Optimized mitigation of heat loss by avoiding wall-to-floor thermal bridges in reinforced concrete buildings

Journal Pre-proof Optimized mitigation of heat loss by avoiding wall-to-floor thermal bridges in reinforced concrete buildings Jiang Lu, Yucong Xue, Zhi Wang, Yifan Fan PII:

S2352-7102(19)32234-X

DOI:

https://doi.org/10.1016/j.jobe.2020.101214

Reference:

JOBE 101214

To appear in:

Journal of Building Engineering

Received Date: 19 October 2019 Revised Date:

22 January 2020

Accepted Date: 23 January 2020

Please cite this article as: J. Lu, Y. Xue, Z. Wang, Y. Fan, Optimized mitigation of heat loss by avoiding wall-to-floor thermal bridges in reinforced concrete buildings, Journal of Building Engineering (2020), doi: https://doi.org/10.1016/j.jobe.2020.101214. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Author statement

Jiang Lu: Conceptualization, Methodology, Writing- Reviewing and Editing, Writing- Original draft. Yucong Xue: Investigation, Writing- Original draft. Zhi Wang: Investigation. Yifan Fan: Investigation, Writing- Original draft.

1

Optimized mitigation of heat loss by avoiding wall-to-floor thermal bridges in reinforced

2

concrete buildings

3

Jiang Lu a*, Yucong Xue b, Zhi Wang b, Yifan Fan b

4 5

a

School of Civil Engineering and Architecture, Zhejiang University of Science and Technology, China

6 7

b

8

*

College of Civil Engineering and Architecture, Zhejiang University, China

Corresponding Author, Email: [email protected]

9

10

Abstract

11

With the improvement of thermal insulation performance of building exterior walls, the

12

proportion of heat loss caused by thermal bridges is increasing rapidly, especially for those

13

buildings with a self-insulation wall. Currently, the Chinese government is boosting the use of

14

self-insulation walls due to its advantages in long service life and convenient construction.

15

However, energy loss through thermal bridges is a crucial problem. Wall-to-floor (beam

16

included) thermal bridge (WFTB) is a primary form of the thermal bridge with the most

17

massive heat flux. In this study, the thermal performance of WFTB was investigated with real

18

scale (1:1) experiments and numerical models. On the basis of the distance between the beam

19

and exterior wall surface (D), three types of WFTB structures are defined, i.e., exposed beam

20

structure (EB, D=0), entirely wrapped beam structure (EW, D=Dwall, the wall thickness) and

21

partially wrapped beam structure (PW, D=0-Dwall). The energy-saving potential of different

22

WFTBs is ranked as PW (when D = 0.67Dwall) >EW>EB. The temperature spatial variation,

23

which is related to the thermal stress of WFTB, is reduced by both the increases of D in PW and

24

the thickness of the insulation layer at the overhanging structure (δ). Moreover, if expanded

25

polystyrene board (EPS), one commonly used insulation material, is used as the insulation layer

26

material, the δ is suggested to be 0.06-0.07Dwall, considering the effectiveness of the thermal

27

insulation, structure safety, and the insulation material saving.

28

Keywords: energy saving, optimization, thermal performance, wall-to-floor thermal bridge,

29

experiments, numerical simulations

30

Nomenclature A area (mm2) AAC autoclaved aerated concrete D distance between the beam and exterior wall surface (mm) Dwall thickness of the wall (mm) E error (dimensionless) EB exposed beam structure EIFS external insulation and finish system EPS expanded polystyrene board EW entirely wrapped beam structure F view factor (dimensionless) h convective heat transfer coefficient (W·m–2·K–1) I ratio of insulation (dimensionless) K heat transfer coefficient (W·m–2·K –1) N number (dimensionless) PW partially wrapped beam structure Q heat flow rate(W) q heat flux (W/m2) RD ratio of the D to the Dwall (dimensionless) Rδ ratio of the δ to the Dwall (dimensionless) T temperature (°C) WFTB wall-to-floor thermal bridge Greek symbols α surrounding heat flux ratio (dimensionless) ∆T temperature difference between indoor and outdoor air δ thickness of insulation layer (mm) ε emissivity (dimensionless) θ angle of the wall from the horizon (dimensionless) σb Stefan-Boltzmann constant (W/m2·K4)

Subscripts 0 physical air air basic basic conv convective heat transfer D certain wall thickness d lower part E equivalent ex exterior/external/outdoor exp on-site experimental result grid grid grou ground HI1-3 indoor heat flux sensor 1-3 in interior/internal/indoor inf influencing area m middle part max maximum min minimum plus additional influenced area rad radiative heat transfer sim simulation result sky sky sol solar irradiance sum summary sur surface T thermal bridge (i.e., beam and floor structure) TI1-9 indoor temperature sensor point 1-9 TO1-9 outdoor temperature sensor point 1-9 total total u upper part un unaffected part var spatial variation δ certain insulation layer depth 31

32

1. Introduction

33

With the largest building area in the world, China is facing a severe problem of rising

34

building energy consumption. In the building section, 906 million tce (ton of standard coal

35

equivalent) was consumed in 2016, accounting for 20% of total energy usage in the whole

36

nation[1]. On average, 51% of a household’s annual energy consumption is for space heating and

37

cooling[2]. One of the most critical factors that impact the heating load is the heat transfer of the

38

building envelope, which accounts for about 70% of total heat loss[3]. Simulations[4][5][6][7] and

39

experiments[8] proved that the performance of the building envelope is crucial for

40

energy-saving. Therefore, the Chinese design code[9][10] for building envelope performance

41

becomes more and more stringent in recent years to decrease heat loss. Response to the code,

42

external insulation and finish system (EIFS) are adopted widely on the wall made by

43

conventional material, such as brick. Under this condition, a layer of insulation material (e.g.,

44

expanded polystyrene, extruded polystyrene) needs to be installed on the exterior surfaces of

45

the wall, which insulates thermal bridges simultaneously. However, insulation materials require

46

replacement in a decade or two decades because of their limited lifetime, which causes

47

inconvenience for residents, additional cost, and carbon emission. Moreover, the fall off and

48

fire incidents due to external insulation materials increase recently. Therefore, the Chinese

49

government starts to promote using self-insulation wall, which is built by materials with low

50

thermal conductivity, such as ceramisite concrete (0.53 W·m–1·K–1), autoclaved aerated

51

concrete (0.27 W·m–1·K–1) and pumice concrete (0.19 W·m–1·K–1)[11][12]. The wall built by

52

using the aforementioned materials can satisfy the Chinese design standard[13][14] without an

53

additional insulation layer. In the self-insulation wall, the thermal bridges are often uninsulated,

54

and thus become the weak parts on thermal insulation[15][16]. Improving the thermal

55

performance of thermal bridges attracts more and more attention. Therefore, it is urgent to

56

understand better on the heat transfer in thermal bridges and propose a suitable method to

57

reduce the heat loss.

