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Pollutant dispersion: why is stack height not enough?

If the stack is not tall enough, the plume is captured by the recirculation zone behind the building and brought down. What matters is not absolute height but position relative to that zone.

The aim in designing a stack or exhaust outlet is that the released gas does not reach receptors (fresh air intakes, neighbouring buildings, pedestrian areas) above an acceptable concentration.

The recirculation zone behind a building

A low-pressure, recirculating wake forms behind a structure. Any release entering that zone is dragged downwards and brought to roof or ground level.

The critical question is therefore not "how many metres is the stack" but "does the release stay above that zone". The height of the zone depends on the building's width and height; a wide, low building leaves a larger wake than a narrow, tall one.

Plume rise must be accounted for

A hot, fast release rises further after leaving the stack, through momentum and buoyancy. That increases the effective stack height.

But the opposite also occurs: if the exit velocity is low, the wind over the stack pulls the plume down (stack downwash). The ratio of exit velocity to local wind speed is therefore a design criterion, required to stay above a certain value.

Short range, hard problem

For long-range dispersion, Gaussian models are adequate and fast. For short-range dispersion around buildings the geometry dominates: vortices, corner accelerations, roof separation zones. A Gaussian model cannot see these; a field solution is required. See the wind and pedestrian comfort note.

Modelling notes

Several wind directions. The worst case is usually not the prevailing direction but the one that puts the receptor in the wake.

Buoyant release. In hot gas the density difference sets the transport; an isothermal model misses the plume rise entirely. See the natural convection note.

Transient concentration. The acceptance criterion is usually a short-term peak concentration, not an average. A steady-state average shows instantaneous peaks as markedly lower than they are.

References

  1. Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
  2. Morsi, S. A. & Alexander, A. J. (1972). An investigation of particle trajectories in two-phase flow systems. Journal of Fluid Mechanics, 55(2), 193–208. DOI: 10.1017/S0022112072001806

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