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Interzone short wave radiative couplings through windows and large openings : proposal of a

simplified model

H. Boyer T. Berthomieu, F. Garde, A. Bastide, T. Mara, F. Miranville

Université de La Réunion

harry.boyer@univ-reunion.fr

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Plan

• Introduction• Initial short wave model and basic

problem • Matricial approach of the couplings • Simulations versus experiments • Conclusion

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Introduction

• Single zone short wave repartition modeling

• What about multizone cases ?

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The basic problem Given indoor diffuse d0 value (W), how to compute short wave radiation leaving the zone ?

•With hypothesis of no direct couplings

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Basic problem solution

=

=

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Transmitted diffuse radiation

With hypothesis of no direct couplings

Direct incident in the zone Diffuse window transmittance

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Extension to multizone case

• Use of interzone short wave matrix of couplings …

• …very similar to matrical airflow matrix

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An example on indoor coupling matrix

1 3

4

2

0

8

21

Zone 0 1 2 3 4 Zone

0

1

2

3

4

Windows

Bay window

Sliding door

• 8 % on incident solar inputs of zone 4 will

be transfered to zone 2

• 21 % of solar inputs of zone 2 zone 4

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Some properties of this matrix

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4

2

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0 1 2 3 4 Zone

0

1

2

3

4

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+ + + + = 37 %15 + 0 +0 +0 +21

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Final calculation of net diffuse values

• For zone i, di0 is the incident diffuse radiation and di the net

diffuse radiation resulting of the couplings. di ?

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• If aij = 0, the matrix is Id and

• Sum of the 3 equations traduces short wave conservation

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CODYRUN

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CODYRUN’s block solving strategy

•4 basic blocs

•All heat transfer modes taking into account

•Fully coupled approach

•Numerous software ouputs available

for thermal analysis (heat fluxes, …)

Airflow model

Thermal model

Humidity model

CO2 model

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Outputs of CODYRUN software

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Elements of validation

West façade

East façade

N

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Incoming solar radiation

0

50

100

150

200

250

300

1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229

half hours

W/m

²

Measure -> In

Incoming solar radiation

0

50

100

150

200

250

300

1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193 205 217 229

half hours

W/m

²

Measure -> In

CODYRUN

• Incident radiation correctly modeled (=4%)

• Errors linked to uncertaincies on measurments

• Peak in measure linked to single sensor use

Analysis of solar radiation input

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Outgoing solar radiation

0

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10

15

20

25

1 12 23 34 45 56 67 78 89 100

111

122

133

144

155

166

177

188

199

210

221

232

half hours

W/m

²

Measure -> Out

Outgoing solar radiation

0

5

10

15

20

25

1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166 177 188 199 210 221 232

half hours

W/m

²

CODYRUN

Measure -> Out

• Outgoing radiation weak values

• Errors mainly linked to the model

Analysis of radiation output in a zone

N

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• Existence of direct coupling between Living room

and Room 2

Short wave exchanges ROOM2 -> LIVING ROOM

0

50

100

150

200

250

300

1 6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

101

106

111

116

121

126

131

136

141

half hours

W

meas.

Short wave exchanges ROOM2 -> LIVING ROOM

0

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100

150

200

250

300

1 6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

10

1

10

6

11

1

11

6

12

1

12

6

13

1

13

6

14

1

half hours

W

meas.

Phi SW 4->2 (W)

Analysis of couplings between 2 zones

N

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Conclusion

• The proposed method using a diffuse coupling matrix method

- obtains good results for in/out exchanges

- is acceptable only in case of non direct couplings

• Model improvements can be made easily, but need complete

geometrical description of the building.

• Multi sensor experiments will be used to

validate such an approach