58

Numerical models are usually adopted to analyze the thermal performance of the thermal

59

bridge[17][18][19][20][21][22]. Xie et al.[23] developed an equivalent slabs approach to obtain

60

temperature distribution of thermal bridges accurately and quickly. Ge et al.[24] simulated the

61

energy performance of a whole building and suggested that the existence of thermal bridges

62

increases the annual space heating energy demand by 38%-42%. As the wall-to-floor (beam

63

included) thermal bridge (WFTB) has the most massive heat flux among all types of thermal

64

bridges[8], some methods were proposed to insulate it. Installing a layer of insulation material at

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the exterior surface of WFTB is a conventional method to improve its thermal performance.

66

However, a bimodal profile of exterior surface temperature presents[25][26], resulting in a larger

67

influencing area and the thermal stress at the junctions between the WFTBs and the main part of

68

the exterior wall. Material with low thermal conductivity, such as cross-laminated timber[27] and

69

autoclaved aerated concrete (AAC)[28], could be adopted to block the heat flow in WFTBs.

70

However, the above method increases the risk of jeopardizing the load-bearing structure (i.e.,

71

beam and column). The limited life of materials for blocking the heat flux, such as

72

cross-laminated timber, further increases the risk of structural damage. Prata et al.[29] and

73

Cappelletti et al.[30] showed that the thermal performance of wall-to-window thermal bridges

74

changes significantly with the modifications of their connecting structures. Similarly, we aim at

75

investigating the effect of different WFTB structures on thermal insulation improvement in this

76

study with the performance of load-bearing structure being preserved.

77

Quantitative indexes are essential for evaluating the performance of WFTB. The most

78

frequently used index is the thermal coupling coefficient of the thermal bridge, which was

79

formulated by international standards (ISO 10077-2: 2007[31] and ISO 10211: 2007[32]). It has

80

been adopted by many national and regional standards (the British standard: BS EU ISO

81

10077-2: 2017[33], European standard: EN ISO 10211: 2017[34], and national standard of the

82

People’s Republic of China: JGJ 26-2008[14]) and scientific research[35][36]. However, it does not

83

consider the temperature distribution in the thermal bridge, which is an essential indicator for

84

safety and durability. As mentioned above, the phenomenon of the bimodal profile of exterior

85

surface temperature increases the influencing area caused by WFTB and increases the risk of

86

cracks. As the influencing area and the variation of temperature cannot be described by the

87

existing index, it is necessary to propose new indexes to quantify and reduce these adverse

88

effects correspondingly.

89

In Section 2.1, three typical WFTB structures are identified by reviewing the existing atlas.

90

New indexes for evaluating thermal bridges are defined in Section 2.2. The grid independence

91

tests are carried out and presented in Section 2.5. The on-site experiment in Section 3 then

92

validates the numerical model. The results are analyzed and discussed in Section 4 and 5,

93

respectively. Conclusions are drawn in Section 6.

94

2. Methodology

95

2.1. Identified WFTB structures

96

The frame structure has been utilized in many kinds of buildings, in which beam and

97

column are the load-bearing structure, while walls only serve to divide space. The column is

98

usually arranged at the connection of two walls in the frame structure, and the beam is arranged

99

at the connection of the wall and floor[37]. Normally, beam, column, and floor are made of

100

reinforced concrete with thermal conductivity ranging from 1.28 W/(m·K) to 1.74 W/(m·K)[12].

101

The exterior wall is made of materials with high thermal insulation performance, i.e.,

102

self-insulation materials with thermal conductivity ranging from 0.10 W/(m·K) to 0.60

103

W/(m·K)[12]. The connection between walls and structures have great potential to become the

104

thermal bridges of the building. As Fig. 1 shows, these thermal bridges can be classified into

105

wall-to-beam thermal bridge (point A), WFTB (point B), and wall-to-column thermal bridge

106

(point C)[27] depending on the position.

107 108

Fig. 1

Different types of thermal bridges.

109

According to the existing atlases[38][39][40], WFTB can be classified into three categories,

110

i.e., exposed beam structure (EB), partially wrapped beam structure (PW), and entirely

111

wrapped beam structure (EW), as shown in Fig. 2.

112 113

(a)

114 (b)

115

116

(c)

117 118

Fig. 2

Illustration of different types of WFTB (cross-section as marked at B in Fig. 1). (a)

119

exposed beam structure (EB), (b) partially wrapped beam structure (PW), and (c) entirely

120

wrapped beam structure (EW).

121

The main difference among different types of WFTB is the distance between the beam and

122

exterior wall surface (denoted as D), as marked in Fig. 2. The values of D in Fig. 2(a) and (c) are

123

0 mm and the thickness of the wall (Dwall) respectively. The beam is partially wrapped by the

124

exterior wall in the second type of structure (Fig. 2(b)) and thus the D has a value between 0 mm

125

and the Dwall. There is a special form of PW, i.e., half-wrapped beam structure (HW, D=0.5

126

Dwall), which is the most common type in actual engineering projects. It can be found in Fig. 2(b)

127

and (c) that when D is larger than 0 mm, the overhanging structure will be constructed to bear

128

the weight of the wall above. The overhanging structure is usually cast by reinforced concrete,

129

which is the same as floors and beams.

