NUMERICAL SIMULATION OF AIR POLLUTION IN CASE OF UNPLANNED AMMONIA RELEASE

Dep. «Hydraulics and Water Supply», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail gidravlika2013@mail.ru, ORCID 0000-0002-8525-7096 Dep. «Hydraulics and Water Supply», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail gidravlika2013@mail.ru, ORCID 0000-0002-1531-7882


Introduction
The ammonia pipeline Toliatti-Odessa was built in the late 70s-early 80s specifically for the transportation of the main products of the Toliatti nitrogen plant for export.The end point of ammonia pipeline is Odessa Port.There are several pumping stations along the route of this pipeline (Fig. 1).These pump stations support the correct pressure in ammonia pipeline.From the point view of industrial safety these pump stations are the chemically dangerous objects [4,6,15].According to the Law of Ukraine for high-risk objects, a PLAS (Emergency Response Plan) document should be developed for such industrial object.Prediction of contaminated zones and detection of Dangerous Level of Contamination is the basis of this document.Therefore, the actual task is to estimate the level of contamination in working areas of the pump station in the case of unplanned ammonia release.

Review of literature sources
To solve the problem of chemical contamination zones formation in the case of unplanned ammonia emissions analytical models are widely used.For example, Berland model was used to predict air pollution in the case of ammonia pipe rupture [6]: Another approach for assessing the zones of chemical contamination is the application of the Gaussian plume model [2,3,[10][11][12][13][14]. The use of the analytical models or Gaussian models allow to calculate quickly zones of chemical contamination.On the other hand, these models have significant lacks because they cannot be used when we model toxic chemical dispersion among buildings.For this purpose, it is necessary to use numerical models [1,8,9] which are based on Fluid Dynamics equations.In Ukraine, there is a certain deficit of such models [8,9].Worthy of note that the application Navier-Stokes equations for this purpose demands using of very fine computational grid and much computational time.

Purpose
The purpose of this paper is to develop a numerical model for computing the chemical contamination of air on the territory of the ammonia pump station for unplanned ammonia release (accidental release or terror act).

Mathematical formulation
To simulate the pollutant dispersion in the atmosphere 2D transport model is used [5,7] x where С is mean concentration; u, v are the wind velocity components;  is the parameter taking into account the process of pollutant chemical decay or washout; μ=(μ х , μ y ) are the diffusion coefficients; Q is intensity of point source emission;   i r r   are Dirak delta function; r i = (x i , y i ) are the coordinates of the point source .
To simulate the wind flow in the case of the buildings at the territory of Pump Station the 2D model of potential flow is used [7] 2 2 where Р is the potential of velocity.The wind velocity components are calculated as follows: Boundary conditions for modeling equations are discussed in [5,7].

Numerical model
The computation of wind pattern and pollutant dispersion is carried out on rectangular grid.To create the form of buildings we use porosity technique or so called «markers method» [1,7].Markers are used to separate the computational cells where flow takes place from the cells which correspond to buildings.
Main features of the finite difference schemes which we use for the numerical integration of modeling equations are shown below.
To solve equation (1) we use change -triangle difference scheme [1,7].The time dependent derivative in Eq. ( 1) is approximated as follows: At the first step convective derivatives are represented in the following way: where 2 At the second step the convective derivatives are approximated as follows: The second order derivatives are approximated as follows: , , , are the difference operators.Using these expressions, the difference scheme for the transport equation can be written as follows: Solution of the transport equation in finitedifference form is split in four steps on the time step of integration dt: -at the first step ( -at the second step ( -at the third step ( At the fifth step (at this step the influence of the source of pollutant emission is taken into account) the following approximation is used: Function  l is equal to zero in all cells accept the cells where source of emission is situated.
This difference scheme is implicit and absolutely steady but the unknown concentration C is calculated using the explicit formulae at each step (so called «method of running calculation»).To solve equation ( 2) we transform it to the «evolution type» 2 2 2 2 where  is 'fictitious' time.
For    the solution of equation ( 3) tends to the solution of equation (2).
To solve equation (3) A. A. Samarskii's change-triangle difference scheme is used.According to this scheme the solution of equation ( 3) is split into two steps: -at the first step the difference equation is , -at the second step the difference equation is .
From these expressions the unknown value P i,j is determined using the explicit formulae at each step of splitting («method of running calculation»).The calculation is completed if the condition 1 , , is fulfilled (where  is a small number, n is the number of iteration).The components of velocity vector are calculated on the sides of computational cell as follows , 1 , , Calculation of velocity components on the sides of computational cell allows to develop the conservative numerical scheme for pollutant dispersion.
For coding of difference formulae, we used FORTRAN language.

Findings
Developed numerical model and code were used to compute ammonia concentrations at the territory of ammonia pump station in the case of unplanned release (Fig. 2).It was supposed that release takes place near building with ammonia pumps (Fig. 3, 4).Sketch of computational region is shown in Figure 4. Figures 5, 6 show modeling results for ammonia emission.Emission rate is Q=17 kg/s and was chosen from literature [6].

Originality and practical value
A 2D numerical model has been developed to compute contamination zones among buildings during the accidental emission of a hazardous substance.The presented 2D numerical model is based on the application of the fundamental equations of aerodynamics and mass transfer.
The peculiarity of the developed model is the use of standard meteorological information and quick calculation.

Conclusions
Numerical 2D numerical model for estimating the level of atmospheric air pollution during the emergency emission of hazardous substances is proposed.Proposed numerical model allows to predict level of pollution of atmospheric air among buildings.The solution of the aerodynamic problem is based on the numerical integration of the equation for the velocity potential.To predict the air pollution, the equation of mass transfer is used.The mass transfer equation takes into account the convective and diffusive transport of pollutants in atmosphere, taking into account buildings situated near the source of emission.Emission of a dangerous substance is simulated by a point source, which is modeled using Dirac's delta function.
Further improvement of the model should be carried out in the direction of creating a 3D numerical model that takes into account the formation of vortices in the air flow.