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The one-dimensional adiabatic flow of equilibrium gas–particle mixtures in variable-area ducts with friction

Published online by Cambridge University Press:  26 April 2006

Guido Buresti  and
Claudio Casarosa
Guido Buresti
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Università di Pisa, Via Diotisalvi 2, 56126 Pisa, Italy
Claudio Casarosa
Affiliation:
Dipartimento di Energetica, Università di Pisa, Via Diotisalvi 2, 56126 Pisa, Italy
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Abstract

A general one-dimensional model for the steady adiabatic motion of gas-particle mixtures in arbitrarily oriented ducts with gradually varying cross-section and wall friction is presented. The particles are assumed to be incompressible and in thermomechanical equilibrium with a perfect gas phase, and the effects of their finite volume and of gravity are also taken into account.

The equations of motion are written in a form that allows a theoretical analysis of the behaviour of the solutions to be carried out. In particular, the results of the application to the model of a procedure that permits the identification and the topological classification of the singular points of the trajectories representing, in a suitable phase space, the solutions of the set of equations defining the problem are described. This characterization of the singular points is useful in order to overcome difficulties in the numerical integration of the equations.

Subsequently, a geometrical analysis is carried out which allows a study of the signs of the local variations of the flow quantities, and shows that some unusual behaviour may occur if certain geometrical and fluid dynamic conditions are fulfilled. For instance, in an upward motion it is possible to have a simultaneous decrease of velocity, pressure and temperature, while in a downward flow an increase of all these quantities may be found. It is also shown that conditions exist in which expansion and heating of the mixture may take place simultaneously, both in accelerating and decelerating flows.

The model is applied to the study of upward motion in particular ducts, having converging-diverging and constant-diverging cross-sections; to this end the equations are integrated numerically by using the Mach number as the independent variable. The results show that even limited variations of the duct diameter may give rise to significant qualitative and quantitative variations in the flow conditions inside the duct and in the mass flow rate. Finally, an example is given of a subsonic downward flow in which a simultaneous increase of pressure, temperature and velocity occurs even in the case of a pure perfect gas.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 256 , November 1993 , pp. 215 - 242
Copyright
© 1993 Cambridge University Press

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