130

2.2. Indexes for the evaluation of thermal bridges

131

In order to evaluate the thermal performance of WFTB comprehensively and accurately,

132

the following four indexes are defined.

133

2.2.1. Influencing area of thermal bridges

134

The variations of wall exterior surface temperature caused by the thermal bridge are

135

evident when the difference between the indoor and outdoor air temperature is significant. To

136

reflect the area influenced by the thermal bridge, influencing area of thermal bridges (Ainf) and

137

the unaffected part of the exterior wall (Aun) is defined, which is illustrated in Fig. 3. Ainf

138

includes two parts, i.e., the physical area of the beam and floor structure (AT,0) and the

139

additional influenced area (AT,plus) due to conduction. Aun is defined as the area where the

140

temperature varies within 0.5 °C/m in every direction. Accordingly, the heat flux can be divided

141

into two parts. One is the basic heat flux of the exterior wall ( qbasic ), assuming the thermal

142

bridge does not exist. qbasic covers the whole exterior wall, including both Ainf and Aun. The

143

other one is the additional heat flux ( qT ) caused by the existence of the thermal bridge, which

144

only covers Ainf.

145 146

Fig. 3

147

2.2.2. Equivalent heat transfer coefficient of the thermal bridges

148 149 150

Different parts of WFTB and its surrounding area.

To evaluate the heat loss through the thermal bridge, the equivalent heat transfer coefficient of thermal bridges (KE) is defined. Eqs. (1-4) are used to calculate KE. The total heat flow rate through the exterior wall surfaces (Qtotal) can be written as Eq. (1).

151

Qtotal =QT +Qbasic = qT ⋅ ( AT,0 + AT,plus ) + qbasic ⋅ ( AT,0 + AT,plus + Aun )

152

where QT is the additional conductive heat flow rate caused by the thermal bridge. Qbasic is the

153

basic conductive heat flow rate of the exterior if there is no thermal bridge. Qtotal can furtherly

154

be written as Eq. (2) with the heat transfer coefficient being integrated into Eq. (1). Eq. (3) can

155

then be obtained by combining specific terms.

156

Qtotal =QT +Qbasic =∆T ⋅ K inf ⋅ ( AT,0 + AT,plus ) + ∆T ⋅ K basic ⋅ ( AT,0 + AT,plus + Aun )

157

Qtotal =∆T ⋅ ( K inf ⋅ AT,0 + K inf ⋅ AT,plus + K basic ⋅ AT,0 ) + ∆T ⋅ ( K basic ⋅ AT,plus + K basic ⋅ Aun )

158

where ∆T is the temperature difference between indoor and outdoor air. Kbasic is the basic heat

159

transfer coefficient of the exterior wall. Kinf is the increased heat transfer coefficient caused by

160

thermal bridges. As KE is defined to reflect the heat transfer ability caused by WFTB, the heat

161

flux used to calculate KE should include both QT and basic heat flux of the exterior wall within

162

the AT,0 (denoted as QT,basic). Therefore, we can equal the first term on the right-hand side of Eq.

163

(3) to K E AT,0 ∆T . KE can thus be obtained in the form of Eq. (4).

164

165 166 167

KE =

QT +QT,basic ∆T ⋅ AT,0

=

K inf ⋅ ( AT,0 + AT,plus ) + K basic ⋅ AT,0 AT,0

=

qT +K basic AT,0

2.2.3. Surrounding heat flux ratio The surrounding heat flux ratio (α) is defined as the ratio of the heat flux in the AT,plus to that in the Ainf, which is given in Eq. (5).



QT − QT ,0   ×100%  QT +K basic ⋅ AT,0 

α = 

168

169

where QT,0 is the heat flow rate through region AT,0.

170

A higher value of α indicates that more heat losses in the AT,plus. Otherwise, the heat losses

171

mainly at region AT,0. Therefore, α can be used to determine whether the surrounding area

172

should be further insulated or not.

173

2.2.4. Spatial variation of the temperature on the thermal bridges

174

The spatial variation of the temperature (Tvar) in region Ainf is quantified by Eq. (6), which

175

is given as the difference between the highest (Tmax) and lowest (Tmin) exterior wall surface

176

temperature in region Ainf.

Tvar =Tmax − Tmin

177 178

A larger value of Tvar indicates the temperature of the exterior wall surface varies a lot with

179

the location. Tvar should be small to achieve smaller thermal stress on the wall and thus to

180

reduce the possibility of wall crack[41].

181

2.3. On-site experiment setup

182

A real-scale test building was built on the campus of Zhejiang University, Hangzhou,

183

China (120.09 °E, 30.31 °N) to evaluate the thermal performance of WFTB with the defined

184

indexes. The climate of the location presents characteristics of hot summer and cold winter. As

185

shown in Fig. 4(b), the test building is a frame structure, which consists of 2 floors and 12

186

rooms (6 rooms on each floor) that can be used to carry out experiments. In this study, only 2

187

rooms are used as test rooms, which is marked in Fig. 4(a) (one room on each floor). The other

188

rooms are prepared for other experiments, which will not be discussed here.

189 190

(a)

191 192

(b)

193 (c)

194 195

Fig. 4

196

building.

Test building: (a) plan view, (b) frame structure, and (c) final appearance of the

197

The floor of the second level, which is also the ceiling of the first level, and the beam of the

198

first level make up the WFTBs of the test building. In this study, the structure type of WFTB in

199

test rooms is EB. The detailed parameters of materials and sizes are shown in Table 1. As the

200

elements of partitions, columns, roofs, doors, and windows are not related to the WFTB study,

201

they are not listed in Table 1.

202

Table 1

Parameters of building envelope in the test rooms.

