MODELLING OF MULTIPHASE FLOWS MODELLING OF MULTIPHASE FLOWS OVER SURFACE WITH PENETRABLE OVER SURFACE WITH PENETRABLE

ROUGH RELIEFROUGH RELIEF

Yevgeniy A. ShkvarYevgeniy A. ShkvarNational Aviation University, Kyiv, National Aviation University, Kyiv,

UkraineUkraine

e-mail: shkvar@ukrpost.nete-mail: shkvar@ukrpost.net

Several kinds of turbulent flows Several kinds of turbulent flows associated with this associated with this

investigationinvestigation

Object of investigation isObject of investigation is a boundary layer developing under a boundary layer developing under

conditions close to atmospheric (over conditions close to atmospheric (over rough surface and with presence of rough surface and with presence of additive phase)additive phase)

The atmosphere from space (source NASA)

Background of the problemBrief information about typical dimensions and

scales

The troposphere is a region of mixing, containing:

1) the largest percentage of the mass of the total atmosphere;

2) 99 % of the water vapor in the atmosphere.

3) All weather phenomena occur within the troposphere.

Atmosphere, its structure and phenomena

Natural convective processes in the neighborhood of the land

Surface relief (roughness and penetrable roughness)

There are many practically interested cases, when relief elements like 1. Land cover irregularities;2. Forests;3. Urban relief (buildings, streets, etc.) may be considered as a special kind of roughness

distributed in the neighborhood of land and having penetrable effect

Sources of Air Sources of Air Pollution:Pollution:

1.1. Smoke; Smoke;

2.2. NaturalNatural airair pollution;pollution;

3.3. Enterprise emissions;Enterprise emissions;

4.4. Exhaust gas emissions;Exhaust gas emissions;

5.5. Forest fires;Forest fires;

6.6. Radiation, chemical Radiation, chemical accidents.accidents.The atmosphere “lives” under strong The atmosphere “lives” under strong

influence influence

of pollutions with different natureof pollutions with different nature

Goal of the researchGoal of the research Construct the simple model of the atmospheric Construct the simple model of the atmospheric

boundary layer that will be able to account a boundary layer that will be able to account a rough relief influence on flow properties and rough relief influence on flow properties and

pollution diffusionpollution diffusion

Accounting Accounting factors:factors:

1.1. Surface is covered by Surface is covered by rough relief with rough relief with penetrable structure;penetrable structure;

2.2. Flow can be Flow can be heterogeneous;heterogeneous;

3.3. Atmospheric Atmospheric pollutants have pollutants have properties of scalar properties of scalar passive additives. passive additives.

Negligible factors:Negligible factors:1.1. Land Curvature;Land Curvature;2.2. Earth rotation, Coriolis Earth rotation, Coriolis

effects;effects;3.3. Air compressibility;Air compressibility;4.4. Air stratification;Air stratification;5.5. Radiation;Radiation;6.6. Heating;Heating;7.7. Chemical and Chemical and

mechanical phase mechanical phase interactioninteraction

Investigated geometries Investigated geometries of surface reliefof surface relief

Streamlined surfaceStreamlined surface Penetrable rough Penetrable rough elementselements

Flow directionFlow direction

0

yG

xuG v

uuu GFxpG

yuG

Dyx

uGD

xyG

xuG

tu

G

vu2

v

2 vvvvvGF

ypG

yG

Dyx

GD

xyG

xuG

tG uu

ccccvcc

GFyG

Dyx

GD

xyG

xuG

tG eff

CeffC

((1)1)

(2)(2)

(3)(3)

(4)(4)

Continuity equation:Continuity equation:

Momentum equation in projections on Momentum equation in projections on xx and and yy axes: axes:

Transfer equation of scalar additive concentration :Transfer equation of scalar additive concentration :

Governing equationsGoverning equations

totalfluid VVG HereHere - the effective fluid volume,- the effective fluid volume, 1G

Turbulence modelingTurbulence modelingDifferential k-e approachDifferential k-e approach

)-P( keffk

effk FG

ykG

Dyx

kGD

xyG

xkuG

tk

G

kv

kFfCCG

yG

Dyx

GD

xyG

xuG

tG eff

keffk

)~-P( 21v

;22P222

xG

yuG

yG

xuG

Gt vv

(5)(5)

(6)(6)

teff ii c

t

teffC ScScD

k

teffkD

teffD

DIFFUSIDIFFUSIVEVE COEFFICIENTS & DENSITY COEFFICIENTS & DENSITY DETERMINATIONDETERMINATION

(7)(7)

Model detailsModel details

)0115.0exp(1 yf

)6

Reexp(22.01 tf

2

Rek

t

22

Re2~

yk

xk

2kfct

сс=0,09; с=0,09; с11=1,45; с=1,45; с22=1,92; =1,92; kk=1; =1; =1,3=1,3

*vy

y

Near-wall modificationsNear-wall modifications

The set of model coefficientsThe set of model coefficients

Source modificationsSource modifications

2

2uCF roughfu x

Grough 1

uFF uk roughLk

CF23

(8)(8)

(9)(9)

),( roughroughhfC ),( roughroughrough hfL

0vF

- T. - T. MaryuamaMaryuama

Turbulence modelingTurbulence modeling Algebraic approachAlgebraic approach

tanh*Hut

τky

yχyχky

1

122

112

1)](tanh[sinh][sinh

tanh

;0

;0

if

if

11

1

dxdpdxdp

ydxdp

ydxdp

(10)(10)

(11)(11)

(12)(12)

0215.00168.0 072.0068.01 223.02 4.0k

0

001

s

s

if

if

sy polrough yyys

roughy

Here:Here:

