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Radiative transfers in complex geometry for CFD
modelling the urban canopy
Maya Milliez
Introduction
Importance of energy budget in urban canopies:Increase of day-time radiative absorption.Influence of flow within urban canopies on
turbulent convectionNight-time infra-red radiation trapping.
Interaction between radiative processes and flow and dispersion.
Objectives
Take into account radiation budget in simulations of flow in urban areas.
Introduction of a radiative scheme adapted to 3 dimensional CFD modelling and complex geometry.
Validation with classical cases. Detailed study of the interaction between radiative
fluxes and the flow dynamics.
The radiative scheme Adapted a radiative heat transfer scheme available in Code_Saturne. Solves the radiative transfer equation for a grey semi-transparent media.
I (x, S) intensity of radiation, for the propagation direction S
. (I(x, S) S) = -KI(x, S) + KIb(x, S)
Srad (x, S) = - . ( I(x, S) S d) 0x
y
zx
S
I(x,S)
Spatial discretization: same as dynamics. Angular discretization: Discrete Ordinate Method (DOM)
(Ndir = 32 or 128).
K : absorption coefficient, Ib : black body intensity
Short Wave Radiation
SD = direct
Se = diffused by environment (multi reflections)
SDSd
Se
SD Sd
Sd = diffused by atmosphere
Upper boundary conditions: Coupled with classical atmospheric scheme Simple model
(“Bird clear sky model”, Bird and Hulstrom (1981)). Observations
(SD + Sd +Se)
(SD + Sd +Se)
Long Wave Radiation
La = LW from atmosphere Le = LW from environment
(multi reflections)
La
Le
La
Upper boundary conditions: Coupled with classical atmospheric scheme
Simple model : La = c(T,e)
Observations
(La + Le)
(1- ) (La + Le)
(La + Le)
L*= (La + Le) -
L = +(1- ) (La + Le)
Surface temperature The surface temperature is modelled with a force-restore
method (Deardroff, 1978):
dT/dt = (2) / F* – (T – Tg/b)
= earth angular frequency
= thermal admittance
Tg/b = deep ground /building temperature
F* = total net flux
= S* + L* - QH – QE - QF
Validation : Short Wave Aida (1982)
S
N
W E
Ndir = 128 or 32
Flat : -3.3 %
Cubes : - 5 %
Validation : Long Wave Nunez and Oke (1977)
L* T
Validation : Mock Urban Setting Test
Temperature of the faces of a container in the middle of the array
(September 25th 2001)
Conclusions: Developed a new atmospheric radiative scheme in Mercure_Saturne
Advantages: Adapted to CFD modelling Adapted to complex geometry (memory) Non transparent media
But … Less accurate (DOM) Computation time Will be improved
Applications : 3D radiative transfers between the buildings. Fog, clouds...
Thank you