CONVERGENCE OF SIMPLIFIED AND STABILIZED MIXED ELEMENT FORMATS BASED ON BUBBLE FUNCTION FOR THE STOKES PROBLEM

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｒｄｅｒｔｏｇｅｔｒｉｄｏｆｔｈｅｒｅｓｔｒｉｃｔｉｏｎｔｏｄｉｓｃｒｅｔｅＢａｂｕｓｋａ＿Ｂｒｅｚｚｉ’ｓｃｏｎｄｉｔｉｏｎｓｉｎｒｅｓｅａｒｃｈｅｓｏｆｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔ (ＭＦＥ)ｍｅｔｈｏｄｓ,ｏｎｅｕｓｕａｌｌｙｕｓｅｓｔｈｅｓｔａｂｉｌｉｚｅｄＭＦＥｍｅｔｈｏｄｓｆｏｒｍａｔ[1] .Ｔｈｅｒｅａｒｅａｎｕｍｂｅｒｏｆｓｔａｂｉｌｉｚｅｄｍｅｔｈｏｄｓ (ｓｅｅ ,ｅ.ｇ .,Ｒｅｆｓ.[1- 7]ａｎｄｔｈｅｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ) ,ｗｈｉｃｈｈ…     

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.     

BEHAVIOR OF OBSTRUCTED SQUARE BUOYANT VERTICAL JETS IN STATIC AMBIENT （Ⅰ）—— VERIFICATION OF MATHEMATICAL MODEL AND NUMERICAL METHOD

Some experiments were made for the buoyant jet from a square orifice with a square disc placed on it in static ambient and concentration along the axis in self-similar area behind disc was measured. And at the same time a three-dimensional mathematical model was established to simulate the whole flowing under different conditions. All the results predicted by the numerical calculation were substantiated by the experiments. The results were compared with experiential formula for obstructed round buoyant vertical jets in static ambient and it was found that the two concentration distributions had good accordance. Star shape of temperature isolines on cross-sections in the near areas from the disc was found and it was a very special figure for obstructed square buoyant vertical jets with a square disc. The shape will transform to concentric circles gradually alike to the round buoyant vertical jet in self-similar area with increasing of the distance from the disc.     

ELECTROELASTIC FIELD FOR AN IMPERMEABLE ANTI-PLANE SHEAR CRACK IN A PIEZOELECTRIC CERAMICS PLATE

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｅｔｏｔｈｅｉｎｔｒｉｎｓｉｃｃｏｕｐｌｉｎｇｃｈａｒａｃｔｅｒｉｓｔｉｃｓｂｅｔｗｅｅｎｅｌｅｃｔｒｉｃａｎｄｅｌａｓｔｉｃｂｅｈａｖｉｏｒｓ,ｔｈａｔｉｓ,ａｐｐｌｉｅｄｍｅｃｈａｎｉｃａｌｌｏａｄｉｎｇｐｒｏｄｕｃｅｓｅｌａｓｔｉｃｄｅｆｏｒｍａｔｉｏｎ ,ａｓｗｅｌｌａｓｅｌｅｃｔｒｉｃｆｉｅｌｄ ,ａｎｄｃｏｎｖｅｒｓｅｌｙｅｌｅｃｔｒｉｃｆｉｅｌｄｃａｎｇｉｖｅｒｉｓｅｔｏｅｌａｓｔｉｃｄｅｆｏｒｍａｔｉｏｎ ,ｐｉｅｚｏｅｌｅｃｔｒｉｃｍａｔｅｒｉａｌｓｈａｖｅ…     

AN IMPROVED ARC-LENGTH METHOD AND APPLICATION IN THE POST-BUCKLING ANALYSIS FOR COMPOSITE STRUCTURES

Based on the conventional arc- length method, an improved arc- length method with high-efficiency is proposed. The weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc- length . An approximate expansion method for the accumulated and expected arc-length is used to ensure the convergence at given load levels in large range of applications. Numerical results show that the improved arc-length method has well adaptability and higher efficiency in the post-buckling analysis of plates and sheik structures for tracing whole load-deflection path and obtaining the convergence values at any specified load levels.     

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)     

Two phase boundary layers in laminar film boiling

The laminar film boiling is analyzed by means of an integral procedure. The method treats the film boiling as a two phase boundary layer problem; thereby the effect of the interfacial shear on the heat transfer rate can be investigated. The problem is attacked by simultaneously solving the vapor and liquid boundary layer equations. An extensive comparison of the predicted results with the exact solutions substantiates the validity of the present integral procedure. Even the details of the velocity and temperature profiles turn out to be in close agreement with the exact solutions.     

