ENVIRONMENTAL AND INDUSTRIAL CFD SIMULATIONS Turbulence models in the environmental flow

1
ENVIRONMENTAL AND INDUSTRIAL CFD
SIMULATIONSTurbulence models in the
environmental flow

• Zbynek Janour
• Institute of Thermomechanics AS CR, Dolejškova 5
  Prague 8, 182 00, Czech Republic,

2
Overview

• Introduction,
• Equations,
• Turbulence,
• Atmospheric Boundary Layer,
• Closure Problem,
• Models,
• Boundary Conditions,
• Applications
• Conclusion

3
Introduction

• The most fluid on the world belongs to the
  atmosphere and the ocean,
• Geophysical fluid dynamics

4
Introduction
5
Equations
Reference coordinate system
Inertial coordinate system
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Equations

• Inertial coordinate system
• Continuity equation
• The equation of motion
• The energy equation

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Equations

• Reference coordinate system
• R perpendicular distance from the rotation
  axis,
• The last term on the r.h.s. can be included into
  the gravitation force

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Equations

• Reference coordinate system
• Continuity equation
• The equation of motion
• Coriolis force
• or

f10-4
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Turbulence

• Is the atmosphere turbulent?
• According to Tennekes, Lumley A First Course in
  Turbulence the turbulence flow has following
  characters
• Irregular - Y,
• Diffusive - Y,
• Large Re 109 - Y,
• 3D vorticity fluctuations - Y,
• Dissipative needs energy supply - Y/N,
• Continuum - Y,
• Turbulent flows are flows - Y

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Turbulence

• Wake behind a jet turbulent / nonturbulent ?
• The answer It is not flow it is a picture of
  the former turbulent wake

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Turbulence

• Energy sources
• Atmospheric Boundary Layer (ABL)
• Free atmosphere
• Clouds,
• Clear-Air Turbulence (CAT)

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Turbulence

• Characteristic scale
• Velocity U,
• Length in horizontal direction L,
• Length in vertical direction H,
• -pressure ?P,

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Turbulence
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Turbulence
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Turbulence

• Turbulent flow - L102
• ?
• Atmospheric Boundary Layer (ABL)
• Free atmosphere
• Clouds,
• Clear-Air Turbulence (CAT)

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Turbulence

• The ABL
• Layer of air directly above the Earth surface
  in which effects of the surface (friction,
  heating and cooling) are felt on time scales less
  than a day, and in which significant fluxes of
  momentum, heat or matter are carried by turbulent
  motions on scale of the order of the depth of the
  boundary layer or less

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Turbulence
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Turbulence

• Cloud
• Cumulus-type cloud associated with thunderstorm

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Turbulence

• CAT
• Shear turbulence without visible manifestations.
• It occurs outside of clouds,
• In only about 20 of the free atmosphere below 12
  km,
• is even less common above 12 km and occurs in
  only about 2 near 17 km,
• It generally occurs in stable conditions,
• It has not cased severe structure damage of
  aircraft.

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Turbulence

• Atmospheric turbulence differs from most
• laboratory turbulence in
• Heat convection coexists with mechanical
  turbulence,
• The rotation of the earth becomes important for
  many problems

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Atmospheric Boundary Layer (ABL)

• The ABL is the region in which the large-scale
  flow of the free atmosphere adjusts to the
  boundary condition imposed by the earths surface

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ABL

• Small-scale maximum - turbulent peak
• Large-scale maximum - synoptic peak
• Spectral gap around 1 cycle/hour

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ABL

• Fluctuations with frequency smaller than 0.1
  cycle/km belongs to the mean value
• Fluctuations with frequency large than 0.1
  cycle/km belongs to the turbulent fluctuations
• Reynolds
  conditions

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Equations
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Closure problem
New dependent variables
New dependent variables
Closure problem, etc.
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Model taxonomy

• Ensemble-averaged equations
• Integral models,
• First-order closure models,
• Second-order closure models,
• Reynolds-stress models,
• Volume-averaged equations
• Large Eddy Simulation (LES)
• Full simulation
• Direct Numerical Simulation (DNS)

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Integral models

• Reynolds equations are integrated over at
  least one coordinate direction and the number of
  independent variables decreases

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Integral models
Mixed Layer
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Integral models
Where is
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Integral models
Equations for velocity and temperature jumps
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Integral models
Equations for heat and momentum fluxes at the
inversion base
9 equations for 10 dependent variables
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Integral models
Models for zi
-
we entrainment velocity
-
Rb Richardson number
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First-order closure models

