Die Trennung von Gas-Dampf-Gemischen durch Kondensation im senkrechten Rohr bei hohen Reynolds-Zahlen

Zusammenfassung Der Wärme- und Stoffübergang bei der Kondensation von Dampf aus einem Gas-Dampf-Gemisch bei sehr hohen Reynolds-Zahlen wurde theoretisch und experimentell untersucht. In einem senkrechten Messingrohr wurde ein Gemisch aus Monofluortrichlormethan (R11) und Stickstoff mit Gaskonzentrationen X_G+~0,01...0,42 bei Re +~70000... 450000 gekühlt; die Reynoldszahl der Kondensatfilmstromungerreichte Werte von über 1000. Eine mathematische Methode wurde entwickelt, um verschiedene Größen als Funktion der Hauptparameter Gaskonzentration, Reynoldszahl des Gemisches und Kühllange darzustellen.

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The separation of gas-steam-mixtures by condensation in a vertical tube at high reynold-numbers

Heat and mass transfer for condensation from a gas-vapor-mixture with very high Reynolds-numbers was analyzed on a theoretical and experimental basis. A mixture of monofluorotrichloromethane (R 11) and nitrogen was cooled in a vertical brass tube. The gas concentrations and the Reynolds-numbers comprised the ranges X_G t+~0.01...0.42 and Re t+~70,000...450, 000; the Reynolds-number of the condensate film flow reached values of above 1000. A mathematical method was developed to show the various values as function of the main parameters, such as gas concentration, Reynolds-number of the mixture and cooling length.

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Bezeichnungen a, b Koeffizienten - b dimensionslose Schichtdicke - c_p spezifische Warmekapazität - d Durchmesser - D Diffusionskoeffizient - F Oberfläche - g Fallbeschleunigung - h spezifische Enthalpie - m Massenstrom - p Druck - q Wärmestromdichte - Q Wärmestrom - r Verdampfungsenthalpie - s Filmdicke - t Temperatur - U allgemeiner Funktionswert - U Umfang - v spezifisches Volumen - w Geschwindigkeit - x Molanteil - y Massenanteil - z Längskoordinate der Rohrströmung - X,Y,Z allgemeine unabhangige Variablen - Wärmeübergangskoeffizient - Stoffübergangskoeffizient - dynamische Viskosität - Wärmeleitkoeffizient - kinematische Viskosität - Dichte - Tautemperatur - Partialdruckanteil - Molmasse Indices a außen - B Bezugszustand - D Dampf - f Phasengrenzfläche - G Gas - gem Gemisch - i innen - k Strömungskern - K Kondensat - Kv konvektiv - L Kolbenstellung - m mittel - W Wand - z örtlich, an der Stelle z - Funktionswert integraler Mittelwert - 0 bei z=0 (Eintritt)     

An actuator-disc model for the prediction of abrupt stall in an axial compressor rotor

The representation of loss in a cascade by the appearance of blockage has been extended to deal with blade rows by the use of a source distribution to represent this blockage, and in the case of the actuator disc approximation, the presence of sources is confined to an axi-symmetric dìstribution over the actuator disc. It is found that if a typical dependence of loss (and consequently diffusion ratio) upon incidence for each section of an axial compressor rotor is represented in this manner, the influence of blockage on the axial velocity distribution may be found using the potential equation combined with the usual actuator disc approximation. Study of the behaviour of the controlling ordinary differential equation for the axial velocity ahead of the disc reveals that as the flow is reduced, the equation contains a singularity within the range of radius and a meaningful solution does not exist. This result is interpreted as the limit to continuous operation and reasonable agreement between this predicted limit and the appearance of abrupt stall (experimentally) is found.     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

ON SOME PROPERTIES OF LIENARD SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒａｇｅｎｅｒａｌｉｚｅｄＬｉｅｎａｒｄｓｙｓｔｅｍｓｏｆｔｈｅｆｏｒｍ ｘ=ｈ(ｙ) -Ｆ(ｘ) , ｙ=-ｇ(ｘ) ,( 1 )ｗｈｅｒｅｔｈｅｆｕｎｃｔｉｏｎｓＦ ,ｇａｎｄｈａｒｅＬｉｐｓｃｈｉｔｚｃｏｎｔｉｎｕｏｕｓａｎｄｓａｔｉｓｆｙＦ( 0 ) =ｈ( 0 ) =0 ,ｘｇ(ｘ) >0 ,　　ｘ≠ 0 . ( 2 )Ｔｈｅｒｅｈａｖｅｂｅｅｎｍａｎｙｓｔｕｄｉｅｓｆｏｒｌｏｃａｌａｎｄｇｌｏｂａｌｐｒｏｐｅｒｔｉｅｓｏｆｓｏｌｕｔｉｏｎｓｆｏｒｓｙｓｔｅｍ ( 1 ) ,ｓｅｅ[1 -9] .ＳｅｔＣ+=(ｘ,ｙ)｜ｈ(ｙ…     

Elongational viscosity by fiber spinning

Isothermal melt, fiber-spinning was recently analyzed by means of a nonlinear, integral, constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear-thinning, and extension thinning or thickening when either the drawing force or the draw ratio is specified. The predictions agreed with experimental data on spinning of polystyrene, low-density polyethylene, and polypropylene melts. The predicted apparent elongational viscosity along the threadline (which, as shown in this work, must be identical to that measured experimentally by fiber spinning type of elongational rheometers) is compared with the true elongational viscosity predicted by the same constitutive equation under well-defined experimental conditions of constant extension rate, independent of any strain history. It is concluded that the apparent elongational viscosity, as measured by fiber-spinning, approaches the true elongational viscosity at low Weissenberg numbers (defined as the product of the liquid's relaxation time multiplied by the extension rate). At moderate Weissenberg numbers, the two viscosities may differ by an order of magnitude and their difference grows even larger at high Weissenberg numbers.     

