Radiative transfers in complex geometry for CFD modelling the urban canopy Maya Milliez.

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