Advertisement

Lazy Plume Stack Effect Above Chimneys

Chapter
  • 54 Downloads

Abstract

A natural draft chimney is defined by the existence of buoyancy and a solid wall barrier between two regions of fluids that differ in density. This familiar concept is approximately true for chimneys of relatively small flow area-to-height ratios. When its plume source parameter exceeds 1.0, the usual chimney does not fully define the region of buoyancy difference, but the height is extended by a plume-chimney, the magnitude has to date not been experimentally measured. Plumes are flows of free boundary layer in nature, making it virtually impossible to measure the pressure drop. The approach taken here was to employ a CFD software to perform simulations of heated chimney systems at four source Richardson numbers ranging between 0.044 and 0.53 under normal natural convection mode, and then simulated again effectively as jets, but matching the plumes’ Reynolds numbers and temperature changes, achieving partial dynamic similarity. The values of effective plume-chimney height (EPCH) agreed with existing empirical formulae by 2–75%. A good correlation was found between the EPCH and the inverse square of the maximum entrainment coefficient, signifying that the degree of stack effect depends on hindering the entrainment process.

Keywords

Lazy plume Chimney CFD Zero-gravity Large source area Richardson number 

Nomenclature

F(z)

Buoyancy flux at height z (m4s−3)

g

Gravitational acceleration constant at sea level (ms−2)

ho

Effective plume-chimney height (m)

hSW

Solid-walled chimney height (m)

Ke

Velocity head entrance loss coefficient (–)

Kex

Velocity head exit loss coefficient (–)

L

Characteristic dimension of plume source (m)

M(z)

Momentum flux (m4s−2)

Q(z)

Mass flux at height z (kgm−2s−1)

Rio

Richardson number at source (–)

r

Plume radius (m)

ro

Plume source radius (m)

Ta

Ambient temperature (°C)

To

Hot air temperature in collector and tower (°C)

u

Angular velocity (ms−1)

ve

Entrainment velocity (radial) (ms−1)

vmax

Maximum entrainment velocity at a given height (ms−1)

wc

Plume vertical centreline velocity (ms−1)

wco

Plume vertical centreline velocity at source (ms−1)

wo

Plume source mean velocity (ms−1)

z

Vertical height from plume source (m)

α

Entrainment coefficient (–)

Γo

Plume source parameter (–)

Δptotal

Total pressure drop (Pa)

Δppipe

Pipe wall frictional pressure drop (Pa)

ΔpInlet

Pipe inlet entrance pressure loss (Pa)

ΔpOutlet

Pipe outlet pressure loss (Pa)

ΔpCompressor

Available compressor pressure head (Pa)

ΔT

Temperature rise in the collector (K)

ρa

Ambient air density (kgm−3)

ρav

Mean heated air density in the cylinder (kgm-3)

ρo

Plume source mean density (kgm−3)

Notes

Acknowledgements

The author would like to offer his sincere thanks to the Ministry of Higher Education, Malaysia, for the kind assistance provided through fundamental grant No. FRG0022-TK-1/2006, and the provision of funding by Heat Transfer and Fluid Flow Services (HTFS) towards plume studies above air-cooled heat exchanger project at National Engineering Laboratory (NEL-TÜV), U.K.