Element Wall

Beam Floor Other

Material (outside-inside or down-top) Cement mortar Autoclaved aerated concrete (AAC) Cement mortar Expanded polystyrene board (EPS) Reinforced concrete Cement mortar Cement mortar Reinforced concrete Masonry mortar

Thickness (mm) 20 240 20 20 240 20 20 100 5

Thermal conductivity (W/m·K) 0.93 0.27 0.93 0.04 1.74 0.93 0.93 1.74 0.93

203

Self-recording thermometers [platinum resistance, Tianjianhuayi Inc., Beijing, China]

204

with a measurement range of -20-80 °C and measurement accuracy of ±0.3 °C were both

205

arranged at the test room and roof to measure the real-time outdoor and indoor air temperature,

206

as shown in Fig. 5. A radiation shield was adopted at the outdoor measuring point to reduce the

207

effect of sky radiation, as shown in Fig. 5(a). The outdoor temperature measuring point was

208

1500 mm right above the roof. The indoor temperature measuring point was in the center of the

209

test room with a height of 1500 mm. Expanded polystyrene board (EPS) is one of the most

210

common types of insulation material and thus is adopted in this study for heat transfer analysis.

211 212

(a)

213 214

(b)

215

Fig. 5

Air temperature measuring point: (a) outdoor, and (b) indoor.

216

Thermocouples [copper-constantan, Tianjianhuayi Inc., Beijing, China] and heat flux

217

sensors [JTC08A, J.T. Technology Inc., Beijing, China] were adopted to measure surface

218

temperatures and heat fluxes. The sensors mentioned above were connected to a dynamic data

219

acquisition system [JTDL-80, J.T. Technology Inc., Beijing, China] for continuous recording of

220

the required data. The detailed parameters of the measuring system are shown in Table 2. The

221

analog-digital converter [AD7712, Analog Devices, Inc., Massachusetts, the U.S.A.] with 24

222

bits was adopted in the system.

223

Table 2 Parameters of the measuring system for temperature and heat flux. Measurement range of temperature -20-100 °C

Measurement accuracy of temperature ±0.5 °C

Resolution of temperature 0.1 °C

Measurement range of heat flux 0-2000 W/m2

Measurement accuracy of heat flux ±5%

Resolution of heat flux 0.1 W/m2

Sampling frequency 15 min

224

The position of temperature and heat flux sensors are marked in Fig. 6. In the figure, ‘T’

225

represents thermocouples ‘H’ represents the heat flux sensor. ‘I’ and ‘O’ represents indoor and

226

outdoor, respectively. Accordingly, ‘TI1-9’ are indoor thermocouples 1-9. ‘TO1-9’ are outdoor

227

thermocouples 1-9. ‘HI1-3’ are indoor heat flux sensors 1-3. Measurement results of TI1-9,

228

TO1-9, and HI1-3 are denoted as TTI1-9, TTO1-9, and qHI1-9 respectively.

229

230 231 232

Fig. 6

Temperature and heat flux measuring points.

The heat transfers between the exterior surface and the surrounding environment are displayed in Fig. 7.

233 234

Fig. 7

Heat exchange at the exterior surface of a wall.

235

As commonly known, the heat passing through the wall is lost by two mechanisms at the

236

exterior wall surface, i.e., convection (qconv) and long-wave radiation (qrad). As the exterior wall

237

surface also receives the solar irradiation (qsol), the heat balance can be written as Eq. (7)[42]. It

238

should be mentioned that qsol can be neglected at night.

239

qtotal =qconv +qrad − qsol

240

As qrad is generally considered as three separate parts (i.e., the radiation exchange between

241

the exterior building surface and the exterior surrounding air, the sky, and the ground, denoted

242

as qair, qsky and qgrou, respectively), qrad thus can be expressed as Eq. (8).

243 244

q rad = qair + qsky + qgrou

The radiation exchange components can be calculated according to Eqs. (9-11)[42].

245

4 4 qair =Fair ⋅ σ b ⋅ ε ⋅ (Tsur,ex +273.15 ) − (Tair,ex +273.15 )   

246

4 4 qsky =Fsky ⋅ σ b ⋅ ε ⋅ (Tsur,ex +273.15 ) − (Tsky +273.15 )   

247

4 4 qgrou =Fgrou ⋅ σ b ⋅ ε ⋅ (Tsur,ex +273.15 ) − (Tgrou +273.15 )   

248

where Fair, Fsky, and Fgrou are view factors for air, sky, and ground, respectively, which can be

249

calculated as Eqs. (12-14)[42]. σb is the Stefan-Boltzmann constant with the value of 5.669×10-8

250

W/m2·K4[43], ε the emissivity of the exterior surface of the temperature sensor. Tsur,ex, Tair,ex, Tsky,

251

and Tgrou are the temperature of wall exterior surface, outdoor air, sky, and ground, respectively.

252

θ  Fair =0.5 (1 + cos θ ) ⋅ 1 − cos  2 

253

254 255 256

Fsky =0.5 (1 + cos θ ) ⋅ cos

θ 2

Fgrou =0.5 (1 − cos θ )

where θ is the angle of the wall from the horizon. qconv can be calculated according to Eq. (15)[43].

257

qconv =hex ⋅ (Tsur,ex − Tair,ex )

258

where hex is the convective heat transfer coefficient on the exterior surface of the wall. In this

259

case, a tinned thermocouple with a ε of 0.04[43] is chosen as the temperature sensor. According

260

to the experience and recorded data by city meteorological station, Tsur,ex, Tair,ex, and Tgrou can be

261

assumed as 5 °C, 0°C, and 0 °C, respectively. Tsky is 6 °C lower than the Tair[42], i.e., Tsky equals

262

to –6 °C. The θ is 90° as the wall is vertical to the horizon. The hex is set as 23.0 W/(m2·K)

263

according to reference [44]. Therefore, it can be calculated that qrad is 2 W/m2, and qconv is 115

264

W/m2. The result shows that the radiative heat transfer is much less than the convective heat

265

transfer. Hence qrad can be neglected, and qconv can be considered as qtotal.

266

Therefore, the convective heat transfer coefficients, which will be adopted to obtain

267

boundary conditions for the numerical simulations, are calculated based on Eqs. (16-21) and

268

measured surface temperatures and heat fluxes.

