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Turbulent plumes with internal generation of buoyancy by chemical reaction

Published online by Cambridge University Press:  05 July 2010

A. N. CAMPBELL  and
S. S. S. CARDOSO
A. N. CAMPBELL*
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB23RA, UK
S. S. S. CARDOSO
Affiliation:
Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB23RA, UK
*
†Email address for correspondence: anc31@cam.ac.uk
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Abstract

Turbulent plumes, which are seen in a wide number of industrial and natural flows, have been extensively studied; however, very little attention has been paid to plumes which have an internal mechanism for changing buoyancy. Such plumes arise in e.g. industrial chimneys, where species can react and change the density of the plume material. These plumes with chemical reaction are the focus of this study. An integral model describing the behaviour of a plume undergoing a second-order chemical reaction between a component in the plume (A) and a component in the surrounding fluid (B), which alters the buoyancy flux, is considered. The behaviour of a reactive plume is shown to depend on four dimensionless groups: the volume and momentum fluxes at the source, the parameter ϵ which indicates the additional buoyancy flux generated by the reaction and γ which is a dimensionless rate of depletion of species B. Additionally, approximate analytical solutions are sought for a reactive plume rising from a point source of buoyancy when species B is in great excess. These analytical results show excellent agreement with numerical simulations. It is also shown that the behaviour of a reactive plume in the far field is equivalent to an inert plume issuing from a virtual source downstream of the real source, and the dependence of the location of the virtual source on ϵ and γ is discussed. The effects of varying the volume flux at the source and the Morton source parameter Γ0 are further investigated by solving the full governing equations numerically. These solutions indicate that ϵ is important in determining the buoyancy generated by the reaction, and the length scale over which this reaction occurs depends on γ when γ > 1. It is also shown that when the dimensionless buoyancy ϵ < − 1, the reaction can cause the plume to collapse.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 655 , 25 July 2010 , pp. 122 - 151
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Agrawal, A. & Prasad, A. K. 2004 Evolution of a turbulent jet subjected to volumetric heating. J. Fluid Mech. 511, 95–123.CrossRefGoogle Scholar
Agrawal, A., Sreenivas, K. R. & Prasad, A. K. 2004 Velocity and temperature measurements in an axisymmetric turbulent jet with cloud-like off-source heating. Intl J. Heat Mass Transfer 47, 1433–1444.CrossRefGoogle Scholar
Batchelor, G. K. 1954 Heat convection and buoyancy effects in fluids. Q. J. R. Meteorol. Soc. 80, 339–358.CrossRefGoogle Scholar
Bhat, G. S. & Narasimha, R. 1996 A volumetrically heated jet: large-eddy structure and entrainment characteristics. J. Fluid Mech. 325, 303–330.CrossRefGoogle Scholar
Bhat, G. S., Narasimha, R. & Arakeri, V. H. 1989 A new method of producing local enhancement of buoyancy in liquid flows. Exp. Fluids 7, 99–102.CrossRefGoogle Scholar
Caulfield, C. P. 1991 Stratification and buoyancy in geophysical flows. PhD thesis, University of Cambridge, Cambridge, UK.Google Scholar
Caulfield, C. P. & Woods, A. W. 1995 Plumes with non-monotonic mixing behaviour. Geophys. Astrophys. Fluid Dyn. 79, 173–199.CrossRefGoogle Scholar
Clarke, J. F. & McChesney, M. 1964 The Dynamics of Real Gases. Butterworths.CrossRefGoogle Scholar
Conroy, D. T. & Llewellyn Smith, S. G. 2008 Endothermic and exothermic chemically reacting plumes. J. Fluid Mech. 612, 291–310.CrossRefGoogle Scholar
Conroy, D. T., Llewellyn Smith, S. G. & Caulfield, C. P. 2005 Evolution of a chemically reacting plume in a ventilated room. J. Fluid Mech. 537, 221–253.CrossRefGoogle Scholar
Dahm, W. J. A. 2005 Effects of heat release on turbulent shear flows. Part 2. Turbulent mixing layers and the equivalence principle. J. Fluid Mech. 540, 1–19.CrossRefGoogle Scholar
Diez, F. J. & Dahm, W. J. A. 2007 Effects of heat release on turbulent shear flows. Part 3. Buoyancy effects due to heat release in jets and plumes. J. Fluid Mech. 575, 221–255.CrossRefGoogle Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.Google Scholar
Hanna, S. R., Chang, J. C. & Zhang, X. J. 1997 Modelling accidental releases to the atmosphere of a dense reactive chemical (uranium hexafluoride). Atmos. Environ. 31, 901–908.CrossRefGoogle Scholar
Hunt, G. R. & Kaye, N. G. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377–396.CrossRefGoogle Scholar
Hunt, G. R. & Kaye, N. B. 2005 Lazy plumes. J. Fluid Mech. 533, 329–338.CrossRefGoogle Scholar
Ishimine, Y. 2007 A simple integral model of buoyancy-generating plumes and its application to volcanic eruption columns. J. Geophys. Res. 112, B03210.Google Scholar
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361–376.CrossRefGoogle Scholar
List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189–212.CrossRefGoogle Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151–163.CrossRefGoogle Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
Priestley, C. H. B. & Ball, F. K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Meteorol. Soc. 81, 144–157.CrossRefGoogle Scholar
Scase, M. M., Caulfield, C. P., Dalziel, S. B. & Hunt, J. C. R. 2006 Time-dependent plumes and jets with decreasing source strengths. J. Fluid Mech. 563, 443–461.CrossRefGoogle Scholar
Tacina, K. M. & Dahm, W. J. A. 2000 Effects of heat release on turbulent shear flows. Part 1. A general equivalence principle for nonbuoyant flows and its application to turbulent jet flames. J. Fluid Mech. 415, 23–44.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Venkatakrishnan, L., Bhat, G. S. & Narasimha, R. 1999 Experiments on a plume with off-source heating: implications for cloud fluid dynamics. J. Geophys. Res. 104, 14271–14281.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin/Cummings.Google Scholar
Woods, A. W. & Caulfield, C. P. 1992 A laboratory study of explosive volcanic eruptions. J. Geophys. Res. 97, 6699–6712.CrossRefGoogle Scholar