Heat loss through wall/slab/foundation joint for high-rise buildings

Assignment 1 -

Report

Calculation of heat loss through

wall/slab/foundation joint for

high-rise buildings

Kasper U. Nielsen

Kathrine N. Brejnrod

Theis H. Pedersen

Title page

Title: Assignment 1 - Report

Subtitle: Calculation of heat loss through wall/slab/foundation joint for

high-rise buildings

Written by: Kasper U. Nielsen [201300234]

Kathrine N. Brejnrod [20062459]

Theis H. Pedersen [201300223]

Report: Assignment 1

Study: Architectural Engineering

Course: Energy-efficient building envelope design

School: Aarhus School of Engineering

Project period: 30. Jan. – 18. Feb. 2014

Mentor: Steffen Petersen

Pages: Main report: 8 normal sider [2400 anslag]

Basis for decision making: 2 sider

Appendices: 9 sider

Chapter 1 - Introduction

#Table of Contents

1 Introduction ...................................................................................................................... 1

1.1 Prerequisites ............................................................................................................. 3

2 Method .............................................................................................................................. 5

2.1 Steady state condition............................................................................................... 5

2.1.1 Method of modelling ........................................................................................ 5

2.1.2 Method of calculating ....................................................................................... 8

2.2 Transient calculation ................................................................................................ 9

2.2.1 Method of modelling ........................................................................................ 9

2.2.2 Method of calculation ..................................................................................... 10

2.3 Surface temperature – Condensation risk ............................................................... 11

3 Results ............................................................................................................................ 13

3.1 Original model ....................................................................................................... 13

3.2 Attempts of improvement ....................................................................................... 13

4 Analysis & Discussion ................................................................................................... 15

4.1 Steady state calculation vs. Transient simulation ................................................... 15

4.2 Original construction .............................................................................................. 16

4.2.1 Heat loss ......................................................................................................... 16

4.3 Alternative build-ups .............................................................................................. 16

4.4 Final suggestion ..................................................................................................... 17

5 Conclusion ...................................................................................................................... 19

6 Bibliography ................................................................................................................... 21

7 Appendix ........................................................................................................................ 23


Assignment 1 - Report

Kasper Ubbe Nielsen;Kathrine N. Brejnrod;Theis H. Pedersen Side 1

1 Introduction

The current report concerns the heat loss through the complex building joint, illustrated on

Figure 1, between the outer wall and the ground slap. The joint works as a thermal bridge

with a higher heat transmission than the homogeneous parts where only one-dimensional

heat transfer occurs. A Thermal bridge is defined as an area with lower insulating properties

than the surrounding construction. Therefore it is important to reduce the thermal bridges to

ensure a minimum overall heat loss.

Apart from the challenge concerning the heat loss, the joint can also contribute to indoor

climate issues. Due to the increased heat loss related to the thermal bridge, the surface

temperature will be lower in this area, which in some cases can lead to condensation and

thereby maintenance problems such as mildew or mold growth.

The joint will be examined in the simulation program HEAT2 to determine the effects of the

thermal bridge and thereby calculate the linear transmission coefficient �, so a comparison

with applicable legal requirements can be made. In the Danish building regulation it states

that � should be less than 0.40 W/m*K and 0.20 W/m*K if there is floor heating. The

coldest indoor surface temperature at the joint will also be determined, to evaluate the risk of

moisture related problems.


Side 2 Assignment 1 - Report

Kasper Ubbe Nielsen;Kathrine N. Brejnrod;Theis H. Pedersen

Figure 1 – Original construction principle

The heat loss through the joint will be calculated according to two methods: a steady state

and a transient calculation method. This is to clarify the accuracy of the steady state method

compared to the transient method, and evaluate the advantages and the disadvantages of the

different methods. For further information see chapter 2.

On the basis of the examination of the heat loss and the surface temperatures, an evaluation

of opportunities of improvements will be made, and an alternative build-up will be

suggested.




1.1 Prerequisites

Where information has been missing realistic assumptions have been made. Table 1 shows

the prerequisites regarding the properties of the different materials in the joint. The more

specific prerequisites for the two different calculation methods, respectively steady state and

transient, will be listed thoroughly in the relevant sections.

Table 1 - Prerequisities

Element Heat

cond. λ

[W/m*K]

Density

[kg/m³]

Spec. heat

cap. - Cp

[kJ/kg*K]

Vol. Heat

cap.

