单位球上加权 Bergman-Nevanlinna空间到 Blo ch-型空间上乘法,复合,微分算子的乘积

文章用径向导数定义了 H(B)空间上的微分算子,从而研究了单位球上加权Bergman-Nevanlinna 空间到 Bloch-型空间上乘法,复合,微分算子的乘积,给出了这类乘积有界和紧的充要条件。     

Magnetohydrodynamic shock propagation in non-uniform ducts

Zusammenfassung Es wird die Störung bestimmt, die ein gleichförmiger magnetohydrodynamischer Stoss beliebiger Stärke durch eine Querschnittsveränderung der Strömung erleidet. Beim Durchgang durch die Querschnittsveränderung ändert sich die Stärke des Stosses, und die Strömung bleibt nicht länger isentropisch. Es ergeben sich zwei verschiedene Störungsanteile, nämlich ein stationärer, der unmittelbar durch die Querschnittsveränderung hervorgerufen wird, und ein zeitlich veränderlicher Anteil, der von der Reflektion des ersten Anteils an dem Stoss herrührt.Die Untersuchungen, die auf ein einatomiges Gas beschränkt sind, enthalten gewisse bekannte gasdynamische Ergebnisse als Spezialfälle.

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Sponsored by the United States Army under Contract no. DA-11-022-ORD-2059.     

Note on flow instability in heated ducts

Zusammenfassung Das Problem der Stabilität der Strömung durch beheizte horizontale Kanäle gegen zweidimensionale Störungen wird in linearisierter Form als Variationsaufgabe behandelt. Die Abhängigkeit der Stabilitätsparameter von der Gestalt des Kanals wird untersucht und verglichen mit dem Fall der Stabilität der von unten beheizten Flüssigkeitsschicht.     

Modelling of two-phase incompressible flows in ducts

An improved level-set method for capturing interfaces combined with a second-order projection method for solving the time-dependent incompressible Navier–Stokes equations is implemented to compute two-phase viscous flows of Newtonian fluids on Cartesian staggered meshes. Various arrays of deformable droplets are suspended in an ambient fluid of different viscosity in ducts and the deformation and migration of droplets as they move along the duct are computed and discussed.     

Numerical analysis of turbine blade cooling ducts

The cooling of turbine blades in turbines is enhanced by providing the cooling ducts with ribs, so-called turbulators. It is investigated how these ribs influence the heat transfer of the cooling air on the blades. A model is given to study this problem such that it lends itself to a numerical approach. A detailed discussion is given of the problem involved. It is shown how the ideas are implemented in a numerical code. The results of the simulations are assessed showing a practical way to test the quality of these cooling ducts.     

Group Twisted Tensor Bipro ducts over Hopf Group Coalgebras

In this paper, we introduce the concept of a group twisted tensor biproduct and give the necessary and su？cient conditions for the new object to be a Hopf group coalgebra.     

Numerical studies of laminar flow in ducts and pipes

In part I a method is introduced for the numerical solution of swirling axisymmetric laminar flow situations. Consideration is given to finite difference formulation, boundary condition implementation, iterative solution strategies and pressure calculation. Part II is devoted to the application of the method to non-swirling flow problems. Some of these problems are well covered in the literature whilst others are new. Swirling flows are considered in Part III. In particular, details of separation and vortex breakdown induced by swirl are discussed. All results are supplemented by a selection of contour plots to indicate the nature of the flows predicted.     

Unsteady,laminar, incompressible flow through rectangular ducts

Résumé L'étude porte sur la théorie de lécoulement non permanent d'un fluide visqueux incompressible dans de canaux rectangulaires d'allongement divers, sous l'influence d'un gradient de pression arbitraire, dépendant du temps. Des solutions ont été obtenues dans 4 cas particuliers: 1. gradient de pression impulsif, 2. gradient de pression constant et établi brusquement, 3. gradient de pression en fonction harmonique du temps, 4. gradient de pression à une composante constante et une composante harmonique. On donne les répartitions de vitesse, les coefficients de frottement et la dissipation d'énergie par unité de longueur.

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This paper summarizes the second portion of the Ph. D. Thesis [1]²) byC. Fan.     

