Druck - Molmasse - kinematische Zähigkeit - Dichte - Stromfunktion Indizes a Ausströmung - d Dampfphase - e Einströmung - f flüssige Phase - i Phasengrenze - i=1, 2 Komponente - n Normalenrichtung     

Untersuchung von Einzelblasen an ölbeschichteten Oberflächen mit künstlichen Keimstellen

Zusammenfassung An feinpolierten, ölbeschichteten V2A-Oberflächen mit jeweils einer gebohrten (d=140 µm) und einer geätzten (d=47 µm) Vertiefung als Keimstelle wurde für Wasserblasen das Wachstum, der Abreißdurchmesser und die Abreißfrequenz gemessen. Für die wärmetransportgesteuerte Blasenbildung liefert der Vergleich mit Beziehungen, die für reine Metallflächen gewonnen wurden, gute Übereinstimmung, so daß keine Einfluß der Ölschicht erkennbar wurde.

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Investigation of single vapor bubbles on surfaces covered with a thin oil film with artificial nuclei

For single vapor bubbles, the growth rates, the detachment diameter, and the frequency were measured on single artificial nuclei, either drilled (d=140 µm) or etched (d=47 µm) into a highly polished stainless steel plate which was covered with a thin oil film. For evaporation controlled by heat transport, good agreement was observed with relations from literature which were obtained for clean surfaces; thus, an effect of the oil film could not be discovered.

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Formelzeichen a Temperaturleitfähigkeit - D _a Blasenabreißdurchmesser - f Blasenfrequenz - Ja Jakob-Zahl - Pr Prandtl-Zahl /a - q Wärmestromdichte - R Blasenradius - T Temperatur - dynamische Zähigkeit - Wärmeleitfähigkeit - Dichte - Oberflächenspannung - Zeit Indizes g Gas, Dampf - l flüssig - s Sättigung - w Wand Herrn Prof. Dr.-Ing. Karl Stephan zum 60. Geburtstag gewidmet     

Qualitative analysis of finite-gap solutions of the KgΦ equation by the automorphic approach

By the automorphic approach and the use of computer graphics, we carry out a qualitative analysis of finite-gap periodic solutions of the Kg equation. Graphs are constructed for multiphase solutions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 31–41, 1987.     

Addendum to the paper “on a theorem of Miranda”

An existence theorem is proved for closed convex surfaces whose principal radii of curvature regarded as functions of the unit normal vectorn satisfy the equation

Estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems

Majorants of the fractal dimension and of the number of determining modes for unbounded sets, invariant with respect to operators of semigroups of classes 1 and 2, are obtained. They are computed for the Navier-Stokes equations (two- and three-dimensional) under the first boundary condition and under periodicity conditions in the spaces and .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 105–129, 1987.     

On immersions ofn-dimensional Lobachevskií space in 2n-dimensional Euclidean space withn principal direction fields

In this article we prove that the principal direction fields are holonomic and use them to introduce curvilinear coordinates on an immersed region in terms of which the linear element of Lobachevskií space is written in the form where The fundamental system of equations is established for an immersion ofn-dimensional Lobachevskií space into 2n-dimensional Euclidean space withn principal direction fields for the functions _i and, and a way of constructing an arbitrary local analytic immersion is shown.Translated from Ukrainskií Geometricheskií Sbornik, No. 28, pp. 3–8, 1985.     

Taylor expansion of effective Hamiltonians by Monte Carlo simulations with fixed block spins

Monte Carlo simulations with fixed block spins allow the computation of Taylor expansion kernels for effective Hamiltonians. The expansion can be performed around arbitrary block spin configurations \(\bar \phi\) and does not suffer from truncation errors. Monte Carlo calculation of the Taylor kernels offers a ready possibility to check whether the effective Hamiltonian has good locality properties in the neighborhood of a given configuration \(\bar \phi\) . The method is applied in a renormalization group study of the 2-dimensional critical Ising model. The results show that one has to deal with a “large field problem”, as had been expected from rigorous renormalization group studies.     

Cubic surfaces in AG(3, q) and projective planes of order q 3

Spread sets of projective planes of order q ³ are represented as sets of q ³ points in A AG(3, q ³). A line through the origin in A can be interpreted as a space A ₀ AG(3, q), and the spread set induces a cubic surface L in A ₀. If the projective plane is a semifield plane of dimension 3 over its kernel, then L has the property that it misses a plane of A ₀. Determining all such surfaces L leads to a complete classification of the semifield planes of order q ³, whose spread sets are division algebras of dimension 3.An alternative proof of a result due to Menichetti, that finite division algebras of dimension 3 are associative or are twisted fields, follows with the classification.     

Properties of nonlinear waves in dissipative-dispersive media with instability

Wave processes in dissipative-dispersive media with instability described by a fourth-order nonlinear evolution equation are considered. Analytic solutions in the form of solitary and cnoidal waves are obtained. The existence of a critical value of the dispersion coefficient beyond which an initial disturbance (in particular, white noise) is transformed into a structure is demonstrated by numerical modeling.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 130–136, July–August, 1990.     

Crystal structure and vibrational spectra of hydrazinium (2+) tri-μ-fluoro bis[pentafluorozirconate (IV)] fluoride and vibrational spectra of its hafnium analogue

Monoclinic (N₂H₆)₃Zr₂F₁₃·F crystallizes in space group P2₁-C ₂ ² (No. 4) with unit cell dimensionsa=5.670(1),b=10.984(2),c=10.601(2) Å,=93.88(1)°,V=658.7(4) ų andZ=2. Two different types of N₂H₆ ²⁺ ions are present. One is involved in strong H-bonds to F^– ions in infinite chains running along the a axis (the shortest N-F distance is 2.437(5) Å), and the other links the structure through weaker bi- and trifurcated H-bonds to fluorine ligands of the Zr₂F₁₃ ^5– ions. The N-N bond lengths range from 1.430(5) to 1.446(5) Å with apparently no meaningful correlation to the type of N₂H₂ ²⁺ ions. The Zr₂F₁₃ ^5– ions have very nearly C₂ point symmetry and are formed by joining two distorted bicapped trigonal prisms of ZrF₈-units through a common face. Distances of Zr-F terminal bonds range from 2.015(2) to 2.112(2) Å and of bridging bonds from 2.133(2) to 2.212(2) Å. (N₂H₆)₃Hf₂F₁₃·F is isomorphous. The vibrational spectra of the two compounds are nearly identical, with the exception of a strong infrared band, which is assigned to a stretching mode with the moving central atom within the anion. The anion part of the spectrum is simple, showing broad unresolved bands. The cation part shows two types of N₂H₆ ^– ions. H-Bonding is strongly present in the spectra, but no simple correlations with the H-bond strength is evident.