269

hex,u =

qHI3  TTO9 + TTO8 +TTO7  3 

270

hex,m =

qHI2  TTO6 + TTO5 + TTO4    − Tair,ex 3  

271

hex,d =

qHI1  TTO3 + TTO2 + TTO1    − Tair,ex 3  

272

hin,u = Tair,in

273

hin,m = Tair,in

274

hin,d =

  − Tair,ex 

qHI3 T +T +T  −  TI9 TI8 TI7  3   qHI2 T +T +T  −  TI6 TI5 TI4  3  

qHI1 T +T +T  Tair,in −  TI3 TI2 TI1  3  

275

where Tair,in is the indoor air temperature, hex,u the convective heat transfer coefficient of the

276

upper part of the exterior surface, as shown in Fig. 6, which can be calculated based on qHI3,

277

THI7-9, and Tair,ex. Similarly, hex,m, and hex,d are heat transfer coefficients of the middle and lower

278

part of the exterior surface, while hin,u, hin,m, and hin,d are heat transfer coefficients of the upper,

279

middle and lower part of the interior surface.

280

As hex varies in a wide range when wind speed changes[45][46], a test period free from wind

281

should be chosen to ensure the hex steady. Therefore, calm midnight with an overcast sky (from

282

22:00 28/01/2015 to 3:00 29/01/2015) was selected as the test period. According to the Chinese

283

national standard[47], the difference between Tin and Tex should be higher than 15.0 °C for the

284

energy efficiency test of a building envelope. Therefore, split type air conditioners were utilized

285

to control the indoor air temperature to be around 26.0 °C during tests. Tin and Tex during the test

286

is given by Fig. 8. As shown in Fig. 8, the indoor and outdoor air temperatures were around

287

26.0 °C and 3.0 °C respectively and barely changed with time.

288 289

Fig. 8

290

2.4. Numerical models

Indoor and outdoor air temperature during the test period.

291

Xie et al.[23] proved that the heat transfer processes in WFTB could be approximated by a

292

two-dimensional (2D) model. Therefore, the 2D model was built in this study, considering both

293

accuracy and time efficiency. Commercial software, COMSOL Multiphysics [5.4.0.225,

294

COMSOL Inc., Stockholm, Sweden], was used to perform numerical simulations. The

295

geometry of the 2D WFTB structure is shown in Fig. 9. At the interior and exterior surfaces of

296

the wall, the third type boundary condition is adopted with indoor/outdoor air temperature and

297

heat transfer coefficients on interior/exterior wall surface being specified, as shown in Eq. (22).

298

q = h ⋅ (Tair − Tsur )

299

where q is the heat flux, h the convective heat transfer coefficient, Tair and Tsur the air and

300

surface temperature.

301

Following Real et al. and Ge et al.[48][49], the adiabatic boundary condition is adopted at

302

truncations of the wall and floor. Based on field measurement results (Fig. 8), outdoor and

303

indoor air temperatures are set to be 3.0 °C and 26.0 °C, respectively. convective heat transfer

304

coefficients for different parts of wall surfaces are calculated according to Eqs. (16-21), which

305

are given in Table 3. Moreover, the properties of building envelope materials and sizes are set

306

according to values in Table 1.

307

Table 3

Convective heat transfer coefficients adopted in numerical models. hex,u W/(m2·°C) 3.6

hex,m W/(m2·°C) 6.3

hex,d W/(m2·°C) 4.5

hin,u W/(m2·°C) 5.9

hin,m W/(m2·°C) 8.0

hin,d W/(m2·°C) 5.1

308 309 310

Fig. 9

Illustration of the simulated model.

According to the code of China[50], the masonry mortar with a thickness of 5 mm was

311

utilized to connect the AAC and reinforced concrete (Fig. 6 and Fig. 9).

312

2.5. Grid-independent tests

313

In this grid-independent test, there is a total of 7 tests with different grid numbers (Ngrid).

314

The detailed parameters set in those tests are listed in Table 4. Fig. 10 shows example figures of

315

grid independence tests (Test 1, Test 3, and Test 5). Because the surface temperature is a crucial

316

parameter for the calculation of the defined four indexes, the average temperature of the interior

317

surface and exterior surface are adopted as the indicator to determine whether the result is

318

dependent on the Ngrid or not.

319

Table 4

Detailed grid information of different tests.

Test

Max. grid size (mm)

Min. grid size (mm)

Max. growth rate

Grid number (Ngrid)

1 2 3 4 5 6 7

538.0000 32.2000 16.3000 10.0000 7.0000 5.0000 3.8000

81.5000 0.1220 0.0326 0.0326 0.0326 0.0326 0.0200

2.00 1.20 1.10 1.10 1.05 1.05 1.05

1974 3843 8641 16935 31284 59178 103245

320

321

322

(a)

(b)

323

324

(c)

325 326

Fig. 10 Figures of grid independence tests: (a) Test 1, (b) Test 3, and (c) Test 5.

327

As shown in Fig. 11, the interior and exterior surface temperature changes within 0.001 °C

328

when Ngrid is larger than 8641, i.e., Test 3. The grid format in Test 6 is adopted in the following

329

simulations with the overall consideration of the time efficiency, spatial resolution, and

330

accuracy.

331 332

(a)

333

(b)

334 335

Fig. 11 Average temperature with different grid number (Ngrid): (a) interior surface, and (b)

336

exterior surface.

337

3. Study cases and validation of numerical models

338

The existence of a thin masonry mortar layer, which was mentioned in Section 2.4 and

339

indicated in Fig. 9, may affect the heat transfer in WFTB. Therefore, another case without the

340

masonry mortar layer (simulation 2) was also simulated to rule out its influences. Fig. 12 shows

341

the consistent results of simulations and an on-site experiment. The phenomenon of the

342

“bimodal profile of exterior surface temperature”, which was also observed in references [25]

343

and [26], presents in our results (Fig. 12).

344 345 346 347

Fig. 12 Exterior surface temperature of WFTB. Table 5 presents the Tsur,ex obtained by the on-site experiment and simulations. The error, which is calculated according to Eq. (23), is listed in Table 5.