[MJ/m³*K]

Remarks

Concrete 2.7 2300 1 2.3

Lightweight

concrete

0.49 - - 1.83 In accordance with

HEAT2 database.

Type:

Lightweight concrete

IEA

Insulation 0.037 30 1.03 0.0309 In accordance to

Rockwool Energy

designer

Clay (soil) 2 - - 2 In accordance to DS

418 Annex D.1

Base plaster 0.52 1300 0.41 0.53 In accordance with

HEAT2 database.

Type:

Concrete cellular

IEA

Chapter 2 - Method



2 Method

In the following section the methods used to calculate and evaluate the multidimensional,

one dimensional and linear heat loss coefficient is elaborated. The methods and prerequisites

described in DS 418 – section 6 (DS418, 2002), section 5.3 in Lecture Note on Thermal

Bridges (Petersen, 2013) and section 3.3.2 in Cold Bridges (Rode, 2001) is used in the

following calculation. Demands and further prerequisites that are not found in the above

literature are found in the Danish Building Regulation – §7.6 (Energistyrelsen, 2010). If not

found in the above, the source is stated at its relevance. Furthermore it is important to state

that the following calculations are based on internal measures.

2.1 Steady state condition

2.1.1 Method of modelling

2.1.1.1 Soil

The steady state situation only considers the one situation with a ∆T of 32 °C (Outdoor: -

12°C, Indoor: 20 °C), thereby no dynamics are considered. The modelling in HEAT2 is

based on the prerequisites mentioned in the above regarding surfaces resistances, though the

most important manner is the simplifications that is made regarding insulating effect of the

soil layer below and around the building part. Hence this is a steady state calculation, the

dynamic influence of the varying outdoor temperature are not concerned. In reality the deep

soil layer temperature is a function of the outdoor temperature and close to the mean outdoor

temperature if one digs deep enough and only observing the vertical heat flow (horizontal

boundary condition). If observing the near-field of the soil layer (still vertical heat flows),

under the building slab, this would be affected/warmed by the building, which differs from

the soil layers at same depth but under free ground. Regarding horizontal heat flows (vertical

boundary conditions), it is accepted to use an adiabatic boundary condition in a somewhat

far-field, this part is elaborated further in the following. Therefore a method of accounting

for the effect of the soil layers is needed. This manner is discussed in Cold Bridges (Rode,

2001) where three possible options are mentioned.

Chapter 2 - Method



Option 1 – The use of an adiabatic horizontal boundary condition at far-filed depths that

imitates the vanishing vertical heat flows at such depths.

Option 2 – The use of the mean annual outdoor temperature at some depth below the ground

as a horizontal boundary condition.

Option 3 – The use of the mean annual outdoor temperature at a depth equal to the depth,

that corresponds to the thermal resistance of the soil layer, as specified in DS 418,

amendment 4 (DS418, 2002), and the conductivity of the specific soil, as a horizontal

boundary condition.

Both option 1 and option 2 has their disadvantages. By implementing a horizontal adiabatic

boundary condition (Option 1) causes the temperature in the far-field of the soil to be a

function of the outdoor temperature, which, according to Appendix B.1, leads to a soil

temperature to cold and thereby a high and unrealistic heat loss towards the ground. Option 2

approaches a more realistic method, though not knowing the specific depth of where to place

the boundary condition may lead to imprecise and unrealistic results, hence if the depth is

chosen to small the temperature in the soil below the slab would be to warm, due to the lack

of influence of the outdoor temperature. If the depth is chosen to be too large, the same

situation as for option 1 occurs, where the temperature below the slab would be to cold, due

to too much influence of the outdoor temperature, according to Appendix B.2.

Option 3 accounts for the conductivity and the thermal resistance of the soil, by setting the

depth as a function of the two. This is, based on Appendix B.3, assessed to be the most

realistic method of the three, and thereby the method which is used the following calculation.

Chapter 2 - Method



2.1.1.2 Joint

As for the modelling depths of soil, it also goes for the construction parts of the joint. It is

needed to set a modelling distance for the wall and for the slab in a scale, so that the

influence of the joint isn’t noticeable. For the wall, a modelling distance of 1.5 meters is

suitable. For the slab, a modelling distance of 4.0 meters is needed, this due to the multi-

dimensional effect of the outdoor temperature to the soil layers below the slab. As seen in

Figure 2 and Figure 3, the heat flow at these distance are not influenced by the joint (it is

seen by the parallel flux arrows, which illustrates one-dimensional heat flow), hence it is

assessed that these distances are sufficient.