References

  1. Abraham, G., & Eysink, W. D. (1969). Jets issuing into fluids with a density gradient. Delft Hydraulic Laboratory Publication, 66, 145–175.Google Scholar
  2. Ashrae, (2017). ASHRAE Handbook- Fundamentals, Fluid Flow, 3.8, S.I. Edition, ISBN 978-1-939200-58-7.Google Scholar
  3. Briggs, G. A. (1969). Optimum formulas for buoyant plume rise. Philosophical Transactions of the Royal Society of London, 265, 197–203.Google Scholar
  4. Caulfield, C. C. (1991). Stratification and Buoyancy in Geophysical Flows. PhD thesis, University of Cambridge, UK.Google Scholar
  5. Carazzo, G., Kaminski, E., & Tait, S. (2008). Journal of Geophysical Research, 113 (B09201), 1–19.  https://doi.org/10.1029/2007jb005458.
  6. Carlotti, P., & Hunt, G. R. (2017). An entrainment model for lazy turbulent plumes. Journal of Fluid Mechanics, 811, 682–700. Cambridge.Google Scholar
  7. CHAM. http://www.cham.co.uk/phoenics/d_polis/d_lecs/general/maths.htm. Concentration, Heat and Momentum Limited, Bakery House, 40 High Street, Wimbledon Village, London, SW19 5AU.
  8. Chen, Y. S. & Kim, S. W. (1987). Computation of turbulent flows using an extended k-e turbulence closure model, NASA CR-179204.Google Scholar
  9. Chen, C. J., Nikitopoulos, C.P. (1979). On the near field characteristics of axisymmetric turbulent buoyant jets in uniform environment. International Journal of Heat Mass and Transfer, 22, 245–255. Elsevier.Google Scholar
  10. Chu, C. M. (2006). Use of chilton-colburn analogy to estimate effective plume chimney height of a forced draft air-cooled heat exchanger. Heat Transfer Engineering, 27 (9), 81–85. Taylor and Francis, Philadelphia, U.S.A.Google Scholar
  11. Chu, C. M. (2005). Improved heat transfer predictions for air-cooled heat exchangers. Chemical Engineering Progress, A.I.Ch.E. 101 (11), 46–48. November, New York, NY.Google Scholar
  12. Chu, C. M. (2002). A preliminary method for estimating the effective plume chimney height above a forced-draft air-cooled heat exchanger operating under natural convection. Heat Transfer Engineering, 23, 3–13. Taylor and Francis, London.Google Scholar
  13. Chu, C. C. M. (1986). Studies of the Plumes above Air-Cooled Heat Exchangers Operating under Natural Convection, Ph.D. thesis, Department of Chemical Engineering, University of Birmingham, United Kingdom.Google Scholar
  14. Chu, C. M., Rahman, Hieng R. Y. T., & M. M. (2017). Simulation of effective plume-chimney above natural draft air-cooled heat exchangers, POWERENERGY2017-3435. In Proceedings of the ASME 2017 Power and Energy Conference, PowerEnergy2017, June 26–30, 2017, Charlotte, North Carolina, USA.Google Scholar
  15. Chu, C. M., Rahman, M. M., Kumaresan, S. (2016). Improved thermal energy discharge rate from a temperature-controlled heating source in a natural draft chimney, Applied Thermal Engineering, 98, 991–1002. Elsevier.Google Scholar
  16. Chu, C. M., Farrant, P. E., & Bott, T. R. (1988). Natural convection in air-cooled heat exchangers, In 2nd UK National Conference on Heat Transfer, pp 1657–1688, IChemE/IMechE Publication.Google Scholar
  17. Crawford, T. V., & Leonard, A. S. (1962). Observations of buoyant plumes in calm stably air. Journal of Applied Meteorology, 1, 251–256.CrossRefGoogle Scholar
  18. Doyle, P. T., & Benkly, G.J. (1973). Use fanless air coolers. Hydrocarbon Processing, July, 81–86.Google Scholar
  19. Fan, L. (1967). Turbulent buoyant jets into stratified or flowing ambient fluids, Report KH-R-15. Pasadena, California, USA: California Inst. of Technology.Google Scholar
  20. Fox, D. G. (1970). Forced plume in a stratified fluid. Journal Geophysical Research, 75(33), 6818–6835.CrossRefGoogle Scholar
  21. Haaland, S. E. (1983). Simple and explicit formulas for the friction factor in turbulent pipe flow. Journal of Fluids Engineering, March, 83–90.Google Scholar
