Non-linear approximations for natural convection in a horizontal annulus

Two different problems are proposed as approximations of the usual system modelling natural convection under the Oberbeck-Boussinesq assumptions. The error is evaluated by means of the norm of its gradient in the Hilbert space. The average Nusselt number is also estimated.     

Vector green's function method for unsteady Navier-Stokes equations

Summary The Green's function method is reformulated in general terms to treat vector unsteady and nonlinear equations. The particular expressions of the adjoint linear operator, the Green's formula and the integral representation of the solution are derived for unsteady Navier Stokes equations. The appropriate fundamental solutions for incompressible and for certain compressible flows have been obtained in closed form. Both the positive features and the possible limits of the method are briefly outlined.

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Sommario Si riformula in termini generali il metodo della funzione di Green per estenderlo al caso di equazioni vettoriali e non lineari. In particolare si ricavano le espressioni della formula di Green e della rappresentazione integrale della soluzione per le equazioni di Navier Stokes non stazionarie. Si ottengono le soluzioni fondamentali in forma chiusa sia per il caso di fluidi comprimibili che incomprimibili. Si discutono infine brevemente i lati positivi ed i possibili limiti della metodologia illustrata.

     

A boundary-integral equation method for free surface viscous flows

Summary A boundary integral equation method is proposed for the solution of viscous recirculating flows with free surfaces. In particular the method is applied to thermocapillary convection and to drop formation, both in micro-gravity conditions, the latter to test its capability to handle real unsteady problems.The presence of non linear terms in Navier-Stokes equations leads to a volume integral, which has to be approximated by a linearization procedure.Several numerical results for thermocapillary flows, both with fixed and moving free surface, are discussed in comparison with previously obtained finite difference solutions. Some preliminary results, and in particular the time evolution of the free surface shape, are also presented for the drop formation problem. Only plane two dimensional fields are considered for both problems.

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Sommario Si propone un metodo basato sulla soluzione di equazioni integrali di contorno per flussi viscosi con superficie libera. Tale metodo è applicato allo studio della convezione termocapillare ed al processo di formazione di una goccia, entrambi in condizioni di microgravità. La presenza dei termini non lineari nell'equazione di Navier-Stokes comporta un integrale di volume che viene approssimato mediante un processo di linearizzazione.Risultati numerici per flussi termocapillari con superficie libera sia fissa che mobile sono confrontati con altri ottenuti in precedenza con un metodo alle differenze finite. Si presentano inoltre alcuni risultati preliminari sul problema della formazione della goccia ed in particolare l'evoluzione nel tempo della configurazione geometrica della superficie libera. Nei due casi si analizzano solo campi bidimensionali.

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Presented at the VII National Conference AIDAA, Naples, September 1983.

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In leave of absence from Tianjin University, China.     

Vorticity shedding from a lentil-shaped body at large incidence in uniform flow

The 2D flow about a lentil-shaped body at high incidence in uniform stream is numerically simulated for high Reynolds numbers. The separation points are fixed on the body edges and the vorticity released through a Kutta-like condition is spatially discretized by point vortices. Their Lagrangianinviscid dynamics is described by using both aconformal mapping and aboundary elements method. The present results are in good agreement with previous calculations but still not satisfactory when compared with the experiments.The aim of the present work is to investigate the effect of different Kutta conditions and the effect of different amalgamation procedures in the far wake on global quantities such as theStrouhal number or the total shed circulation. Other remarkable effects induced either by the action of viscosity or by the rising of secondary 3D motion, may not be analyzed by the present simplified model.