Solitary fluid transients in rectangular ducts with transverse magnetic fields

Summary This paper treats a fluid hammer wave which is propagating into a fully developed MHD duct flow and which is produced by suddenly closing a valve at some cross section of a rectangular, insulating duct with a uniform transverse, applied magnetic field. The Mach and magnetic Reynolds numbers are assumed to be small, while the Hartmann number is assumed to be large. For a small interaction parameter, the electromagnetic effects on the fluid hammer wave are small and consist of both dispersion and dissipation. The dispersion is cumulative and becomes larger for large time, while the dissipation remains small for all time.Résumé Cet article traite de l'onde de choc produite par la fermeture subite d'une vanne et qui se propage dans un fluide conducteur d'electricité s'écoulant dans une conduite isolante de section rectangulaire à laquelle est appliqué un champ magnétique transversal et homogène. On admet que le nombre de Reynold magné tique et le nombre de Mach sont petits, alors que le nombre de Hartmann est grand. Pour des faibles valeurs du paramètre d'interaction, les effets électromagnétiques sur l'onde de choc sont petits et comprennent une dispersion et une dissipation. La dispersion est cummulative et augmente avec le temps, alors que la dissipation reste toujours petite.     

Global uniqueness of steady subsonic Euler flows in three-dimensional ducts

We show for certain boundary conditions, under suitable assumptions on the velocity field, the steady compressible Euler flows in three-dimensional straight ducts must be irrotational, and hence, prove global uniqueness of uniform subsonic flows in these ducts. The proof depends on careful analysis of transport equations of vorticity and theory of second-order elliptic equations in bounded or unbounded domains.     

Periodic fluid transients in cylindrical ducts with transverse magnetic fields

Summary This paper treats periodic fluid transients in liquid metals contained in constant-area circular ducts with uniform, transverse, applied magnetic fields. The magnetic Reynolds and Mach numbers are assumed to be small, and the Reynolds number is assumed to be large. By the use of a complex coordinate transformation, closed-form solutions are obtained for the perfectly conducting duct. By the same technique, solutions in series of Mathieu functions are obtained for the fully insultating duct. A method for solving the dispersion relation for each case is outlined, and sample numerical results are presented.

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Résumé Cet article traite des ondes de compression périodiques dans un métal liquide contenu dans une conduite circulaire avec une section droite qui est constante et avec un champ magnétique transversal et uniforme que l'on applique. Ici on suppose que le nombre magnétique de Reynolds et le nombre de Mach sont petits et que le nombre de Reynolds est grand. A l'aide d'une transformation complexe des corrdonnées on obtient des solutions éxactes pour une conduite qui est parfaitement conductrice. Par le même technique on trouve les solutions pour la conduite parfaitement isolante dans une série de fonctions de Mathieu. Une méthode pour la solution de l'équation de dispersion est esquissée et des exemples de résultats numériques sont présentés.

     

Self-dual Co des with Symplectic Inner Pro duct

In this paper, we discuss a kind of Hermitian inner product — symplectic inner product, which is different from the original inner product — Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.     

Combined free and forced laminar convection in internally finned square ducts

Analysis is presented for the heat transfer performance of square ducts with internal fins from each wall in the case of combined free and forced convection by fully developed laminar flow. Numerical results are obtained for the Nusselt number and the pressure drop parameter for various values of finlengths and heat source parameter. For various values of Rayleigh numbers, the Nusselt number increases with the increase in finlength and decreases with the increase in heat source parameter.

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Zusammenfassung Es wird eine Analyse für den Wärmeaustausch von quadratischen Rohren mit inneren Rippen an jeder Wand im Falle einer Kombination von freier und erzwungener Konvektion bei voll entwickelter laminarer Strömung gegeben. Numerische Resultate für die Nusselt-Zahl und den Druckabfall-Koeffizienten für verschiedene Rippenbreiten und Parameter der Wärmequelle werden erhalten. Für einige Werte der Rayleighzahl wächst die Nusselt-Zahl mit der Rippenbreite und fällt mit wachsendem Parameter der Wärmequelle.