  22. Henderson-Sellers, (1983). The zone of flow establishment for plumes with significant buoyancy. Applied Mathematical Modelling, 7, 395–397. Butterworth.Google Scholar
  23. Hunt, G. R., & van den Bremer, T. S. (2010). Classical plume theory: 1937–2010 and beyond, IMA Journal of Applied Mathematics, 76, 424 − 448. Oxford University.Google Scholar
  24. Hunt, G. R., & Kaye, N. B. (2005). Lazy plumes. Journal of Fluid Mechanics, 533, 329–338. Cambridge.Google Scholar
  25. Kaye, N. B. (2008), Turbulent plumes in stratified environments: a review of recent work. Atmosphere-Ocean 46 (4), 433–441. Taylor and Francis.Google Scholar
  26. Kaye, N. B. & Hunt, G. R. (2009). An experimental study of large area source turbulent plumes, International Journal of Heat and Fluid Flow, 30, 1099–1105. Elsevier.Google Scholar
  27. Kelley, O. & Stout, J. (2004). A “Hot Tower” above the eye can make hurricanes stronger. https://www.nasa.gov/centers/goddard/news/topstory/2004/0112towerclouds.html.
  28. Launder, B. E., & Spalding, D. B. (1974). The numerical computation of turbulent flow. Computer Method in Applied Mechanics and Engineering, 3, 269.CrossRefGoogle Scholar
  29. Li, X. X., Duniam, S., Gurgenci, H., Guan, Z. Q., & Veeraragavan, A. (2017). Full scale experimental study of a small natural draft dry cooling tower for concentrating solar thermal power plant. Applied Energy, 193, 15–27. Elsevier.Google Scholar
  30. List, E. J. & Imberger, J. (1973). Turbulent entrainment in buoyant jets and plumes. Journal of the Hydraulics Division Proceedings ASCE, 99, 1461–1474.Google Scholar
  31. Malin, M. R. (1986). The decay of mean and turbulent quantities in vertical forced plumes. Applied Mathematical Modelling, 11, 301–314, Butterworth.Google Scholar
  32. Marjanovic, G., Taub, G. N., & Balachandar, S. (2017). On the evolution of the plume function and entrainment in the near-source region of lazy plumes. Journals Fluid Mechanics, 830, 736–759. Cambridge University Press.Google Scholar
  33. Morton, B. R., Taylor, G. I., & Turner, J. S. (1956). Turbulant gravitational convection from maintained and instantaneous sources. In Proceedings of the Royal Society of London, Series A, 234, 6 March, pp. 1–22.Google Scholar
  34. Morton, B. R. (1959). Forced plumes. Journals Fluid Mechanics, 5(1), 151–163. Cambridge.Google Scholar
  35. Quintiere, J. G., & Grove, B.S. (1998). A unified analysis for fire plumes. In Twenty-Seventh Symposium (International) on Combustion/The Combustion Institute, pp. 2757–2766.Google Scholar
  36. Rahman, M. M., Chu, C. M., Tahir, A. M., Misran, M. A., Ling, L. (2017). Experimentally identify the effective plume chimney over a natural draft chimney model. In IOP Conference Series: Materials Science and Engineering 217 012002, International Conference on Materials Technology and Energy, 20–21 April 2017, Curtin University, Malaysia.Google Scholar
  37. Sinnott, R.K., & Towler, G. (2009). Coulson and Richardson’s Chemical Engineering: Chemical Engineering Design (5th ed., Vol. 6). Oxford: Pergamon Press.Google Scholar
  38. Sneck, H. J., & Brown, D.H. (1974). Plume rise from large thermal sources such as dry cooling towers, ASME Journals of Heat Transfer, 232–238.Google Scholar
  39. Tan, K. J. Y. (2019). Plume-Chimney temperature profile simulation and data analysis using computational fluid dynamics (CFD), Final Year Project thesis, Chemical Engineering Programme, Universiti Malaysia Sabah.Google Scholar
  40. Zhou, X. P., Yang, J. K., Xiao, B., Hou, G. X., & Xing, F. (2009). Analysis of Chimney Height for Solar Chimney Power Plant, Applied Thermal Engineering, 29, 178–185. Elsevier.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversiti Malaysia Sabah, Jalan UMSKota KinabaluMalaysia

Personalised recommendations