highly insulated slabs and short time-step simulations ... net-zero energy buildings and for better power ... modeling phase change materials (PCM) embedded.
Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
𝑞̇
𝑞̇
𝑞̇
,
=
𝑏
𝑇
,
−
𝑐
𝑇
𝑑
𝑞̇
,
−
,
𝑞̇
,
=
𝑎
𝑇
−
,
𝑏
𝑇
𝑑
𝑞̇
,
−
∑
∑
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𝑎 𝑑
=
∑
∑
𝑏 𝑑
=
,
∑
𝑐
∑
𝑑
=𝑈
Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
∆𝑥 =
𝛼 𝛥𝑡𝑏 (𝑤ℎ𝑒𝑟𝑒 𝐹𝑜 = 200) 𝐹𝑜
𝑞̇
𝑞̇
𝑇 𝑑 … 𝑇 𝑇 𝑇 = [𝐴] … + [𝐵] 𝑇 𝑑𝑡 𝑇 𝑞̇ 𝑞̇
𝐶 𝐹𝑜 =
𝛼=
𝛼 𝛥𝑡𝑏 𝐿
𝑇 𝑇 = [𝐶] … + [𝐷] 𝑇 𝑇
𝑑𝑇 = 𝑈 (𝑇 𝑑𝑡
− 𝑇 ) + 𝑈 (𝑇
𝑞̇ = 𝑈(𝑇 − 𝑇 )
𝑘 𝜌 𝐶
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−𝑇)
Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
𝐴(𝑛𝑥, 𝑛𝑥) 𝐵(𝑛𝑥, 𝑛𝑢) 𝑧𝑒𝑟𝑜𝑠(𝑛𝑥, 𝑛𝑢) ⎡ ⎤ 𝐼(𝑛𝑢) ⎥ 𝑀 = ⎢𝑧𝑒𝑟𝑜𝑠(𝑛𝑢, 𝑛𝑥) 𝑧𝑒𝑟𝑜𝑠(𝑛𝑢, 𝑛𝑢) 𝛥𝑡𝑏 ⎢ ⎥ ⎣𝑧𝑒𝑟𝑜𝑠(𝑛𝑢, 𝑛𝑥) 𝑧𝑒𝑟𝑜𝑠(𝑛𝑢, 𝑛𝑢) 𝑧𝑒𝑟𝑜𝑠(𝑛𝑢, 𝑛𝑢)⎦
𝛷=𝑒
𝛥𝑡𝑏
𝐹1 = 𝛷(1: 𝑛𝑥, 𝑛𝑥 + 1: 𝑛𝑥 + 𝑛𝑢) 𝐹2 = 𝛷(1: 𝑛𝑥, 𝑛𝑥 + 𝑛𝑢 + 1: 𝑛𝑥 + 2 𝑛𝑢) 𝐴 = 𝛷(1: 𝑛𝑥, 1: 𝑛𝑥) 𝐶 = 𝜌 × 𝐶 × 𝐿 = 2200 × 840 × 0.3 𝐽 = 554400 𝑚²𝐾
𝐵 = 𝐹1 + 𝐴 ∗ 𝐹2 − 𝐹2 𝐶 =𝐶
554400 𝐽 = 138600 4 𝑚 𝐾 554400 𝐽 𝐶2 = = 277200 2 𝑚 𝐾 1 𝑊 𝑈1 = = ℎ = 8.3 𝑅1 𝑚 𝐾 1 𝑘 1.7 𝑊 𝑈2 = 𝑈3 = = = = 11.33 𝑅2 𝐿 0.15 𝑚 𝐾 2 1 𝑊 𝑈4 = = ℎ = 34.5 𝑅4 𝑚 𝐾
𝐷 = 𝐷 + 𝐶 ∗ 𝐹2
𝐶1 = 𝐶3 =
𝑑𝑇 𝑈1 𝑈2 = × (𝑇 − 𝑇 ) + × (𝑇 − 𝑇 ) 𝑑𝑡 𝐶1 𝐶1 8.3 = × (𝑇 − 𝑇 ) 138600 11.33 + × (𝑇 − 𝑇 ) 138600
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Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
𝑑𝑇 𝑈2 𝑈3 = × (𝑇 − 𝑇 ) + × (𝑇 − 𝑇 ) 𝑑𝑡 𝐶2 𝐶2 11.33 = × (𝑇 − 𝑇 ) 277200 11.33 + × (𝑇 − 𝑇 ) 277200
𝐷 =
7.537 −0.009171
−0.009171 23.68
𝑑𝑇 𝑈3 𝑈4 = × (𝑇 − 𝑇 ) + × (𝑇 − 𝑇 ) 𝑑𝑡 𝐶3 𝐶3 11.33 = × (𝑇 − 𝑇 ) 138600 34.5 + × (𝑇 − 𝑇 ) 138600
𝑑 𝑇 𝑇 𝑑𝑡 𝑇 11.33 138600 22.66 − 277200 11.33 138600
19.63 ⎡− 138600 ⎢ 11.33 =⎢ 277200 ⎢ ⎢ 0 ⎣ 8.3 ⎡ 0 ⎤ ⎢138600 ⎥ 𝑇 +⎢ 0 0 ⎥ 𝑇 34.5 ⎥ ⎢ 0 ⎣ 138600⎦
⎤ ⎥ 𝑇 11.33 ⎥ 𝑇 277200 ⎥ 𝑇 45.83 ⎥ − 138600⎦ 0
𝑞̇ = ℎ (𝑇 − 𝑇 ) = 8.3 (𝑇 − 𝑇 ) 𝑞̇
= ℎ (𝑇 − 𝑇 ) = 34.5 (𝑇 − 𝑇 )
q̇ q̇
=
−8.3 0 +
0 0
8.3 0
