MODELING AND SIMULATION OF TURBULENT PENETRATIVE CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN - PowerPoint PPT Presentation

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MODELING AND SIMULATION OF TURBULENT PENETRATIVE CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN

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Title: MODELING AND SIMULATION OF TURBULENT PENETRATIVE CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN


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

2
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

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.

4
Objectives
  • ?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.

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.

6
Governing Equations in RANS-approach
7
  • Transport Equations
  • for heat and mass fluxes

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.

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

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

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.

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.

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.

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 .

19
Numerical Method
Fr , Fz turbulent fluxes of momentum, heat and
mass
Semi-implicit alternating direction scheme
20
Mesh
  • ?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
21
Main 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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23
Calculation 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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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
  • ?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.
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