E=

348

Texp − Tsim Texp

×100%

349

where E is the error, Texp the exterior surface temperature obtained by on-site experiment, Tsim

350

the simulated exterior surface temperature.

351

According to Table 5, it is found that measured result of TO4 and TO7 (i.e., the height of

352

WFTB equals 400 mm and 1020 mm) had the largest E. The reason to explain the phenomenon

353

is that the temperature gradients are extremely large in those areas (i.e., the gaps between

354

reinforced concrete and AAC). A small error on the measuring location can lead to a big

355

difference in the temperature signal. The simulations results, in general, agreed well with the

356

on-site experiment, as Fig. 12 shows.

357

Table 5

Exterior surface temperature and error.

Height of WFTB Corresponding measuring point On-site experiment simulation with

mm

Temp. Temp.

°C °C

0

200

400

600

750

900

1020

1220

1420

TO1

TO2

TO3

TO4

TO5

TO6

TO7

TO8

TO9

6.9 6.8

6.9 6.9

8.6 7.4

6.4 11.3

6.7 6.5

6.9 6.5

6.9 12.0

8.2 8.3

7.5 7.8

masonry mortar simulation without masonry mortar

Error Temp. Error

% °C %

+1.4 6.8 +1.4

0.0 6.9 0.0

+14.0 7.4 +14.0

–76.6 11.0 –71.9

+3.0 6.5 +3.0

+5.8 6.5 +5.8

–73.9 11.7 –69.6

–1.2 8.2 0.0

–4.0 7.8 –4.0

358

Comparing the results of simulation 1 (model with masonry mortar) and simulation 2

359

(model without masonry mortar) in Fig. 12 and Table 5, it can be found that masonry mortar

360

rarely affects the thermal performance of WFTB. The masonry mortar layer is therefore

361

neglected in the following simulations considering the model complexities and time efficiency.

362

As shown in Fig. 12, the exterior surface temperature is influenced by WFTB from a

363

height of 75 mm to 1470 mm, which indicates that the Ainf is 1395 mm. Since the floor height in

364

the tested building is 3000 mm, WFTB influences about half of the area of the wall, which

365

causes serious problems both in energy-saving and thermal comfort. The Tsur,ex at the region AT,0

366

is lower than that at region Aun, presenting the apparent phenomenon of “bimodal profile of

367

exterior surface temperature” and relatively high Tvar of 5.70 °C[8]. KE is calculated to be 0.97

368

W/(m·K) based on Eqs. (1-4). According to Eq. (5), α is 27.51%, suggesting that about 1/3 of

369

heat losses from the region AT, plus.

370

4. Optimization for the WFTB

371

4.1. Distance between the beam and exterior surface of the wall (D)

372

Different Ds lead to the various structures of WFTB, which could impact thermal

373

performance. To understand the impacts, we simulated and analyzed thirteen thermal bridge

374

models with different Ds in this section. Error! Reference source not found. shows the

375

models, which contain EB (Case D1 with D=0 mm), PW (Case D2-12 with D=20-220 mm),

376

and EW (Case D13 with D=240 mm). When D equals 120 mm, the WFTB is HW (Case D7).

377

The wall material parameters of the building envelope are set according to Table 1.

378

According to the design code of China[44], the Tair,in and Tair,ex are set to be 18.0 °C and –3 °C

379

respectively. The convective heat transfer coefficients of the interior (hin) and hex are set as 8.7

380

W/(m2·K) and 23.0 W/(m2·K)[44]. It should be noted that a layer of EPS (20 mm), which is

381

marked by white color (as shown in Error! Reference source not found. Case D11), is utilized

382

on the outside of the overhanging structure in Cases D1-D13. This thickness is chosen to match

383

the thickness of cement mortar in the non-thermal-bridge region (i.e., the walls) and thus make

384

the exterior wall surface smooth.

Case D1: D=0 mm

Case D2: D=20 mm

Case D3: D=40 mm

Case D4: D=60 mm

Case D5: D=80 mm

Case D6: D=100 mm

Case D7: D=120 mm

Case D8: D=140 mm

Case D9: D=160 mm

Case D10: D=180 mm

Case D12: D=220 mm

Case D11: D=200 mm

Case D13: D=240 mm

385

Fig. 13 WFTB structure with different distances between the exterior surface of the beam and

386

exterior wall surface.

387

The Tsur,ex at different heights is shown in Fig. 14. The cases with similar trends are not

388

shown here to display the results clearly. Otherwise, it would be too crowded to identify

389

individual cases easily. The bimodal type profile of exterior surface temperature is evident in all

390

cases.

391 392

Fig. 14 The exterior surface temperature (Tsur,ex) of WFTB with different Ds.

393 394

395

396

To make the results are easier to compare, a non-dimensional parameter RD is defined as Eq. (24). RD is the ratio of the D to the Dwall.

RD =

D Dwall

The results of the four indexes are shown in Fig. 15, Fig. 16, and Fig. 17.

397 398

Fig. 15 The influencing area (Ainf) with different Ds.

399

The Ainf increases first (from 0 mm to 100 mm) then decreases (from 100 mm to 240 mm)

400

with D. Among all 13 cases (Cases D1-D13), the largest Ainf is 1090 mm when D is 80 mm

401

(Case D5) and 100 mm (Case D6), while the smallest Ainf (720 mm) achieves at D=240 mm

402

(EW, Case D13). As the value of D is discrete for different cases, the largest value of Ainf

403

probably lies between 80 mm (RD=0.33, Case 5) and 100 mm (RD=0.42, Case D6), indicating

404

that the Ainf is largest when the WFTB is in the form of PW with 0.33
405 406

(a)

407 408

(b)

409

Fig. 16 Results of equivalent heat transfer coefficient (KE) with different D, (a) Cases D1-D13.

410

(b) KE in another set of simulations with different D (when Dwall is 300 mm).

