I am looking for an equation or an open source simulation tool to calculate the dilution of contaminated air (Bq/m3) which gets out of a chimney with a vertical speed v and afterwards gets transported to a point of interest at a distance x with a horizontal velocity u. Let's assume that all the air output and surroundings have the same temperature and pressure, so to consider above all dilution by mixing with fresh air. Any suggestions? Thank you!
There are a lot of free simulation tools available on the internet. The selection depends on the precise task (jet and plume behaviour, single situations vs. annual averages, inclusion of ground structures, stack downwash etc.). The critical part of your question is "open source". That might be much more difficult.
I did some stack simulations using FDS (Fire Dynamic Simulator). Although this numerical model is widely used for in-door fire simulations, it is quite useful for atmospheric flow as well.
https://www.youtube.com/watch?v=I5ZG-cFMlmw
A list of available models is given on the following Wikipedia page.
https://en.wikipedia.org/wiki/List_of_atmospheric_dispersion_models
If you are looking for a free simulation tool (not open source) and if you also want to include annual averages, I'd recommend GRAL. I did not use it myself (yet), but I reviewed the application for stack dispersion studies in urban areas in Australia. This would be my choice:
http://lampz.tugraz.at/~gral/index.php
There are free programs that allow us to model how air pollutants spread, but obviously they will depend of many factors, such as the air temperature, the exit temperature of the pollutants, whether they are fixed or moving emissions and the direction and speed of the wind, to name a few.
Most of the methods used to estimate the atmospheric dispersion problem described in your question are based on the approximation of dispersion by Fick's law (the flux is directly proportional to the gradient) leading to the Gaussian plume formula or the Eulerian advection-diffusion models.
One of the possible solutions is described in:
https://www.witpress.com/elibrary/wit-transactions-on-ecology-and-the-environment/157/23269
If you are interested in a high-precision solution, I would recommend the Fokker-Planck equation. A good analysis of this subject is presented in the following thesis.
https://pdfs.semanticscholar.org/e839/d3303518599e96d4e5d2ed04e83b92111bf7.pdf
Thank you for answering. I found an equation in the attached IAEA document (page 24, eq 7) which fits perfectly for my situation. The equation is: Ca= B*Qi / (u*x2) with Ca the concentration at the point of interest (Bq/m3), Qi the released concentration per unit of time (Bq/s), B a constant equal to 30 for the situation, x the distance between release vent and point of interest [m] and u the speed of the wind [m/s]. Please find all the details to the prerequisites in the publication.
This equation is applicable to the situation where the receptor is on the same surface as the source, i.e. there is no stack and no vertical discharge velocity present. For the situation described in your question, this equation would over-predict the concentration at the receptor point.
Ok. Thank you Ingo, better so than the opposite. In radiation protection we are used to conservative calculations. Have you got any idea of the percentage of the error in neglecting the vertical speed (let's say v~5m/s and u~4m/s)?
For a simple model of the iso-thermal plume, you would have to calculate a virtual stack height which is the sum of the actual stack height and an additional height depending on discharge velocity, flow rate and wind speed. If you look at the picture in my first response, you can imagine, where the virtual source would be located. From that virtual source, you have a linear growth of the plume width... until the lower part of the plume is reflected on the ground.
So, if you are exposed to pollution from the stack, you may want to stand right at the stack, because there is no pollution - and the equation from the book gives you maximum pollution there. If you are far away from the stack, the equation would give you a reasonable good match.
And no, I don't have the equation for the virtual stack height at hand - would have to do some literature review first.
- Badges
- Science topic
- Similar topics
- Geoscience
- Cartography
- Mapping