VISCOPLASTIC SOLUTION TO FIELD AT STEADILY PROPAGATING CRACK TIP IN LINEAR- HARDENING MATERIALS

An elastic-viscoplastic constitutive model was adopted to analyze asymptotically the tip-field of moving crack in linear-hardening materials under plane strain condition. Under the assumption that the artificial viscosity coefficient was in inverse proportion to power law of the rate of effective plastic strain, it is obtained that stress and strain both possess power law singularity and the singularity exponent is uniquely determined by the power law exponent of the rate of effective plastic strain. Variations of zoning structure according to each material parameter were discussed by means of numerical computation for the tip-field of mode Ⅱ dynamic propagating crack, which show that the structure of crack tip field is dominated by hardening coefficient rather than viscosity coefficient. The secondary plastic zone can be ignored for weak hardening materials while the secondary plastic zone and the secondary elastic zone both have important influence on crack tip field for strong hardening materials. The dynamic solution approaches to the corresponding quasi-static solution when the crack moving speed goes to zero, and further approaches to the HR (Hui-Riedel) solution when the hardening coefficient is equal to zero.     

DYNAMIC ANALYSIS OF A SPATIAL COUPLED TIMOSHENKO ROTATING SHAFT WITH LARGE DISPLACEMENTS

ＩｎｔｒｏｄｕｃｔｉｏｎＲｏｔａｔｉｎｇｓｈａｆｔｓａｒｅｔｈｅｍｏｓｔｖｉｔａｌｃｏｍｐｏｎｅｎｔｓｏｆｍｏｄｅｒｎｉｎｄｕｓｔｒｉａｌａｎｄｐｏｗｅｒｇｅｎｅｒａｔｉｏｎｆａｃｉｌｉｔｉｅｓ.ＤｕｅｔｏｔｈｅｉｍｐｏｒｔａｎｃｅｏｆｔｈｅｓｅｃｏｍｐｏｎｅｎｔｓｔｈｅｒｅｗｅｒｅｗｉｄｅｌｙｓｔｕｄｉｅｓｏｎｔｈｅｖｉｂｒａｔｉｏｎｂｅｈａｖｉｏｒｏｆＥｕｌｅｒ＿Ｂｅｒｎｏｕｌｌｉｒｏｔａｔｉｎｇｓｈａｆｔｓｕｓｉｎｇａｎａｌｙｔｉｃａｌａｎｄｎｕｍｅｒｉｃａｌｍｅｔｈｏｄｓ[1- 4 ].Ｈｏｗｅ…     

GLOBAL ATTRACTOR FOR HASEGAWA-MIMA EQUATION

The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated.     

EXPONENTIAL STABILITY OF INTERVAL DYNAMICAL SYSTEM WITH MULTIDELAY

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔａｂｉｌｉｔｙｏｆｔｈｅｉｎｔｅｒｖａｌｍａｔｒｉｘａｎｄｕｎｃｅｒｔａｉｎｓｙｓｔｅｍｗｉｔｈｔｉｍｅｄｅｌａｙｈａｖｅｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｒｅｓｅａｒｃｈｅｒｓｉｎｔｈｅｐａｐｅｒｓ [1 -1 3 ] .Ｔｈｅｓｔａｂｉｌｉｔｙａｎｄαｅｘｐｏｎｅｎｔｉａｌｓｔａｂｉｌｉｔｙｏｆｔｈｅｆｏｌｌｏｗｉｎｇｉｎｔｅｒｖａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｗｉｔｈｓｉｎｇｌｅｔｉｍｅｄｅｌａｙ ｘ(ｔ) =Ｎ[Ｐ ,Ｑ]ｘ(ｔ) +Ｎ[Ｃ ,Ｄ]ｘ(ｔ-τ)ｈａｖｅｂｅｅｎｃｏｎｓｉ…     

The elastic-plastic stress distribution near the flat surfaced notch with cycloidal tip in a work-hardening material

Summary Based on a deformation theory of plasticity, the stress distribution near an edge crack having finite root radius in strain-hardening material is given for the case of antiplane shear (Mode III). The approximate solution is derived in an analytical form by using Neuber's result and integral J by Rice.

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Übersicht Unter Zugrundelegung der Deformationstheorie der Plastizität wird die Spannungsverteilung in der Nähe eines Randrisses mit endlichem Radius für den Fall des nichtebenen Schubspannungszustandes (Mode III) und eines dehnungsverfestigenden Materials gegeben. Die angenäherte Lösung wird durch Verwendung der Ergebnisse von Neuber sowie dem J-Integral von Rice in analytischer Form erhalten.

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In honour of the 70th birthday of Professor H. Neuber.