a.f. kurbatskiy institute of theoretical and applied mechanics sb ras novosibirsk state university

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NATO ASI Conference, Kyiv -2004 1 MODELING AND SIMULATION OF TURBULENT PENETRATIVE CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN HEAT ISLAND IN STABLY STRATIFIED ENVIRONMENT A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University Novosibirsk, Russia L.I. Kurbatskaya Institute of Computational Math. and Math. Geophysics SB RAS Novosibirsk, Russia

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MODELING AND SIMULATION OF TURBULENT PENETRATIVE CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN HEAT ISLAND IN STABLY STRATIFIED ENVIRONMENT. A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University Novosibirsk, Russia L.I. Kurbatskaya - PowerPoint PPT Presentation

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Page 1: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 1

MODELING AND SIMULATION OF TURBULENT PENETRATIVE

CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN HEAT

ISLAND IN STABLY STRATIFIED ENVIRONMENT

A.F. KurbatskiyInstitute of Theoretical and Applied Mechanics SB RAS

Novosibirsk State UniversityNovosibirsk, Russia

L.I. KurbatskayaInstitute of Computational Math. and Math. Geophysics SB RAS

Novosibirsk, Russia

Page 2: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004

O u t l i n e

Introduction Objectives Turbulent Transport Models for

Environmental Stratified Flows Modeling and Simulation of Urban

Heat Island Phenomenon and Pollutant Dispersion

Numerical Results Conclusion

Page 3: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 3

Introduction

For stratified atmospheric flows the LES models and third-order closure models should be considered as fundamental research tools because of their large computer demands.

A growing need for detailed simulations of turbulent structures of stably stratified flows motivates the development and verification of computationally less expensive closure models for applied research in order to reduce computational demands to a minimum.

Page 4: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 4

ObjectivesThe algebraic modeling techniques can be used

in order to obtain for buoyant flows the fully explicit algebraic models for turbulent fluxes of the momentum, heat and mass.

The principal object of this work is the development of three-four-parametric

turbulence model minimizes difficulties in simulating of turbulent transport in stably stratified environment and reduces efforts needed for the numerical implementation of model.

cE 2

Page 5: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 5

Governing Equations

Governing equations describing the turbulent stratified environmental flows are being written down in the hydrostatic approximation at absence of the Coriolis force and radiation with use a Boussinesq approximation.

Page 6: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

6NATO ASI Conference, Kyiv-2004

Governing Equations in RANS-approach

TgxP

uux

U

xtD

UDi

iji

j

i

j

i

1

jjj

uxxtD

DPr

cu

xC

ScxtDCD

jjj

Page 7: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 7

Transport Equations

for heat and mass fluxes

cgx

Ucu

cuEx

Ucu

xC

uutD

cuD

gcx

Uuc

uE

cx

Uu

xuu

tD

uD

icj

ijc

icj

ij

jji

tcu

i

ij

ij

ij

ij

jji

tu

i

)1(

)1(

22

1

222

1

D

D

Page 8: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 8

Explicit Algebraic Expressions for Turbulent Fluxes

The explicit algebraic models for the turbulent heat flux vector and turbulent mass vector were derived by truncation of the closed transport equations for turbulent fluxes of heat and concentration by assuming weak equilibrium, but retaining all major flux production terms.

For turbulent stresses we applied eddy viscosity expression.

Page 9: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 9

CLOSURE: full explicit turbulent fluxes models for active (heat) and passive (mass) scalars

2

21

222

1

2

21

2 1θ 2 2 (1 )

2

11(1 ) 2 ,

2

2 12 2 (1 )

2

(1

jij T t t

i j i

j it i

i j j

jij D t c t

i c j i

UUE R Eu C R C

x C x x

U U C EC R g

x x x C

UUE C R Eu c C R D

x x x

22

1

11) 2 .

2

Turbulent stresses

/ / (2 / 3) .

j i cc t i

i j j c

i j t i j j i ij

U U C ED R g c

x x x

u u U x U x E

Page 10: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 10

CLOSURE: three-equation model

for active (heat) scalar field 2E ε θ

E E

1 2

22

,

,

1.