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Nomenclature A cross sectional area of the duct - B _2k Bernoulli numbers - c _p specific heat at constant pressure - D _h hydraulic diameter of finless duct - E _n complex constants (20) - F heat source parameter,Q/c _p - F _n () defined by Equation (14) - G(, , , ) Green's function (15, 16) - g gravitational acceleration - H() Heaviside function - h() defined by Equation (22) - i imaginary unit,i ²=–1 - ImW imaginary part ofW - K(,t) kernel of the integral equation, defined by (25) - k thermal conductivity - L pressure drop parameter, –D _h ² (p/x+ _w )/ - l fin length of each fin, Figure (1) - N _u Nusselt number, Equation (32) - p pressure - Q heat generation rate - R() defined by Equation (26) - R _A Rayleigh number, _w gc _p D _h ⁴ /k - ReW real part ofW - T dimensionless temperature, (t–t _w )/(c _p D _h ² /k) - T _mx dimensionless mixed mean temperature, Equation (33) - t fluid temperature - t ₀ reference temperature atx=0 - u local axial velocity - mean axial velocity - V u/ - W complex function defined by Equation (6) - w suffix denoting wall conditions - W ₀ defined by Equation (9) - W ₁ W–W ₀, Equation (18) - x axial coordinate along the length of the duct - y, z cross-sectional coordinates - constant temperature gradient, t/x - coefficient of thermal expansion of the fluid - fluid density - _n - dynamic viscosity - () Dirac delta function - ² Laplacian operator, ²/y ²/²/z ² - , y/D _h ,z/D _h      

Efficient solver for swirling flow problems in ducts with variable radius

The paper presents preliminary results of a work in progress addressing the hydrodynamic stability of swirling flows problems in ducts with variable radius which imply mathematical modeling, dynamic and stability investigations. The proposed quasi-analytical method aims to obtain the velocity profiles with a low order approximation method of which the computation costs were neglijable and regain the central stagnation zone developed in the fluid. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Design of axisymmetric ducts for incompressible flow with vorticity.

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function and the function as independent variables where for irrotational flow can be recognized as the velocity potential function, for rotational flow ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on finite differences on a uniform mesh is employed. The technique described is capable of tackling the so–called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct wall shapes. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Periodic fluid transients in rectangular ducts with transverse magnetic fields III

Summary This paper treats periodic fluid transients in a liquid metal contained in a constant-area, perfectly conducting rectangular duct with a uniform magnetic field applied perpendicular to one pair of the duct's walls. The Mach numberM is assumed to be small and viscous effects are assumed to be negligible. A previous paper treated this problem with the additional assumption that the magnetic Reynolds numberR _m is much smaller thanM, which excluded the Alfvén wave mechanism. On the other hand, ifR _m is much larger thanM, then the transients are the well-known Alfvén waves in an incompressible fluid. The present paper treats the case between these two extremes withR _m=M, where is an arbitrary constant. For this case there are three classes of wave modes: one class of Alfvén waves which involve no disturbances to the fluid pressure and two classes of waves which involve a coupling of the acoustic and Alfvén wave mechanisms. Dispersion relations are presented for all three classes.

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Résumé Cet article traite d'ondes de compression périodiques d'un métal liquide contenu dans une conduite rectangulaire à section droite constante et avec des parois parfaitement conductrices. On applique un champ magnétique homogène et qui est perpendiculaire à deux parois. On admet que le nombre de Mach,M, est petit et que la viscosité est negligeable. Dans un article précédent ce probléme a été traité avec l'hypothèse que le nombre magnétique de Reynolds,R _m, est plus petit queM. Dans ce cas, il n'y a pas d'ondes d'Alfvén et on trouve les deux types d'ondes acoustiques. Si l'on admet queR _m est plus grande queM, on ne trouve que des ondes d'Alfvén. Le présent article traite le cas intermédiaire. On admet queR _m=M et que est une constante arbitraire. On trouve les trois types d'ondes. Pour le premier type d'ondes, il n'y a pas de perturbation de la pression. Pour les deux autres, les mécanismes des ondes acoustiques et des ondes d'Alfvén sont couplés. On détermine les équations de dispersion pour les trois types d'ondes.