NUMERICAL SIMULATION OF TOXIC CHEMICAL DISPERSION AFTER ACCIDENT AT RAILWAY

Dep. «Hydraulics and Water Supply», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail gidravlika2013@mail.ru, ORCID 0000-0002-1531-7882 Dep. «Hydraulics and Water Supply», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail lili.muntyan@gmail.com, ORCID 0000-0002-1659-7740


Introduction
Many accidents at railways result in toxic chemicals emissions [1].These emissions pose potential risk to human health and environment.To predict the damage after these emissions Government Instructions are used.These Instructions are based on simple empirical formulae which do not take account many physical factors, such as, wind profile, diffusion, etc.For example, to predict the width of polluted area the following expression is used in these Instructions where L is the length of polluted area (the L value is determined using the special Table ), n is parameter which depends on the atmosphere condition (stable, neutral, etc.).
In some cases CFD models are used [2−4, 9, 10, 12, 15] but these models are comprehensive for the regular users.
For a quick evaluation of toxic chemical concentrations in atmosphere fast hazard tools are very in need.It is very important for practice to have tools which take into account important details and, on the other hand, are not time consuming.

Purpose
The purpose of this work is the development of numerical model to predict the atmosphere pollution after accidents at railways.

Methodology
Mathematical model of pollutant dispersion.To simulate the toxic chemical dispersion in atmosphere 3-D transport equation is used [2,8,15] ( ) ), where C is air concentration of toxic chemical; , , u v w are the wind components in the x, y and z directions; s w is gravitational settling velocity; σ is the chemical decay coefficient; k is the precipitation scavenging coefficient;

( )
, , x y z µ = µ µ µ are the eddy diffusivities for the three coordinate directions; ( ) x y z are the coordinates of the point source.
This equation is numerically integrated using the following boundary conditions: − at the entrance boundary: where в С is known concentration.At the exit boundary (for example, this is the plane = , where x L is distance from the entrance plane) the boundary condition is used in the following difference form where ( ) is the last computational cell and ( ) , , i j k is the previous computational cell.At the ground (z=0 plane) the boundary condition is where n is normal to this plane, 0 α > is coeffi- cient which takes into account toxic chemical interaction with ground.
The initial condition (at time 0 t = ) can be written as 0 C = in the computational region or 0 C С = , , (where 0 С is the known concentration at the site where the instant emission took place and 0 C = in the other part of the computational region.
In the developed numerical model the following approximations for wind speed and diffusion coefficient are used: where 1 u is wind speed at height 1 10 Numerical model.To solve transport equation (1) the implicit change -triangle scheme is used.The main features of this scheme are shown below.
According to the principles of this implicit scheme development the time dependent derivative is approximated as following: At the first step of development the convective derivatives are represented as follows: At the second step the convective derivatives are approximated as following: The second order derivatives are approximated as following: , , 1 2 In these expressions , , are the difference operators.Using these expressions the difference scheme for the transport equation can be written as follows: .
Solution of this equation is split in four steps on the time step of integration dt :

∑
Function l δ is equal to zero in all cells accept the cells where the ' l ' source of emission is situ- ated.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»).
The initial condition at each time step is written as following [11]: FORTRAN language was used to code the developed numerical model.

Findings
The developed generic code «EMISSION» was used to solve the following problem.A train with toxic chemical (NH3) moves near Railway Station «Illarionovo» (Dniepropetrovsk Region, Ukraine) and at time t=0 the instant emission of NH3 takes place.This emission results in NH3 cloud formation (Fig. 2).Position of this instant emission is schematically shown as «star» in Fig. 1   From the practical point of view it is important to evaluate the ground pollution intensity.To solve this problem the following expression was integrated ( ) ( ) where G is mass of the pollutant whish felt down the ground site S, t is time, T is period of integration.«Rectangular method» was used for the numerical integration of this expression.Results of soil pollution prediction after accident are shown in Tabl.1.Soil Pollution Dynamics.In the case of private owners demands to pay their losses after the accident it is important to know the toxic chemical felt down the different sites, for example, the private fields.At present to evaluate the ecological damage in Ukraine, in the case of ground pollution the following formulae is used where П is polluted area [m 2 ], К is money coefficient (grivni, dollars) declared by Administration Regulations.
As it is clear from Eq. ( 3) to make the adequate evaluation of the ecological damage D it is necessary to obtain the correct information about П.The developed generic code can solve this problem using formulae (2) which is calculated for marked cells of the computational region.These cells indicate the area, for example, of the farm fields (Fig. 2, Site #1and Site # 2).In Tabl.2 results about these sites pollution are presented.

Originality and practical value
A new numerical model to predict atmosphere pollution after accidents at railways was developed.The model is based on the 3-D transport equation.The developed model takes into account wind profile, diffusion, emission rate and source movement This model allows to evaluate the ecological damage in the case of different emissions at railways.The model can be useful in the field of safety prediction of transport routes and risk assessment.

Conclusions
The article contains results of numerical simulation of air pollution near Illarionovo station after accident at railway.To simulate the process of air pollution the 3-D developed numerical model was used.The developed numerical model takes into account the main physical processes which influence the pollutant dispersion in atmosphere.The future work in this field will be connected with development of fluid dynamics model to simulate the pollutant dispersion over the complex terrain.

5 C
-are concentrations at each time step.
and «arrow» indicates the direction of the train movement.The train keeps moving after the accident and long term emission of NH3 ( 5 / sec q kg = ) follows the instant emission.So we have scenario «instant exhaust of toxic chemical + long term emission of it».

Fig. 1 .Fig. 2 .
Fig. 1.Satellite image near Railway Station «Illarionovo» : × 10 5 grams Results from Tabl.2 show that the most contaminated area is formed at Site #1 which is influenced by initial cloud and following emission from moving train.