Plume Rise

 

Plume rise is a critical input to models concerning solitary stacks. In most cases the plume from a chimney does not move horizontally with the wind as soon as it leaves the stack.

It will continue to rise depending on such factors as its efflux velocity and its temperature. This means that calculations need to be done not on the basis of actual stack height h but on the sum of h and the plume rise . We normally give the symbol for effective stack height as H. In fact plume rise can, in some circumstances, increase the stack height by a factor of two to ten times the actual stack height.

Empirical Models of Plume Rise

Many early studies on this subject were empirical and were thus only capable of being strictly applied to the conditions in which they were generated. Nevertheless it is instructive to look at some of these models as they indicate to us the important parameters which affect plume rise.

In the equations, which follow, the following symbols are adopted:

: plume rise (m)
Vs : stack exit velocity (m/s)
D : internal stack diameter (m)
u : wind speed (m/s)
p :atmospheric pressure (hPa)
Ts : stack gas temperature (K)
Ta : air temperature (K)
Qh : heat emission rate of stack (k cal/s)
A : a coefficient dependent on stability
Values of Coefficient A
Stability A
Unstable 2.65
Neutral 1.08
Stable 0.68
In all these models and the fundamental ones discussed below the wind speed required is usually the average wind speed over the altitude range through which the plume rises. This can be difficult to obtain since we do not know how far the plume will rise. An iterative process starting with the wind speed at stack height should work but it is probably not worth using anything other than the wind speed at stack height for most purposes.
Holland's equation
Was developed for large sources (with stack diameters between 1.7 and 4m and stack temperatures between 82 and 204oC).

Concawe

Developed an equation suitable for large buoyant plumes.
Rauch ,Lucas, Moore and Spurre developed regression equations on single sets of data, which gave slightly different formulae.
Rauch ,Lucas, Spurr and Moore

 

And Moses and Carson (from which this survey of regression equations is drawn) developed a regression equation based on numerous sources:

Holland suggested that the results of his equation be modified depending on stability. For unstable conditions a factor of between 1.1 and 1.2 x plume rise should be used. For stable conditions a value between 0.8 and 0.9 times should be used. There would seem to be good justification to use these factors if applying all the plume rise models above except for that of Moses and Carson.

What is instructive here is the fact that different empirical equations arise for different circumstances. The value of empirical models should not be overlooked if data is available for a particular stack over a wide range of conditions. It is possible that this would be more accurate than the more fundamental models that are now in use.