,

,

,

,

,

- the model’s coefficients- the model’s coefficients

;

0 poly

0 roughy

lny

U+Smooth surfaceSmooth surface

- V. Movchan’ - V. Movchan’ formulaformula

Boundary conditionsBoundary conditions,0u ,0v ,0k ;0~

.0nc

),(yfu ,0v ),(yco ),(ykk );(y

,0nu

,0nv

,0nk

,0n

Streamlined surface:Streamlined surface:

Initial cross-section Initial cross-section (input boundary):(input boundary):

,

Output boundaries of Output boundaries of computational domain:computational domain:

Numerical MethodNumerical MethodGridGrid – nonuniform orthogonal staggered;– nonuniform orthogonal staggered;

+ Leonard’, Zijlema’ 3-rd order schemes;+ Leonard’, Zijlema’ 3-rd order schemes; Calculation procedureCalculation procedure – Thomas algorithm.– Thomas algorithm.

MethodMethod – SIMPLE– SIMPLE

Testing of elaborated Testing of elaborated modelsmodels

Predictions of flow Predictions of flow properties for several properties for several

geometries of rough relief geometries of rough relief and their comparison with and their comparison with

the experimental datathe experimental data

Flow behind penetrable Flow behind penetrable obstaclesobstaclesExperimental data source:

P. H. A. Barbosa; M. Cataldi; A. P. S. Freire,

“Wind tunnel simulation of atmospheric boundary layer flows”

J. Braz. Soc. Mech. Sci. vol.24 no.3 Rio de Janeiro July 2002

Flow phenomena:

This flow was artificially thickened for making its parameters to be similar for typical atmospheric flows

Velocity profiles comparison in Velocity profiles comparison in semi-logarithmic coordinatessemi-logarithmic coordinatesInvestigated case: Flow behind rods array with 160 Investigated case: Flow behind rods array with 160

mm ,Umm ,U∞∞=3 m/s=3 m/s

876543210

30

25

20

15

10

5

0

-5

a) a) Experiments Experiments P. H. A. Barbosa; M. Cataldi; A. P. S. Freire (Brazil, 2002);

b) Predictions on the base of this modelb) Predictions on the base of this model

Skin friction coefficient vs. Skin friction coefficient vs. ReReδδ****

Investigated case: Flow behind rods array with 160 Investigated case: Flow behind rods array with 160 mm ,Umm ,U∞∞=3 m/s=3 m/s

Experiments Experiments P. H. A. Barbosa; M. Cataldi; A. P. S. Freire (Brazil, 2002);

Flow over penetrable rough Flow over penetrable rough relief relief

(short rough zone (short rough zone LLroughrough=0.5m, =0.5m, ρρroughrough=0.25=0.25))Cf δ*

H=δ*/δ**

9,686,44,83,21,60

0,0058

0,0051

0,0045

0,0038

0,0032

0,0026

0,0019

0,0013

0,0006

9,686,44,83,21,60

0,0179

0,0166

0,0154

0,0141

0,0128

0,0115

0,0102

0,0090,0077

0,0064

0,0051

0,0038

0,0026

0,0013

9,686,44,83,21,60

2,3

2,2

2,1

2

1,9

1,8

1,7

1,6

1,5

Flow over penetrable rough Flow over penetrable rough relief relief

(short rough zone (short rough zone LLroughrough=0.5m , =0.5m , ρρroughrough=0.25=0.25))

U, CU, C

kk

εε

ννtt

Flow over penetrable rough Flow over penetrable rough reliefrelief

(continuous rough zone (continuous rough zone LLroughrough=6.5m, =6.5m, ρρroughrough=0.25=0.25))

9,686,44,83,21,60

0,0058

0,0051

0,0045

0,0038

0,0032

0,0026

0,0019

0,0013

0,0006

9,686,44,83,21,60

0,0205

0,0179

0,0154

0,0128

0,0102

0,0077

0,0051

0,0026

9,686,44,83,21,60

3

2,8

2,6

2,4

2,2

2

1,8

1,6

Cf δ*

H=δ*/δ**

Flow over penetrable rough Flow over penetrable rough reliefrelief

(continuous rough zone (continuous rough zone LLroughrough=6.5m , =6.5m , ρρroughrough=0.25=0.25))

U, CU, C

kk

εε

ννtt

Flow over penetrable rough Flow over penetrable rough reliefrelief

(rough array (rough array LLroughrough==4x4x0.5m, 0.5m, ρρroughrough=0.25=0.25))

9,686,44,83,21,60

0,0058

0,0051

0,0045

0,0038

0,0032

0,0026

0,0019

0,0013

0,0006

9,686,44,83,21,60

0,0205

0,0179

0,0154

0,0128

0,0102

0,0077

0,0051

0,0026

9,686,44,83,21,60

3

2,8

2,6

2,4

2,2

2

1,8

1,6

1,4

Cf δ*

H=δ*/δ**

Flow over penetrable rough Flow over penetrable rough reliefrelief

(rough array (rough array LLroughrough==4x4x0.5m , 0.5m , ρρroughrough=0.25=0.25))

U, CU, C

kk

εε

ννtt

ConclusionConclusion

Presented model is able to account an Presented model is able to account an influence of penetrable roughness on the influence of penetrable roughness on the turbulent flow properties;turbulent flow properties;

This model predicts an influence of rough This model predicts an influence of rough relief on a scalar additive transfer;relief on a scalar additive transfer;

Algebraic approach to turbulence Algebraic approach to turbulence modeling is acceptable for this kind of modeling is acceptable for this kind of viscous flows;viscous flows;

Penetrable roughness can be used as Penetrable roughness can be used as an effective tool of air protection. an effective tool of air protection.