Cold Inflow-Free Solar Chimney pp 75-102 | Cite as

# Lazy Plume Stack Effect Above Chimneys

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## 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*(m^{4}s^{−3})*g*Gravitational acceleration constant at sea level (ms

^{−2})*h*_{o}Effective plume-chimney height (m)

*h*_{SW}Solid-walled chimney height (m)

*K*_{e}Velocity head entrance loss coefficient (–)

*K*_{ex}Velocity head exit loss coefficient (–)

*L*Characteristic dimension of plume source (m)

*M*(*z*)Momentum flux (m

^{4}s^{−2})*Q*(*z*)Mass flux at height

*z*(kgm^{−2}s^{−1})- Ri
_{o} Richardson number at source (–)

*r*Plume radius (m)

*r*_{o}Plume source radius (m)

*T*_{a}Ambient temperature (°C)

*T*_{o}Hot air temperature in collector and tower (°C)

*u*Angular velocity (ms

^{−1})*v*_{e}Entrainment velocity (radial) (ms

^{−1})*v*_{max}Maximum entrainment velocity at a given height (ms

^{−1})*w*_{c}Plume vertical centreline velocity (ms

^{−1})*w*_{co}Plume vertical centreline velocity at source (ms

^{−1})*w*_{o}Plume source mean velocity (ms

^{−1})*z*Vertical height from plume source (m)

- α
Entrainment coefficient (–)

- Γ
_{o} Plume source parameter (–)

*Δp*_{total}Total pressure drop (Pa)

*Δp*_{pipe}Pipe wall frictional pressure drop (Pa)

*Δp*_{Inlet}Pipe inlet entrance pressure loss (Pa)

*Δp*_{Outlet}Pipe outlet pressure loss (Pa)

*Δp*_{Compressor}Available compressor pressure head (Pa)

*ΔT*Temperature rise in the collector (K)

*ρ*_{a}Ambient air density (kgm

^{−3})*ρ*_{av}Mean heated air density in the cylinder (kgm

^{-3})*ρ*_{o}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.

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