Figure 2 - Illustration of flux arrows in the wall

Figure 3 - Illustration of flux arrows in the deck at edge

Chapter 2 - Method



2.1.2 Method of calculating

The way to calculate the heat loss through this joint is to observe the actual joint as a form of

lump that leads to a multidimensional heat flow, compared to the one-dimensional heat loss

through the homogenous constructions that are joined. This is best expressed in a linear-loss

coefficient, as a function of the length of the actual joint, in accordance with (EN ISO

10211-1, 1995). In a section like this, it is sufficient to calculate the multi-dimensional heat

loss as the two-dimensional (2D) heat loss.

So in basic, the method is to compare the one-dimensional heat loss, through the

homogenous constructions, with the total two-dimensional heat loss of the joint. The method

to separate the two situations is to place suitable adiabatic resistances, such that only one-

dimensional heat flow is possible. The placement of these resistances for this particular joint

is seen on Figure 4 below. Furthermore it is seen that only one-dimensional heat flow is

present.

Figure 4 - Illustration of fictive resistances to force 1D heat flow

The calculation of the one-dimensional can also be done manually by:

�� ∙ � ∙ ∆��

��

Chapter 2 - Method



Next step is to choose suitable calculation-mesh that gives an adequate result. By adequate

meaning the relation of calculation time vs. precision of result. A criterion of for the

precision is stated in (EN ISO 10211-1, 1995) as a maximum change of heat flux of 1%

when comparing to meshes. Finally one has to subtract the calculated one-dimensional heat

loss from the calculated two-dimensional heat loss and divide it by the design temperature

difference used in the calculation.

2.2 Transient calculation

The linear heat loss coefficient for the joint is now determined based on transient simulations

according to the methodology of DS 418 appendix D.1 (DS418, 2002). In contrary to the

steady state method, the transient method takes the variations of the outdoor temperature and

thereby variations in the soil temperature into account.

2.2.1 Method of modelling

The 2D transient calculations are performed using the program HEAT2, ver. 8.03. The

model calculated is build up according to DS 418 appendix D.1, and is illustrated in Figure 5

with relevant temperatures, resistance and adiabatic boundaries. The current method

disregards heat flows in the foundations longitudinal direction at a distance of 4m from the

joint as well as heat flows through the adiabatic boundaries set at 20 meters below ground

and 20 meters left of the foundation.

Figure 5 - Transient model

Chapter 2 - Method



To obtain an acceptable accuracy of the simulation a decrease of the numerical grid may not

lead to a significant change in results. According to the method in DS 418 appendix D.1

(DS418, 2002) , the numerical grid is set with a grid size of no more than 0.025m in the

important areas near the joint. The chosen grid for the original construction is shown in

Figure 6, where the area with a maximum grid size of 0.025m X 0.025m is marked in red.

Figure 6 - Mesh division

The calculations must be carried out for numerous years until the system reaches a quasi-

equivalent state where the heat flow through the internal surfaces in December does not

differ more than 1% from the heat flow the previous year in December.

2.2.2 Method of calculation

The temperatures evaluated from the transient calculations are temperatures in the reference

point right below the deck, at a distance of 4 meters from the joint, Figure 5. Also the heat

flows through the internal surfaces are logged in the simulation. Both temperature and heat

flows are logged in the middle of each month and averaged. The period evaluated are only

the months September - May (both months included). The one-dimensional heat flow

through the wall and deck is calculated and subtracted from the two-dimensional results from

the HEAT2 simulation, which then is divided with the averaged difference between the

outdoor and indoor temperature to find the linear heat loss coefficient.

Chapter 2 - Method



2.3 Surface temperature – Condensation risk

As mentioned before, the surface temperature near the thermal bridge is expected lower than

the surrounding surface areas. The low temperature can cause problems due to condensation,

since the relative humidity is depended on the temperature. Every time the RH reaches 100%

surface condensation starts (International Energy Agency, 1990). To investigate if problems

with condensation occur, the lowest internal surface temperature in the joint in determined in

HEAT2, as shown in Figure 7.

Figure 7 - Indoor surface temperature

At a steady state calculation, with an outdoor temperature at -12°C and increased internal

resistance of 0.25 m²*K/W, the lowest internal surface temperature is determined to 11.1°C.

