Velocity and temperature fields past a finite flat plate in a slip flow

Summary The incompressible slip flow past a finite flat plate at zero incidence and at low Reynolds numbers is treated in the Oseen approximation. An analytical expression of the shear stress at the wall is obtained by the integral Fourier transform method. The drag coefficient, the velocity perturbations and the thermal field are numerically evaluated.

---

Sommario Viene trattato il flusso incompressibile con slittamento su di una lastra piana nella approssimazione di Oseen. Per mezzo del metodo delle trasformate integrali di Fourier si è ottenuta un'espressione analitica dello sforzo di taglio alla parete. Si è calcolato numericamente il coefficiente di resistenza, la perturbazione di velocità ed il campo termico.

     

Analytical results on two-phase rows in ducts

A deterministic stochastic approach is successfully applied to the investigation of some problems of the fluid-dynamics of two-phase systems. The method follows the guidelines of the theory of differential equations with random initial conditions.Dusty gas flows and bubble flows are considered in circumstances where the action of the particulate matter on the fluid flow field is negligible. In all the cases, collisions between particles of the disperse phase are neglected. As significant applications, the entrance flow of dust particles in a tube and the behaviour of a population of bubbles imbedded in a pipe-flow subject to an abrupt area, change are considered. The probable distributions of the particles are evaluated as functions of assigned statistical distributions of the objects at the initial time.

---

Analytische Ergebnisse von Zweiphasen-Strömungen in Kanälen

Zusammenfassung Ein deterministisch-stochastischer Ansatz wird erfolgreich auf die Untersuchung einiger Strömungsprobleme von Zweiphasensystemen angewandt. Die Methode entspricht der Theorie von Differential-gleichungen mit zufälligen Anfangsproblemen.Staub-Gas-Strömungen und Blasen-Strömungen werden unter Bedingungen behandelt, bei denen der Einfluß des betreffenden Stoffes auf das Strömungsfeld vernachlässigt werden kann. In allen Fällen werden auch Kollisionen zwischen Partikeln der dispersen Phase vernachlässigt. Als kennzeichnende Anwendungen werden die Eintrittsströmungen von Staub in ein Rohr und das Verhalten eines Blasenschwarmes an einer sprunghaften Querschnittsveränderung eines Rohres behandelt. Die wahrscheinlichen Teilchenverteilungen werden als Funktionen bestimmter Anfangsverteilungen ermittelt.

---

Nomenclature A normalization factor - A,b,c,kj,G,, dimensionless quantities defined in the text - h _a/_c - H _w/_a - J operator defined at page 2 - K Boltzmann constant - p dimensionless pressure - P probability density - p probability - r⁺ radius of the tube, reference length - R radial co-ordinate (dimensionless) - Re Reynolds number of the relative motion of the particles with respect to the fluid - t⁺ reference time, r⁺ /U⁺ - t time (dimensionless) - U⁺ reference velocity - U_a,U_r axial and radial velocity components, respectively, of the fluid flow - 183-01 state vector of a particle - V_a,V_r axial and radial velocity components respectively of a particle - Z dimensionless axial co-ordinate along the tube - viscosity - mass density - diameter of a particle, dimensionless with respect to r⁺ Indexes ()_a air - ()_c coal - ()_t at the time t - ()_w water - ()_o at the time t=o     

Rigorous constructive solution to monodimensional poiseuille and thermal creep flows

Summary A rigorous constructive method is discussed for solving the linear integral equations which govern either the Poiseuille flow and the thermal creep flow of a rarefied gas between parallel plates. In both cases numerical results are presented for the nondimensionalized mass flow rate, and for certain quantities which are closely related to the mass and slip velocities. Critical comparison with previous results is made wherever possible.

---

Sommario Nella nota viene discusso un rigoroso metodo costruttivo per risolvere le equazioni integrali lineari che regolano sia il moto di Poiseuille che il moto di scorrimento termico di un gas rarefatto fra due piastre piane parallele. Per ambedue le situazioni fisiche vengono presentati vari risultati numerici connessi con la portata e con le velocità. Dove possibile, i risultati ottenuti sono confrontati con quelli disponibili nella letteratura.

     

Analytic solutions to problems of radiative transport in an absorbing medium

A method is proposed for solving the linear integral equations governing some problems of radiation transport. The Fourier transform technique provides the solution as a convolution integral of the kernel and a series expansion in orthogonal functions. Two standard problems were considered as an application and the results given in comparison with those obtained by different approaches.     

Analytic solutions to problems of radiative transport in an absorbing medium

A method is proposed for solving the linear integral equations governing some problems of radiation transport. The Fourier transform technique provides the solution as a convolution integral of the kernel and a series expansion in orthogonal functions. Two standard problems were considered as an application and the results given in comparison with those obtained by different approaches.

---

Riassunto Si propone un metodo per risolvere le equazioni lineari integrali del trasporto radiativo. La tecnica della trasformata di Fourier fornisce la soluzione come integrale di convoluzione del kernel e di uno sviluppo in serie di funzioni ortogonali. Come applicazione si sono risolti due problemi classici ed i risultati si sono confrontati con quelli ottenuti mediante altri procedimenti.

---

---

This work was partially supported by the Consiglio Nazionale delle Ricerche, Gruppo di Fisica Matematica.     

Physical and Numerical Experiments on an Under-Expanded Jet

The axial characteristics of axisymmetric under-expanded sonic jets are dealt with, both experimentally and numerically. Experiments were carried out in a test rig where a sonic nozzle discharged into an ambient which could be kept at different pressures. The density measurements were taken by means of a differential interferometer. The numerical simulation was obtained by adapting a code by Bird (1994) which is based on the MonteCarlo method. The comparison between experimental data and numerical results was carried out by considering the density distribution along the axis of the jet. The direct simulation was then applied to explore the jet characteristics in a rather wide range of the dimensionless products upon which the phenomenology depends. New expressions are presented for the density distribution along the jet axis and for the location of the Mach disk. Sommario. Si trattano sia sperimentalmente che numericamente le caratteristiche assiali di getti assialsimmetrici sonici sottoespansi. Gli esperimenti sono stati eseguiti con ugelli sonici in ambienti a pressione variabile. La densità è stata misurata mediante un interferometro differenziale e le simulazioni sono state condotte mediante un codice basato sul metodo MonteCarlo. Il confronto tra dati sperimentali e numerici è basato sulla distribuzione di densità lungo l'asse del getto. La simulazione diretta è stata poi applicata allo studio del getto in un ampio campo di valori dei numeri caratteristici. Si discutono la distribuzione della densità lungo l'asse e la posizione del disco di Mach, ottenute sia dai dati sperimentali che dai risultati numerici e si propongono per esse nuove espressioni.