Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T08:35:08.440Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbott, M. M. & Van Ness, H. C. 1972 Thermodynamics. McGraw Hill.
Bilicki, Z., Dafermos, C., Kestin, J., Majda, G. & Zeng, D. L. 1987 Trajectories and singular points in steady-state models of two-phase flows. Intl J. Multiphase Flow 13, 511–53.Google Scholar
Boothroyd, R. G. 1971 Flowing Gas–Solid Suspensions. Chapman and Hall.
Buresti, G. & Casarosa, C. 1987 A one-dimensional model for the flow of equilibrium gas–particle mixtures in vertical ducts with friction and its application to volcanological problems. Atti del Dipartimento di Ingegneria Aerospaziale, ADIA 87-3. Pisa: ETS Editrice.
Buresti, G. & Casarosa, C. 1989 One-dimensional adiabatic flow of equilibrium gas–particle mixtures in long vertical ducts with friction. J. Fluid Mech. 203, 251–272.Google Scholar
Buresti, G. & Casarosa, C. 1990 A one-dimensional model for the flow of equilibrium gas–particle mixtures in variable-area ducts with friction. Atti del Dipartimento di Ingegneria Aerospaziale, ADIA 90-1. Pisa: ETS Editrice.
Buresti, G. & Casarosa, C. 1992 Geometrical and topological analysis of the one-dimensional flow of homogeneous gas–particle mixtures in variable-area ducts with friction. Atti del Dipartimento di Ingegneria Aerospaziale, ADIA 92-4, Pisa: ETS Editrice.
Crowe, C. T. 1982 Review - Numerical models for dilute gas-particle flows. Trans. ASME I: J. Fluids Engng 104, 297–303.Google Scholar
Dobran, F. 1992 Nonequilibrium flow in volcanic conduits and application to the eruption of Mt. St. Helens on May 1980, and Vesuvius in AD 79. J. Volcanol. Geotherm. Res. 49, 285–311.Google Scholar
Dobran, F., Neri, A. & Macedonio, G. 1992 Numerical simulation of collapsing volcanic columns. C.N.R. Gruppo Nazionale per la Vulcanologia, Volcanic Simulation Group, Pisa, Rep. VSG 92-2.
Giberti, G. & Wilson, L. 1990 The influence of geometry on the ascent of magma in open fissures. Bull. Volcanol. 52, 515–521.Google Scholar
Kaplan, W. 1958 Ordinary Differential Equations. John Wiley & Sons.
Kieffer, S. W. 1982 Dynamics and thermodynamics of volcanic eruptions: implications for the plumes on Io. In Satellites of Jupiter (ed. D. Morrison), pp. 647–723, University of Arizona Press.
Rudinger, G. 1976 Fundamentals and applications of gas-particle flow. In AGARD-AG-222, pp. 55–86.
Shapiro, A. H. 1953 The Dynamics and Thermodynamics of Compressible Fluid Flow. John Wiley & Sons.
Soo, S. L. 1989 Particulates and Continuum: Multiphase Fluid Dynamics. Hemisphere.
Van Wylen, G. J. & Sonntag, R. E. 1976 Fundamentals of Classical Thermodynamics. John Wiley & Sons.
Wallis, G. B. 1969 One-dimensional Two-Phase Flow. McGraw-Hill.
Wilson, L. & Head, J. W. III 1981 Ascent and eruption of basaltic magma on the Earth and Moon, J. Geophys. Res. 86, 2971–3001.Google Scholar
Wilson, L., Sparks, R. S. J. & Walker, G. P. L. 1980 Explosive volcanic eruptions – IV. The control of magma properties and conduit geometry on eruption column behaviour. Geophys. J. R. Astron. Soc. 63, 117–148.Google Scholar