Title: MODELING AND SIMULATION OF TURBULENT PENETRATIVE CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN
1MODELING 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
2O 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
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.
4Objectives
- ?The 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.
5Governing 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.
6Governing Equations in RANS-approach
7- Transport Equations
- for heat and mass fluxes
-
8Explicit 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.
9- CLOSURE full explicit turbulent fluxes models
for active (heat) and passive (mass) scalars
10- CLOSURE three-equation model
- for active (heat) scalar
field
11- CLOSURE four-equation model
- for passive
scalar field
12Modeling 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
13Modeling 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.
14Modeling 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.
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.
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.
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.
18NUMERICAL 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 .
19Numerical Method
Fr , Fz turbulent fluxes of momentum, heat and
mass
Semi-implicit alternating direction scheme
20Mesh
- ?The numerical method uses a staggered mesh.
- ?The difference equations are solved by the
three-diagonal-matrix algorithm.
- Staggered mesh
- ? ? ?
- ? ? ?
- ? ? ?
-
-
z
?r
?r/2
?z
?z/2
r
0
Ur
Uz
?E, ?, T, lt?2gt, C, ltc?gt
21Main Results of Simulation
- ?The 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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23Calculation of Normal Turbulent Stresses
- In this problem a simple gradient transport
model preserves certain anisotropy of the normal
turbulent stresses
is turbulent viscosity.
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27RESULTS 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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29CONCLUSION
- ?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.