411

As for the index of KE (Fig. 16(a)), the smallest value (1.62 W/(m2·K)) presents at D=160

412

mm (Case D9). The largest KE (4.16 W/(m2·K)) shows when D is 0 mm (EB, Case D1). It

413

should be noted that the trend of KE is not monotonous with D. As shown in Fig. 16(a), KE

414

decreases with D on a large slope when D increases from 0 mm (Case D1) to 40 mm (Case D3).

415

The trend of decrease continues, but with a smaller slope, until D reaches 160 mm (RD=0.67,

416

Case D9). It suggests that the minimum conductive heat flux presents in the form of PW with

417

RD = 0.67. It is arguable that this non-dimensional value (RD=0.67) for achieving the minimum

418

heat loss may vary with the thickness of the wall (Dwall). Therefore, we carried out another set of

419

numerical simulations with a different wall thickness (Dwall=300 mm). The results are shown in

420

Fig. 16(b). The minimum KE also reaches RD=0.67 (D=200 mm).

421

The α and the Tvar are shown in Fig. 17(a) and (b), respectively.

422

(a)

423

424 425

(b)

426

Fig. 17 (a) The surrounding heat flux ratio (α) in different cases, and (b) the spatial variation of

427

the temperature (Tvar) with D.

428

In Fig. 17(a), α increases first with D and then decreases, presenting a similar trend with

429

that of Ainf. It indicates that the growing area of the Ainf region helps to enhance the surrounding

430

heat flux ratio. However, differences still exist between the characteristics of Ainf and α. Ainf

431

peaks at RD between 0.33 and 0.42, while α peaks around RD = 0.50 (D = 200 mm, Case D11). It

432

should also be noted that when D increases from 220 mm (Case D12) to 240 mm (EW, Case

433

D13), α decreases fast. It suggests that whether the beam is entirely wrapped by the exterior

434

wall or not affects the value of α significantly.

435

As shown in Fig. 17(b), the Tvar decreases with D monotonously. The slope of Tvar

436

decreasing trend gets smaller as D increases, indicating that the most effective method to reduce

437

Tvar is to change EB to PW. The difference between the largest Tvar (EB, Case D1) and smallest

438

Tvar (EW, Case D13) is 1.26 °C.

439

4.2. Insulation strategy at the overhanging structure

440

With the increase of D, the overhanging structure gradually becomes a major part that

441

loses heat. Under this condition, thermal insulation at the interface between the overhanging

442

structure and outdoor environment has a great potential to improve the overall thermal

443

performance of the exterior wall. To achieve a better thermal insulation effect, the optimal

444

insulation thickness at the overhanging structure (δ) needs to be determined. The increase in δ

445

decreases the length of the overhanging structure. To maintain the safety and stability of the

446

structure, δ should not be larger than one-fourth of the Dwall from experience[38][39][40], i.e., δ<60

447

mm. Therefore, 13 cases are designed with a varies of δ (ranges from 0 to 60 mm). The WFTB

448

structure is fixed as the EW. The arrangement and layout of these 13 cases are shown in Fig. 17.

449

The boundary conditions and parameters of the wall components are the same as those in

450

section 4.1, except the existence of the thermal insulation layer.

Case δ1: δ=0 mm

Case δ2: δ=5 mm

Case δ3: δ=10 mm

Case δ4: δ=15 mm

Case δ5: δ=20 mm

Case δ6: δ=25 mm

Case δ7: δ=30 mm

Case δ8: δ=35 mm

Case δ9: δ=40 mm

Case δ10: δ=45 mm

Case δ11: δ=50 mm

Case δ12: δ=55 mm

Case δ13: δ=60 mm 451

Fig. 18 WFTB structure with a thermal insulation layer at the interface between the

452

overhanging structure and outdoor environment.

453

The Tsur,ex of Cases δ1-δ13 is shown in Fig. 19. Similarly, the bimodal profile of exterior

454

surface temperature presents in all cases except Case δ1. The reason is that the existence of the

455

thermal insulation layer makes the interfaces of the insulated region and the non-insulated

456

region becomes a weak part, as shown in Fig. 19 Case δ13. Cases D1-D13 also present the

457

bimodal profile (Fig. 14) because a thin layer of thermal insulation exists at the overhanging

458

structure in all those 13 cases.

459 460

Fig. 19 The exterior surface temperature (Tsur,ex) of EW type WFTB with different δ.

461

Similar to RD, a non-dimensional parameter Rδ can also be defined as Eq. (25).

462

Rδ =

δ Dwall

463

As can be seen in Fig. 20(a), Ainf increases with δ monotonously, which is different from

464

the effect of D on Ainf. The thermal insulation at the overhanging structure helps to increase the

465

Ainf. However, α does not change with δ monotonously, as shown in Fig. 20(b), because δ

466

affects α in two aspects. On the one hand, δ increases the α as it can decrease the heat transfer in

467

the region of AT,0. On the other hand, it can reduce the KE, and thus reduce the conductive heat

468

flux through the exterior wall. Therefore, α increases with δ first then decreases. The maximum

469

α presents when δ=25-35 mm, i.e., Rδ=0.10-0.15.

470 471

(a)

472 473

(b)

474

Fig. 20 (a) The influencing area (Ainf) with different δ, and (b) the surrounding heat flux ratio

475

(α) in different δ.

476 477

(a)

478 479

(b)

480

Fig. 21 Results of equivalent heat transfer coefficient (KE) with different δ, (a) Cases δ1-δ13,

481

(b) KE in another set of simulations with different δ (when Dwall is 300 mm).

482

There is a limit for the depth of δ, which is 1/4 of the Dwall (Rδ=0.25), due to the concerns

483

on the structure safety. As shown in Fig. 21, the minimum KE (denoted as KE,min) is obtained

484

when Rδ=0.25. The ratio of insulation (I) is defined to reflect the proportion of reduction of KE

485

to the maximum reduction of KE, which can be calculated according to Eq. (19).

I=

486

K E,max − K E,δ KE,max − KE,min

487

where KE,max is the maximum KE (i.e., KE when Rδ equals to 0), KE,δ is the KE at a certain

488

insulation layer depth condition.

