a.f. kurbatskiy institute of theoretical and applied mechanics sb ras novosibirsk state university
DESCRIPTION
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 PresentationTRANSCRIPT
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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. 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
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
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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.
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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
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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.
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Governing Equations in RANS-approach
TgxP
uux
U
xtD
UDi
iji
j
i
j
i
1
jjj
uxxtD
DPr
cu
xC
ScxtDCD
jjj
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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
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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.
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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
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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 .
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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/
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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>
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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.
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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.
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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”.
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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.