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# Calculation Models For The Simulation Of Atmospheric Dispersion Of Gas Clouds

There are several classes of calculation models to simulate the atmospheric dispersion of gas clouds:

1. Gaussian model
2. Jet model
3. Box or slab model
4. Particle simulation model
5. k-ε model representing CFD models

The Gaussian plume model is the classical approach for the simulation of the spreading of neutral (sufficiently diluted) gases incl. pollutants or radioactivity. It is a simple model describing the concentration profile as a solution of the diffusion/advection differential equation with empirical coefficients depending on the atmospheric conditions. This model, however, is inappropriate for treating the buoyant behavior of light or heavy gases.

Dispersion models are often accompanied by a jet release model to calculate the dispersion of a released gas with significant momentum flux, which is the dominant parameter for jets. The jet can be classified into two main zones, a region of adjustment from storage conditions to atmospheric pressure and a region of ˇ§conventionalˇ¨ jet dispersion at ambient conditions. If storage conditions are pressurized, the initial zone of adjustment will possibly include flashing for a liquid or choked two-phase jet. The conventional dispersion region begins with a so-called region of flow establishment, in which similarity profiles for the concentration and axial velocity evolve; following this the jet evolves with self-similar profiles. The main features distinguishing the various jet models are the treatment of the air entrainment and the choice of the similarity profile (e.g., top-hat, Gaussian).

The macro or two-zones mixture model developed by BASF (GiesbrechtH:1980) regards the bursting of a pressure vessel, where the high exit velocity results in a fully turbulent propagation of the vessel contents. Two zones are distinguished: a core zone of the vapor cloud where (cold) liquid droplets are still existing, and a boundary zone. In the core zone, ideal mixture with spatially constant and temporally decreasing concentration is assumed, while in the boundary zone, a spatially constant and temporally decreasing turbulent diffusion coefficient is assumed.

In box or slab models, the released gas cloud is assumed to be of cylindrical shape. The processes of advection (transport by the mean wind field), air entrainment, and gravitational spreading are implemented in empirical correlations which were derived from experiments. Box models were basically developed to simulate heavier-than-air vapor clouds with averaged temperature and concentration. In extended versions, vertical profiles of temperature and concentration can be assumed. Acknowledged box models are the US code DEGADIS (HavensJA:1990) or the British code HEGADAS (McFarlaneK:1990).

Particle simulation models are based on the stochastic nature of the movement of particles in the atmospheric wind field. In a simulation, numerous (typically 5000-15,000) particles are being emitted and their trajectories traced making a statistical analysis of the velocity fluctuations. The turbulent velocity is considered to undergo changes only after a certain time defined as the Lagrange correlation time. The distribution of the particles in a given calculation grid is then a measure for the concentration distribution. An improvement of the model is given by assuming a so-called Markov process for a particle meaning that the fluctuation part is further subdivided into a component representing the capability of remembering, and a random component. The velocity at time t is then composed of a fraction proportional to the ˇ§oldˇ¨ velocity at time t-dt and a remainder produced in a random number generator. One representative particle simulation model is the German code LASAT (MartensR:1991).

State-of-the-art modeling of the transient behavior of gases with either positive or negative buoyancy in the atmosphere is provided by Computer Fluid Dynamics (CFD) models, which simulate complex flow processes by solving the Navier-Stokes equations in an Eulerian 3D (or 2D) calculation grid structure. This approach comprises the conservation equations of mass, momentum, and energy. Apart from being (in most cases) immensely time-consuming, these models require a detailed input of initial and boundary conditions.

In the two-equation k-ε turbulence model, special partial differential equations are solved to describe the transport of turbulence as well as its generation and dissipation. Of all the approaches, the k-ε model offers the highest relative independence of empirical relations. It appears to be the only one to allow a proper simulation of hydrogen dispersion, because it meets the requirements of describing effects such as turbulence energy in the gas cloud, interaction with the atmospheric wind field, the characteristic positive buoyancy, transient sources with initial momentum, and last but not least, gas flow in a complex geometry (buildings, terrain). K-ε modeling has been realized in a variety of computer codes distinguished by the choice of the numerical solution method, which was found to have a significant effect on the calculation procedure.

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