489

As can be seen in Fig. 21, 80% of KE reduction takes place at δ=15 mm (Rδ=0.063, Fig.

490

21(a)) and 20 mm (Rδ=0.067, Fig. 21(b)) for the cases Dwall=240 mm and Dwall=300 mm

491

respectively. Out of this range, KE does not change a lot with δ. Therefore, Rδ = 0.06-0.07 are

492

recommended in engineering projects, considering the effectiveness of the thermal insulation,

493

structure safety, and insulation material-saving. It should be mentioned that the δ should be

494

multiple of 5 mm in actual engineering projects, and thus the depth of δ in different cases is

495

designed based on this principle.

496 497

Fig. 22 The spatial variation of the temperature (Tvar) with δ.

498

Tvar decreases dramatically between δ=0 mm and δ=5 mm, which suggests that the

499

existence of the thermal insulation layer is crucial for the reduction of temperature spatial

500

variation. The implication for the engineering is that as long as the thermal insulation is

501

provided regardless of the insulation layer depth, the thermal stress at the thermal bridge can be

502

reduced substantially. If the purpose is to reduce the temperature variation, it is not helpful to

503

increase δ too much. On the contrary, it can even have a negative effect when δ>25 mm (Fig.

504

22), as Tvar starts to rise with δ in this particular case. The reason is that the α begins to play an

505

important role as δ increases, which modulates the location of Tmin.

506

5. Discussion

507

Results in Section 4.1 show that the types of WFTB structures, i.e., EB, PW, and EW,

508

affect the KE of WFTB a lot. KE decreases with D first then increase. Therefore, an optimum D

509

would exist to retrieve the minimum KE. According to 13 cases with variation in D, we found

510

that KE is smallest when RD=0.67 (i.e., D=0.67Dwall). However, the optimum D value may vary

511

with many parameters, such as the depth of the floor or the thickness of the wall. Because the

512

floor depth usually has a similar value, which is regulated by national standards, throughout the

513

whole country. The wall thickness varies with climate zones. It is thicker in the high latitude

514

region, due to the requirement of thermal insulation in winter. The influences of wall thickness

515

on the optimum D is considered in this study. Two different thicknesses (240 mm and 300 mm)

516

are tested and the same optimum D (RD=0.67) is obtained in both sets of cases. Therefore, D of

517

0.67Dwall is recommended in the WFTB with PW regarding the minimizing of the heat loss. The

518

thermal performance of the building envelope can also be improved by thermal insulation at the

519

overhanging structure. It should be noted that it is not the thicker, the better for the thermal

520

insulation δ. It is suggested that Rδ=0.06-0.07 in engineering projects, considering both the

521

energy- and material-saving. Although the influences of the main parameters, D and δ, are

522

investigated, there are still some limitations for the current study. To isolate the main

523

influencing factors, we make room temperature at the upper-level room and the lower-level

524

room is the same, both in the experiment and in simulations. In reality, the indoor air

525

temperature may not be the same in different rooms, due to the different thermal sensation

526

preferences and energy use behavior of room occupants. The differences in temperature in

527

those different rooms cause the asymmetry of the temperature field, which may be able to affect

528

the characteristics of the thermal bridge. This effect is worth to be further investigated in future

529

studies.

530

It also should be mentioned that the KE is the same as the linear thermal transmittance that

531

defined by ISO 10211: 2017[32] in principle. However, the calculation processes of the two

532

indexes are different. In our index, we divided the total heat flux of thermal bridge into two

533

parts, i.e., QT and QT,basic. In our further study (not included in this paper), we found that when

534

wall material changes, the two parts of the heat flow rate alter simultaneously. The newly

535

defined index (KE) can thus help us understand the composition of the heat flow rate caused by

536

a thermal bridge.

537

6. Conclusion

538

In this study, the characteristics of heat transfer in the wall-to-floor thermal bridge (WFTB)

539

are investigated experimentally and numerically. To quantify the thermal performance of

540

different types of WFTB, we defined four indexes, including influencing area of thermal

541

bridges (Ainf), equivalent heat transfer coefficient of thermal bridges (KE), surrounding heat flux

542

ratio (α), and spatial variation of the temperature on the thermal bridge (Tvar). According to the

543

different distances between the beam and the exterior surface of the wall (Ds), WFTB is

544

classified into exposed beam structure (EB), partially wrapped beam structure (PW) and entire

545

wrapped beam structure (EW). The numerical models are validated by experiment results. Two

546

key parameters, D and insulation thickness at the overhanging structure (δ), are tested.

547

The following conclusions are drawn based on the experimental and numerical results:

548

(1) The KE decreases with D first then increases, while the influences of δ on KE is

549

monotonous in the studied range (0
550

(2) The optimum D for the thermal insulation on WFTB is 0.67Dwall.

551

(3) The suggested δ is 0.06-0.07Dwall, considering the effectiveness of the thermal

552

insulation, structure safety, and insulation.

553

(4) Both the PW and the thermal insulation on the overhanging structure help to reduce

554

the Tvar, which is to the benefit of reducing thermal stress and thus reducing the wall

555

cracks.

556 557 558 559

Acknowledgement The authors appreciate the support from the National Key R&D Program of China (No. 2016YFC0700302).

560

Reference

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Highlights •

Structure of wall-to-floor thermal bridges (WFTBs) impacts the thermal performance.

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New indexes are proposed to quantify the various influences of WFTBs.

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Simulation results of heat transfer on a WFTB agree well with the experiment.

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A structure of WFTB with the largest potential on energy-saving is proposed.

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Optimal thickness of insulation of WFTB for both energy- and material-saving.

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Conflict of Interest Statement

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our manuscript entitled, “Optimized mitigation of heat loss by avoiding wall-to-floor thermal bridges in reinforced concrete buildings”.

Jiang Lu, Ph.D. Associate Professor School of Civil Engineering and Architecture Zhejiang University of Science and Technology Hangzhou 310023 People’s Republic of China E-mail: [email protected] Tel./fax: +86-571-85070518