NUMERICAL SIMULATION OF POLLUTION DISPERSION IN URBAN STREET

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 water.supply.treatment@gmail.com, ORCID 0000-0002-1531-7882 Dep. «Manufacturing and Property Management», National Transport University of Ukraine, Suvorov St., 1, Kyiv, Ukraine, 01010, tel. +38 (044) 280 82 03, e-mail water.supply.treatment@gmail.com, ORCID 0000-0001-5163-5645 Dep. «Manufacturing and Property Management», National Transport University of Ukraine, Suvorov St., 1, Kyiv, Ukraine, 01010, tel. +38 (044) 280 82 03, e-mail water.supply.treatment@gmail.com, ORCID 0000-0001-9918-3895


Introduction
Pollution from vehicles in urban streets is very intensive and can cause harm to humans.For this purpose, it is necessary to predict the level of pollution in streets.Physical modeling, in this case, is very expensive [8].For quick prediction empirical models are used [1].These models are convenient in practice, especially when we must run many «pilot» calculations.But these models do not take into account some important properties of pollutant dispersion process in streets.The main problem is that the process of air pollution in streets takes part in the region having comprehensive geometrical form (presence of buildings, different obstacles, etc).The alternative way is the numerical simulation of this process.Many authors apply CFD simulation to solve the problem [1,3,6,[8][9][10].As a rule, to obtain flow pattern in streets foreign authors use Navier -Stokes equations (this is the model of viscous fluid) coupled with turbulent models.Very often commercial codes are used for this purpose.Worthy of note, that application of Navier -Stokes equations needs application of very fine computational grid during the computational experiment to simulate in detail the process of vortexes formation and their dispersion and interaction in the region.Using the model of viscous fluid, we must use very fine grid inside the boundary layers.This is a real problem if we have big dimensions of the buildings, obstacles in streets.So, in case of Navier -Stokes equations application it is necessary to use powerful PC and every computational experiment consumes much time.This is not convenient when we must run a lot of practical calculations considering different scenario of air pollution in streets and, especially, when we try to find the effective protection measures because in this case we must consider many alternative variants of protection.In this case it would be better to split the study in two steps.At the first step we may find the «satisfying» variant using numerical model which does not consume much time and not take into account some physical features of the process.After that, at the second step, we may use more powerful model to compute in detail the variant of protection which has been chosen.So, for quick calculations at the first step it is important to have CFD models which consume not much computational time but they allow to take into account such important features as obstacles, emission rate, etc.

Purpose
The purpose of this paper is development a numerical model for quick computing of the local air quality near roads.

Aerodynamic equation
To simulate the wind pattern near the road we use model of potential flow.In this case the governing equation is [5]: where Р is the potential of speed.The wind velocity components are calculated as follows: Boundary conditions equation (1) are discussed in [1].To perform numerical integration of this equation rectangular grid was used.
To solve equation of potential flow (1) we used the difference scheme of «conditional approximation».In this case, first of all, we transformed Eq. 1 to equation having «evolution type» [5] 2 2 2 2 where  is «fictitious» time.
For    the solution of equation ( 2) tends to the solution of equation (1).
After approximation of Eq. 2, we split it in the sequence of two difference equations having implicit form [5] , Unknown value of , i j P can be easily determined from each difference equation ( 3) using explicit formulae of «running calculation».As the «initial» condition for Eq. 2 we may use, for, example, P=0 for  =0.

Pollutant Transport Equation
To simulate the pollutant dispersion near road equation of convective -diffusive transfer is used [1,4,7] where С is mean concentration W is width of the computational region; , u v are the wind velocity components; ( , ) are Dirac delta function; t is time.Initial and boundary conditions for Eq. 4 are described in [1,4].
Before solving Eq. ( 2) we made it's physical splitting into the sequence of three equations.These are the following equations:   To solve the first and the second equations in (5) the implicit change -triangle difference scheme was used [1].To solve the third equation from ( 5) Euler method was used [5].
Numerical integration of difference equations is performed using rectangular grid.Values of P, C are determined in the centers of computational cells, values of u, v are determined at the sides of the computational cells.For coding difference equations, we used FORTRAN language.

Findings
Developed numerical model and code were used to compute CO concentrations near road which has barrier at the curb.Numerical simulation was performed for two scenarios.The first one is scenario where barrier has a form of vertical plate (Fig. 1).The second scenario is application of barrier which has additional «short wing» at the top (Fig. 2).«Body» of the vehicle is represented as rectangular.Its form and form of the curb, barrier is represented in numerical model using «markers» (porosity technique).Outlet opening of the vehicle is a passive source of emission.It means that we don't take into account speed of gases which move from it.Arrow indicates the wind direction.
Results of numerical simulations are shown in Fig. 3-5.Fig. 3, 4 represent CO concentration field near road.We can see that application of barrier with «short wing» allows to reduce the width of contaminated zone behind the barrier.In Table 1 we present computed CO concentration behind barriers at height h=1,7 m.Worthy of note that computational time was about 5 sec.for each scenario.It allows to use the developed numerical model for practical application when series of computational experiments must be run.

A model has been developed to compute concentrations near roads. Numerical model is based on application of mass transfer equation and equation of potential flow.
The peculiarity of the developed model is the use quick calculation of contaminated zones and account of geometrical form of vehicle, curb, barriers near the road.

Conclusions
Numerical model for estimating the level of atmospheric air pollution near roads is proposed.Proposed numerical model allows to predict level of pollution with account of geometrical form of vehicle, curb, barriers near the road, intensity of emission rate.The solution of the aerodynamic problem is based on the numerical integration of equation for potential flow.This allows to perform quick calculation of wind pattern near road using PC which are available now in Ukraine.To predict toxic gases concentrations near road convectivediffusive equation is used.Numerical integration of this equation is performed using implicit difference scheme.Using the developed numerical model some numerical experiments were performed to study the influence of barrier form on intensity of local contamination near road.
Further improvement of the model should be carried out in the direction of creating a 3D numerical model.