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