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Sommario Si studia il flusso attorno ad una lente ad elevata incidenza nelle ipotesi di elevato numero di Reynolds e flusso bidimensionale. I punti di separazione sono fissati sulle estremità della lente e la produzione di vorticità da questi è realizzata con opportune condizioni di Kutta. La dinamica dei vortici è descritta con un modello Lagrangiano non viscoso. I risultati, ottenuti sia con l'uso di una trasformazione conforme che con un metodo agli elementi di contorno, sono in ottimo accordo con i risultati di precedenti simulazioni numeriche, ma non sono ancora soddisfacenti se confrontati con gli esperimenti.Si analizza in termini di grandezze globali del flusso, quali il numero di Strouhal e la circolazione totale rilasciata, l'effetto di due diverse condizioni di Kutta e dell'uso di procedure di compattazione della scia lontana. Si conclude che l'uso di diverse condizioni di Kutta produce risultati pressoché identici mentre l'utilizzo di procedure di compattazione della scia può alterare in modo significativo il numero di Strouhal del flusso. Rimangono da analizzare altre possibili cause del disaccordo con le sperimentazioni quali la diffusione viscosa e la probabile presenza di moti tridimensionali.

     

Crack propagation in an orthotropic medium with coupled elastodynamic properties

In this paper the Mode-I elastodynamic problem of a crack propagating in an orthotropic medium is studied under the condition that the matrix of elastodynamic coefficients has repeated eigenvalues. It is shown that the crack is constrained in an elastodynamic state which is defined through a compulsory condition coupling its velocity with the elastic parameters of the orthotropic medium. The dynamic stress and displacement components ahead of the crack tip as well as the energy release rate are explicitly obtained.     

Experimental investigation of the performance of a thermoelectric generator based on Peltier cells

An experimental investigation is carried out to characterize the performance of thermoelectric modules used for electric power generation over a range of different resistance loads. The performance of a Peltier cell used as a thermoelectric generator is evaluated in terms of power output and conversion efficiency. The results show that a thermoelectric module is a promising device for waste heat recovery.     

The significance of histidines in "thyrotropin-releasing" hormone (TRH)

The syntheses and biological activities of 4 analogues of the thyrotropin-releasing hormone (TRH) are described. In these analogues the histidine residue has been replaced by L -lysine, L -α,γ-diaminobutyric acid, β-(3-pyrazolyl)-L -alanine, and L-arginine. All analogues exhibited the characteristic biological responses of TRH. For the β-(3-pyrazolyl)-L -alanine analogue as well as for TRH the bioassays suggest an induction of a strong and rapid resynthesis of thyrotropin (TSH) in higher (μg) concentrations.     

Two arc cracks around a circular rigid inclusion

Summary The problem of two symmetric arc cracks lying between a rigid circular inclusion embedded in an infinite matrix under biaxial loading at infinity is considered. By using the complex variable tecnique, the boundary value problem is solved and stress and displacement components are calculated along the inclusion boundary. Moreover, investigating the local stress field, a stress criterion, already proposed by authors, allowing either the crack extension at the interface or its deviation into the matrix to be taken into account, is applied to study the fracture response of the elastic system. The critical applied loads as well as the angle of the incipient crack extension are expressed in terms of the central angle subtended by the crack arcs.Finally the biaxial load effects are graphically shown and discussed.

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Sommario Si considera il problema piano di due «craks» simmetrici all'interfaccia tra una inclusione circolare rigida e la circostante matrice, in regime di carico biassiale. Facendo uso della tecnica delle variabili complesse, viene risolto il problema dei valori al contorno, ricavando altresi le espressioni delle tensioni e degli spostamenti lungo il contorno dell'inclusione. Inoltre, applicando un criterio tensionale, già proposto dagli autori, che consente di studiare sia la estensione del crack all'interfaccia che la sua deviazione nella matrice, si analizza la risposta del sistema considerato. I valori critici dei carichi applicati, nonchè l'angolo di frattura, risultano espressi in funzione dell'angolo al centro sotteso dai cracks.Infine, vengono illustrati graficamente e discussi gli effetti del carico laterale.

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Financial support of the National Research Council (C.N.R.) (research contribution N. 79.01625.07) is gratefully acknowledged.     

Merging metathesis and photochemical Csp3-H activation: Access to masked β-formyl hexanolides and their rearrangement to furofuranones

β-Masked formyl hexanolides were prepared by a three-step sequence including esterification of homoallylic alcohols, ring-closing metathesis and the photochemically induced addition of dioxanyl radical. When treated under oxidative conditions, the adducts underwent cleavage of the ketal group leading after rearrangement to parent furofuranones, structures found in some biological active compounds.