On a highly accurate computational scheme for the approximate analysis of shear-flexible anisotropie plates

Summary The paper deals with the analysis of shear-flexible anisotropic plates subjected to arbitrary boundary conditions. In order to solve the pertinent boundary value problem, a Ritz-type technique has been developed which, however, ist not based on the standard principle of minimum potential energy but a modification thereof. In this variational theorem, the boundary conditions are satisfied a posteriori as natural constraints, therefore relatively simple trial functions can be used to approximate the displacement variables in the interior of the plate. Extensive studies carried out on a series of relevant examples illustrate that the proposed method represents an inexpensive, reliable and highly efficient tool for solving a wide variety of plate bending problems.

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Ein sehr genaues numerisches verfahren zur näherungsweisen berechnung des tragund deformationsverhaltens schubsteifer anisotroper platten

Übersicht Die vorliegende Arbeit beschäftigt sich mit der Berechnung des Trag- und. Deformationsverhaltens beliebig gelagerter Platten unter Berücksichtigung von Materialanisotropie sowie Schubkrafteinfluß. Beim entwickelten Berechnungsverfahren handelt es sich um eine Ritz-Methode, welche allerdings nicht auf dem Prinzip des Minimums der potentiellen Energie, sondern einer Modifikation davon basiert. Das Besondere an dieser modifizierten Variationsgleichung liegt darin, daß die geometrischen Rand- und Übergangsbedingungen nicht als wesentliche, sondern als natürliche Nebenbedingungen erfüllt werden. Die Genauigkeit und praktische Relevanz der entwickelten Methode wird anhand einiger Representativbeispiele demonstriert.

     

Upper limit of enhancement of boiling heat transfer in a narrow vertical rectangular channel due to passing bubbles

An experimental study has been made of saturated boiling heat transfer for water and R113 in a narrow vertical rectangular channel (2 mm space, 20 mm wide, and 200 mm long) at atmospheric pressure, in which the vertical heated surface (10 mm long and 20 mm wide) is located on one side at a position of 150 mm from its entrance and bubbles are forcibly passed through it at a designated period from 0.33 to 1.0 sec. The experiment shows that the heat transfer coefficients are increased by the bubble passing through the heated surface for the value of thermal diffusivity,a, times period, T₀, of the passing bubbles above about 6×10^–9 m² (a T ₀>6×10^–9 m²) while fora T ₀< 6×10^–9 m², the heat transfer coefficients become independent of the period and the effectiveness of the enhancement of the heat transfer owing to the passing bubble disappears.

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Die obere Grenze der Verbesserung des Wärmeübergangs beim Sieden in einem vertikalen, rechteckigen Kanal infolge von aufsteigenden Blasen

Zusammenfassung Es wurden Experimente über den Wärmeübergang beim Sättigungssieden mit Wasser und R113 in einem engen, vertikalen, rechteckigen Kanal (2 mm Abstand, 20 mm Breite und 200 mm Länge) bei Umgebungsdruck durchgeführt, wobei die vertikale, beheizte Oberfläche (10 mm lang und 20 mm breit) auf der einen Seite in einem Abstand von 150 mm vom Eintritt angeordnet ist und die Blasen zwangsweise durch den Kanal sich mit einem Periodenabstand von 0,033 bis 1,0 s bewegen. Das Experiment zeigt, daß die Wärmeübergangskoeffizienten durch das Vorbeistreichen der Blasen an der beheizten Oberfläche verbessert werden, wenn das Produkt aus Temperaturleitfähigkeit,a, mal der Periode, T₀, der vorbeistreichenden Blasen größer als 6×10^–9 m² liegt, während unterhalb dieses Wertes der Wärmeübergangskoeffizient unabhängig von der Blasenperiode ist und die Effektivität der Wärmeübergangsverbesserung infolge der Blasenströmung verschwindet.

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Nomenclature a thermal diffusivity of liquid - ¯h time-averaged heat transfer coefficient - q _w heat flux at wall - T ₀ period of passing bubble - T _w(t) temperature of heated surface - T _w amplitude of heated surface temperature Greek symbols thermal conductivity - thickness of liquid film     

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.