• K-models based on the hypothesis of
  Boussinesq(1877), who suggested that turbulent
  shearing stress in analogy to viscous stress can
  be related to the mean strain
• Where ?t is eddy viscosity new dependent
  variable

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Eddy viscosity

• ?t constant - Ekman spiral(1905)

   
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Eddy viscosity
Notice ABL thickness ? 1km ? ?t 10
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Eddy viscosity

• Prandts model - Blackadar (1962) generalized by
  Estoqe, Bhumralk (1969) and Yu (1977).
• 
  l-mixing length
• z0 roughness length

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Eddy viscosity
Richardson number
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Two equations models
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Large Eddy Simulation

• The first large-eddy simulations were performed
  by Deardorff (1972 19731974), and were later
  investigated by e.g.,
• Schemm and Lipps (1976),
• Sommeria (1976),
• Moeng (1984),
• Wyngaard and Brost (1984), Schmidt and Schumann
  (1989), Mason (1989). Much of the previous work
• LES has been focused on simulations of the
  convective boundary layers (Nieuwstadt et al.,
  1992).
• The cloudy boundary layers were simulated by
  e.g., Sommeria 1976 Deardorff 1980 Moeng 1986
  Moeng et al. 1996 Lewellen and Lewellen 1996,
  Cuijpers and Duynkerke (1993).

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Boundary Conditions
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Boundary Conditions
The equations of motion has to be supplemented
with initial and boundary conditions in many
papers the conditions are not introduced
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Boundary Conditions

• In limited-area atmospheric models the surface -
  ?S is the only physical boundary of the solution
  domain. All other boundaries are purely
  computational

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Boundary Conditions on the surface
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Boundary Conditions on the surface

• Two methods
• Boundary conditions on the surface
• modification of the equations of motion for
• small turbulence Reynold number increasing
• number of grid points near the wall,
• Wall function

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Boundary Conditions-wall function
for 30 lt z1u/v lt 100
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Roughness length- experience
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Roughness length-models
Petersen z0 D ?f H, where D ?0.5, ?f Af / AT
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Boundary Conditions on the top of the ABL
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Outlet Boundary Conditions
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Inlet Boundary Conditions

• Dirichlet condition determined from
• In-situ measurement a very few data sets,
• Universal profiles
• Ekman spiral,
• Power law,
• .
• -mostly for horizontally homogeneous surface

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Boussinesq approximation
?
limited-area
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Boussinesq approximation
Large scale flow
Small scale fluctuation
Turbulent fluctuation
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Boussinesq approximation
Large scale flow
Hydrostatic approximation
Geostrophic approximation
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Boussinesq approximation
Small scale fluctuation
Continuity equation
Shallow water approximation (incompressible)
Anelastic approximation
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Boussinesq approximation
Reynolds equations

• Notices
• Small scale fluctuation of the pressure and
  potential temperature,
• Buoyant force instead gravitational force,
• Incompressible case

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Boussinesq approximation
F0 for ?i
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Application
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Application
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Application
Dispersion from linen source inside the street
canyon- FLUENT
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Application
Dispersion from linen source inside the street
canyon- FLUENT
experiment
RNG k-? model
k-? model
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Application
Smoke generator

• laser sheet- DANTEC,
• The recordings from the video camera for values
  of the Reynolds number of Re ? U0H/??(2.3 x 104
  2.3 x 105),

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Application

• External velocity Ug1.5m/s,
• liquid is drawn from the cavern into the external
  stream,

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Application

• External velocity Ug4.0m/s

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Application
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Application
A simple model of the UABL

• UABL is similar to the flow over a rough surface,
  with a large roughness length z0 and a defined
  surface heat flux QG
• The horizontally homogeneous atmospheric boundary
  layer horizontal length scale - L ? ?

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Application
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Application

• radiosounding launched in Barcelona,
• indifferent stratification
• influence of topography is more important across
  Internal-Sub-Layer
• artificial mean profile determined from the data
  sets seems to be more suitable for comparison

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Application

• radiosounding launched in Évora,
• indifferent stratification

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Application

• sodar measurement in Prague,
• without stratification assessment

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Application
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Application
Algebraic turbulence models
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Application
Algebraic turbulence models
Plume from point sources in south east Giant
Mountains
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4. Conclusions

• Eddy viscosity models appears
• Quite satisfactory in neutral or stable ABL
• Fail in convective situations
• Reynolds stress models are more suitable,
• Boundary Conditions are complicated and important
  task