NUMERICAL SIMULATION OF AIR POLLUTION TRANSFER

IN URBAN AREAS

P. I. Kudinov, V. A. Ericheva

Dnepropetrovsk National University, Dnepropetrovsk, Ukraine

e-mail: p_kudinov@ukr.net, web: http://Xoptimum.narod.ru

Aims:

Development of numerical methods for incompressible viscid flows

Better understanding of 3D vortex flows formation regularities

Study of pollution transfer in elements of urban areas

Development and analysis of visualization techniques for numerical simulation of 3D vortex flow

Governing equations

0S

dSVn

WWSe

W

dWdWpdSn

dWt

GV

VVnV

The passive admixture model is used. This model is close to truth if the sizes of particles are small enough.All equations can be written in the form of conservation law of some physical variable

WSe

W

dWSdSn

dWt

Vn

here e - effective coefficient of diffusion, S  - sources of .

Mass and momentum conservation of viscose incompressible fluid

Numerical methodDiscrete analogues of governing equations in curvilinear non-orthogonal coordinate system

1000

n

kkk t

WSWSAA

t

WAA

kk

0

ik

k kk

iikk

ikk S

xgdcVA e

11

ik

kkj

ijkk

ik

k

ik SgdSVS ee 110

ei , ej – covariant and contravariant components of local basis.

System of linear algebraic equations is solved by Gauss-Zeydel method. For pressure calculation the modification of SIMPLER algorithm on the case of curvilinear coordinates is used. Verification of developed models and numerical methods was done on test problems of lid driven flow in a square cavity, flow around circular cylinder.

Some typical geometry configurations of urban areas

Courtyard with different wind direction

Long street

Streamlines on the surfaces and numerical “laser knife” visualization in vertical and horizontal cross section of the infinite trench

Trajectories

Pe=104 Pe=106

Pollution concentration in vertical cross sections

Pollution concentration in horizontal cross sections

Pe=104 Pe=106

Pollution concentration in frontal cross sections

Flow in 3D cavity with moving lid

Pollution concentration in vertical cross sections

Pollution concentration in frontal cross sections Pollution concentration in horizontal cross sections

Pe=105

Streamlines on the bottom, side and a), b), c) – windward, d), e), f) – leeward walls of the trench at Re=103 and angles of lid motion

a), d) =5, b), e) =20, c), f) =45

a)

b)

c)

d)

e)

f)

Streamlines on the bottom, side and a), b), c) – windward, d), e), f) – leeward walls of the trench at Re=103 and angles of lid motion

a), d) =60, b), e) =80, c), f) =90

a)

b)

c)

d)

e)

f)

Pollution concentration in vertical cross sections

Pollution concentration in frontal cross sections Pollution concentration in horizontal cross sections

Pe=105

Conclusions and aims for future work

Developed numerical techniques permits to simulate and visualize 3D flows and mass transfer in obstructed geometry.For better understanding of structure of 3D flows we need to use combination of different types of visualization techniques. There is no universal method of visualization of 3D flows. Using of only 2D visualization can lead to loss of important information.

Actual problems are:Development of numerical simulation and visualization methods for unsteady 3D flows and pollution transfer in obstructed geometry.Investigation of regularities of momentum heat and mass transfer in single elements and arrays of typical urban and vegetative canopy geometry.Development of numerical method for aeroelastic problems for flexible canopies.