Three - dimensional unsteady flow

Cartesian computational grid

Understanding the details of the dispersion of pollution and flammable gases in the near wake of buildings and structures is very important for estimating the concentrations or dosages of dangerous contaminants in the event of accidental releases and the consequential effect on personnel in or near the buildings. The dispersion of heavy gases and vapours is the most dangerous case.

The mathematical model predicting distribution of clouds and plumes of dangerous chemical substances from emergency sources of any form and height taking account of a real three - dimensional lay-out of industrial object or city (buildings, structures, industrial equipment) was developed. The model was a result of successive progress of the previous model used for calculation of the dispersion of ammonia vapours in town conditions (see the risk assessment of an ammonia intoxication ).

PHOENICS has been used to calculate the flow field and the contaminant concentration distribution within or near industrial areas.

The standard embedded in PHOENICS k-l model was used to describe the atmospheric turbulent transfer in industrial areas and above ones.

In estimating of the length scale the distance from the nearest wall (DISWAL) was used with modifications taking into account the influence of the atmospheric stability.

The unisotropic eddy viscosity in the atmospheric surface layer was set up according to M.E.Berlyand conception /1/.

The describing of the atmospheric stability was made on basis of the Monin-Obukhov length.

The inlet profiles of wind speed, air temperature and turbulent kinetic energy might be described by analytical expressions obtained from theoretical considerations (for non-dense surroundings) or be taken from the results of computations obtained by the model shown here (for dense surroundings).

The given model of the contaminant clouds and plumes dispersion was applied for assessment of failures consequences connected with 350000 kg benzene spill in the benzene products warehouse of shop of crude benzene rectification at Integrated Iron-and-Steel Works "Severstal" ("NorthSteel") as well as with oil spill at oil pump station "V-Lookie".

The GROUND coding was employed to insert all necessary modifications mostly regarding to turbulence generation or sink, gravitational forces and their effects on turbulence and wind fields.

The EMERGENCY code which is able performing the quantitative assessment of damage caused various hazardous factor fields (e.g. concentration of toxic gases, thermal fields, explosion blast waves) was improved. The latest version of the code represents embedded directly in GROUND FORTRAN statements what allows users to employ EMERGENCY as a fully compatible with PHOENICS tool for the risk analysis.

## Pictures are as follows:

- Figure 1. Comparison of the experimental (wind tunnel) normalized helium concentration behind the building /2/ with the calculation results obtained with use of various turbulent models, a) k-l model; b) k-e model; c) RNG k-e model; d) k-e (Chen and Kim modification) model.
- Figure 2. Streamlines pattern around the isolated building in the case of helium discharge /2/ at various wind speed.
- Figure 3. Vertical normalized concentration profile in the street canyon above the ground source calculated by means of k-l turbulent model at airflow speed 1 m/s, two - dimensional case (experimental (wind tunnel) data were taken from /3/).
- Figure 4. Lateral concentration distribution at level y/H=1 at downwind distance from the source center 2H under various heights of buildings surrounding the ground source (experimental (wind tunnel) data were taken from /3/).
- Figure 5. Lateral concentration distribution at level y/H=1 at downwind distance from the source center 4H under various heights of buildings surrounding the ground source (experimental (wind tunnel) data were taken from /3/).
- Figure 6. Scheme and structure of the industrial area at Integrated Iron-and-Steel Works "Severstal" ("NorthSteel") and magnified view of the benzene products warehouse of shop of crude benzene rectification.
- Figure 7. 2 m height horizontal wind field in the industrial area in 30 min after failure (north wind direction, wind speed at height 10 m - 3,5 m/s, stable atmosphere).
- Figure 8. 2 m height horizontal benzene vapours concentration distribution in 30 min after failure under various thermal stratification of the atmosphere (north wind direction, wind speed at height 10 m - 0,5 m/s) a) unstable atmosphere; b) stable one.
- Figure 9. Gravity current induced heavier-than-air oil vapours at the ground level under pipeline rupture and 40000 m**2 oil spill on the ground surface within the oil pump station (in 30 min after failure).
- Figure 10. Surface with 0,5 probability of the initial response on the oil vapours intoxication (1 hour exposure period was considered), and 2 m height oil vapours concentration field under pipeline rupture and 40000 m**2 oil spill on the ground surface within the oil pump station in 30 min after failure.

Besides above mentioned k-l model, k-e, RNG k-e, Chen-Kim updating of k-e model and turbulent model with constant effective viscosity were tried to closure the described dispersion model.

Comparisons of the computed results obtained by means of various turbulent models for determination of concentration field in the built-up and behind isolated buildings with the data of field and wind tunnel experiments have shown the offered mathematical model and the method of its solution adequately describe spatial structure of the concentration distribution in a building wake and inside a built-up, for an arrangement of the source on ground surface anyway, and can effectively be applied to such cases.

Four considered turbulent models (k-l, k-e, RNG k-e, Chen-Kim k-e) gave a correct qualitative picture of concentration distribution behind the isolated building in the real atmosphere, but quantitatively best results were achieved by using k-l and k-e models. The application complicated RNG k-e and Chen-Kim k-e models did not provide a required degree of accuracy in determination of concentration field, however RNG k-e model most precisely described vertical profiles of wind speed in the vortex zone behind the building.

Use of k-l model (with DISWAL) gave approximately the same degree of accuracy in comparison with k-e model in calculation of concentration field in case of dispersion behind the isolated obstacle, and under dispersion in the built-up, in a number of cases, gave even better results. Taking into account that k-l model is one-equation model and k-e is two-equation one, when the speech goes about reception exact enough and economic computer prediction of concentration distribution in presence of buildings and structures, using k-l turbulent model is most effective.

The calculations of vapours dispersion in real objects showed the influence of the thermal stability of the atmosphere on concentration field in industrial areas was more brightly shown not through the turbulent diffusion directly, as would be in open field, but through influence on structure of the air flows in a built-up.

## References:

M.E.Berlyand. Contemporary Problems of Atmospheric Diffusion and Pollution of the Atmosphere. - Leningrad, 1975. (in Russian).

Mirzai M.H., Harvey J.K., Jones C.D. Wind tunnel investigation of dispersion of pollutants due to wind flow around a small building // Atmospheric Environment, 1994, v. 28, 11, pp. 1819-1826.

Hoydysh W.G., Griffiths R.A., Ogawa Y. A scale model study of the dispersion of pollution in street canyons / For presentation at the 67-th annual meeting of the Air Pollution Control Association, Denver, Colorado, June 9-13, 1974.

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