If TIMEB < 0 then useSsCtfMethod = .TRUE. TIMEB = -TIMEB Else useSsCtfMethod = .FALSE.
T 0 T −34.5 T T 0 34.5 T
Subroutine WALLS If useSsCtfMethod = .TRUE. Subroutine NodesDetermination + Subroutine CtfCoeffGen
0.6147 0.1999 0.01142 𝐴 = 0.09994 0.7725 0.07353 0.01142 0.1471 0.3133 0.1355 0.01029 𝐵 = 0.02049 0.06137 0.002475 0.3142 −8.3 0 0 𝐶 = 0 0 −34.5
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If useSsCtfMethod = .FALSE.
Subroutine TRANS
Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
23
22
Original - 1 h Modified - 12 min Reference
Temperature [°C]
21
20
19
18
17
16 4000
19 18.8
4005
4010
4015 Time [h]
4020
4025
4030
4019.5 Time [h]
4020
4020.5
4021
Original - 1 h Modified - 12 min Reference
18.6
Temperature [°C]
18.4 18.2 18 17.8 17.6 17.4 17.2 17 4018
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4018.5
4019
Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
21
Original - 3 h Modified - 1 h Reference
20.5
Temperature [°C]
20
19.5
19
18.5
18
17.5 4000
4005
4010
4015 Time [h]
4020
4025
4030
18.1
18
Temperature [°C]
17.9
17.8
17.7
17.6
17.5 4015.5
ICF DST SIPS Concrete Insulation Wood
Original - 3 h Modified - 1 h Reference 4016
4016.5 4017 Time [h]
4017.5
4018
Original timebase New timebase Number of nodes Calculation time (DRF method) (SS method) (SS method) (SS method) [h] [h] [-] [s] 1 0.2 255 2 0.25 0.1 323 3.4 0.15 0.05 350 3.7 0.25 0.2 268 2.2 0.5 0.1 333 3.4 3 1 347 3.5
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Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
22 21.5
𝑞̇
DRF method (Timebase = 5h) SS method (Timebase = 1.5h)
21
Temperature [°C]
20.5 20 19.5
𝛥𝑡
19 18.5 18 17.5 17 4000
4005
4010
4015 Time [h]
4020
4025
4030
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Proceedings of BS2013: 13th Conference of International Building Performance Simulation Association, Chambéry, France, August 26-28
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