Summary
A modified set of governing equations for gas-particle flows in nozzles is suggested to include the inertial forces acting on the particle phase. The problem of gas-particle flow through a nozzle is solved using a first order finite difference scheme. A suitable stability condition for the numerical scheme for gas-particle flows is defined. Results obtained from the present set of equations are compared with those of the previous set of equations. It is also found that present set of equations give results which are in good agreement with the experimental observation.
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Abbreviations
- A :
-
Cross-sectional area of nozzle
- A * :
-
cross-sectional area of nozzle throat
- c :
-
solid specific heat of particle
- C D :
-
coefficient of drag
- c p :
-
specific heat of gas at constant pressure
- c v :
-
specific heat of gas at constant volume
- D :
-
viscous drag force for a single solid particle
- d :
-
diameter of particle
- L :
-
length of nozzle
- m p :
-
mass of each solid particle
- Nu:
-
Nusselt number
- p :
-
pressure of gas
- Pr:
-
Prandtle number
- Q :
-
heat transfer from particle to gas phase
- R :
-
gas constant
- r t :
-
nozzle throat radius
- Re:
-
Reynolds number
- T :
-
temperature of gas
- u :
-
velocity of gas
- β:
-
density of particle phase
- μ:
-
viscosity of gas
- ϱ:
-
density of gas
- η:
-
loading ratio
- P :
-
refers to particle phase
References
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Kliegel, J. R., Nickerson, G. R.: Flow of gas-particle mixtures in axially symmetric nozzles, in: Penner, S. S., Williams, F. A., eds.: Detonation and two phase flow, pp. 173. New York: Academic Press. 1962.
Hultberg, J. A., Soo, S. L.: Two phase flow through a nozzle. Astronautica ActaII (3), 207 (1965).
Marble, F. E.: Dynamics of a gas containing small solid particles, pp. 163. 5th AGARDO-graph Colloquium, Pergamon, 1963.
Chang, I. S.: One and two phase nozzle flows. AIAA J18, 1455 (1980)
Doi, T.: Gas-particle nozzle flows and optimum nozzle shape. Institute of Space and Astronautical Science Report, No. 596, Tokyo, Japan, 1981.
Fujii, K., Kutler, P.: Computations of two phase supersonic nozzle flows by a space marching method. AIAA Paper 83-0041 (1983).
Henderson, C. B.: Drag coefficients of spheres in continuum and rarefied flows. AIAA J14, 707 (1976).
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Baruah, C. K., Reddy, N. M.: Limiting gas-particle flows — A new approach. Proceedings of the 15th International symposium on shock wave and shock tube, Berkeley, USA, July 29 to August 1, 1985 Edited by Bershader, D., Hanson, R., Stanford, California: Standorf University Press 1986.
Rudinger, G.: Fundamentals of gas-particle flow. Elsevier Publishing Company 1980.
Pai, S. I.: Two-phase flows. Braunschweig: Vieweg 1977.
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Baruah, C.K., Reddy, N.M. Modified governing equations for gas-particle nozzle flows. Acta Mechanica 71, 215–225 (1988). https://doi.org/10.1007/BF01173948
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DOI: https://doi.org/10.1007/BF01173948