E

DEP D G

DtD

D P P GDt

DP D

Dt R E

Page 11: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 11

CLOSURE : four-equation model

for passive scalar field2 c E ε

.

1

,

,

3

22

cEtD

cD

ERtDD

GtD

D

GtDED

ccc PD

PD

PPD

PD

21

EEE

Page 12: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 12

Modeling of Urban Heat Island

The ability of the proposed full explicit algebraic models for turbulent fluxes of heat and mass to reproduce correctly the environmental flows with a strong thermal stratification was tested on a large-scale circulation flow above an urban heat island

Page 13: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 13

Modeling of Urban Heat Island

In the phenomenon of the unsteady turbulent penetration convection above an urban heat island the two remarkable features are shown.

The first, due to heating from bellow the interactions between stable and unstable regions occur, because the mixed turbulent ground layer to grow into a stable region.

Page 14: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 14

Modeling of Urban Heat Island

The second, there is the entrainment of overlaying non-turbulent fluid into mixed layer causing very step gradients at the interface.

These features explain why the phenomenon of urban heat island represents a very challenging test case for turbulent models.

Page 15: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 15

Objectives

Thus, the principal aim of this investigation is the modeling and simulation of large-scale turbulent circulation flow above the urban heat island and pollutant dispersion in the stably stratified environment.

Page 16: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 16

Limitations of Laboratory

Measurements for Full-scale Simulation

There are important limitations utilized in the laboratory experiment and simulation of the real urban heat-island in the nighttime atmosphere:

Very large heat fluxes from the heater surfaces

Very strong temperature gradients that required to obtain the low aspect ratios (zi/D) and small Froude numbers.

Page 17: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 17

Structure of heat-island circulation

The penetrative turbulent convection is induced by the constant heat flux H0 from the surface of a plate with diameter D. It simulates a prototype of an urban heat island with the low-aspect-ratio plume (zi / D « 1) under near calm conditions and stably stratified atmosphere.

Page 18: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 18

NUMERICAL MODELING OF HEAT ISLAND CIRCULATION

The problem of development of circulation above a heat island is assumed to be axisymmetric.

The domain of integration is a cylinder of a given height .

Page 19: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 19

Numerical Method

fzF

rF

rtzr

1

cCTEUr ,,,,,,: 2

Fr , Fz – turbulent fluxes of momentum, heat and mass

Semi-implicit alternating direction scheme

nn

zn

rnji

nji

nn

zn

rnji

nji

fzF

rF

rt

fzF

rF

rt

12/1,

1,

2/1,

2/1,

12/

12/

Page 20: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 20

MeshThe numerical

method uses a staggered mesh.

The difference equations are solved by the three-diagonal-matrix algorithm.

Staggered mesh

z

r

z

0

r/2

r

z/2

Ur Uz

E, , T, <2>, C, <c>

Page 21: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 21

Main Results of SimulationThe results of simulation correspond to a

quasi-steady state of circulation over an area heat source in stable stratified environment.

Figure (c): shadowgraph picture at t = 240 sec when the full circulation is established.

Page 22: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 22

Page 23: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 23

Calculation of Normal Turbulent Stresses

In this problem a simple gradient transport model preserves certain anisotropy of the normal turbulent stresses

rU

Eu rtr 2

322

zU

Eu ztz 2

322

2Ect is turbulent viscosity.

Page 24: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 24

Page 25: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 25

Page 26: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 26

Page 27: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 27

RESULTS: Temperature profiles

Calculated temperature profiles inside the plume have characteristic “swelling”:

the temperature inside the plume is lower than the temperature outside at the same height creating an area of negative buoyancy due to the overshooting of the plume at the center.

This behavior indicates that the plume has a dome-shaped upper part in the form of a “hat”.  

  

Page 28: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

NATO ASI Conference, Kyiv-2004 28

Page 29: A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University

29

CONCLUSION CONCLUSION

The three-equation model of turbulent transport of heat reproduces structural features of the penetrative turbulent convection over the heat island in a stably stratified environment.

This model minimizes difficulties in describing the non-homogeneous turbulence in a stably stratified environment and reduces computational resources required for the numerical simulation.