Figure 7 also clearly states, that there is a big temperature drop near the thermal bridge. In

order to cause condensation at the corner, at an indoor temperature at 20°C, the relative

humidity should be above approximately 55%, see appendix A, which is equal to 0.0082

kg/kg. To evaluate if this can cause condensation issues, the Danish reference weather data

file (DRY) is used. This is a reference file, so real weather conditions could exceed these

data values. The weather file has been sorted as listed below:

Table 2 - DRY weather file

> 0.0082 kg/kg < -12°C Both conditions met

Hours 1594 48 0

Chapter 2 - Method



Table 2 indicates that condensations cannot occur directly based on the outdoor conditions,

since both demands are not fulfilled at the same time. The reason is that low temperature air

cannot contain as much water as warmer air. However as mentioned previously, the true

weather conditions can differ from the reference file.

Furthermore, an even more important parameter is the human production of water by

exhaling. If two people are sleeping in a small room, without any ventilation, the content of

water in the air could easily exceed RH 55%. To prevent risk of condensation, and thereby

moisture related problems, it is therefore important to ventilate frequently.

Chapter 3 - Results



3 Results

3.1 Original model

The results of both the steady state and the transient calculation are presented in Table 3

below.

Table 3 - Results for the original construction

2D heat loss

[W/m²]

1D heat loss

[W/m²]

∆T

[°C]

ψ

[W/m*K]

TS

[°C]

Steady state 41.09 20.23 32.00 0.63 11.1

Transient 21.98 10.84 14.46 0.77 -

3.2 Attempts of improvement

Results from the different improvements are listed in Table 4. For a visual representation of

the different improvements that has been tried, see Appendix C.

Table 4 - Results for the improvements

2D heat loss

[W/m²]

1D heat loss

[W/m²]

∆T

[°C]

ψ

[W/m*K]

TS

[°C]

Improvement 1 19.74 10.84 14.46 0.62 13.2

Improvement 2 20.74 11.40 14.46 0.65 8.3

Improvement 3 18.50 10.83 14.46 0.53 13.3

Improvement 4 16.18 11.22 14.46 0.34 13.1

Improvement 5 17.04 11.40 14.46 0.39 12.8

Improvement 6 16.90 11.20 14.46 0.39 14.8

Chapter 4 - Analysis & Discussion



4 Analysis & Discussion

4.1 Steady state calculation vs. Transient simulation

The obvious differences of the two methods are given by their respective names. The steady

state solution is a numerical calculation of a “snapshot” incident with a given set of static

boundary conditions. The transient simulation is a numerical calculation representing a

defined timeframe, often a year, which is affected by dynamic boundary conditions that vary

with time, where the calculation is performed for a certain time step including a set of

parameters from the former time step. As it indicates, the time it takes to perform the two

solutions differs a lot. Both solution methods increase in calculation- and simulation time as

the previously mentioned mesh is increased. The error criterion also affects the time, hence

the number of iterations increase.

When to use what? It of course depends of the question asked. The steady state calculation is

a quick method to make a benchmark solution of a given solution, whereas the transient

simulation is a more time consuming, but also precise solution, this of course depends on the

input that is given to the model. For example one could argue whether it is correct or not to

apply a static indoor temperature to the transient model, where a dynamic outdoor

temperature is used.




4.2 Original construction

4.2.1 Heat loss

As stated in Chapter 3, the linear heat loss coefficient through the joint in the original

construction of Ψ = 0.77 W/mK does not comply with the legal requirements of the danish

building regulations on 0.40 W/mK (Energistyrelsen, 2010, 7.6. stk 1).

Figure 8 - Original construction

The high linear heat loss coefficient is due to the huge constructional thermal bridges caused

by the exposed foundation block. As Figure 8 illustrates the heat is easily transmitted from

the deck- and bearing wall elements through the foundation block since no insulation is

“breaking” the thermal bridge, and the extra heat loss through the corner is therefore

considerably.

4.3 Alternative build-ups

To improve the construction, decrease the linear heat loss coefficient and increase the

minimum surface temperature, the thermal bridge must be broken. The impact of several

improvements has been investigated in order to develop a joint that fulfill the Danish

Building Regulations. The improvements are listed in Appendix C.

It is shown from the results that in order to reduce the heat loss through the joint, the break in

insulation has to be eliminated.




As shown at improvement 2 and 6, the minimum surface temperature is greatly affected by

the addition of a small insulation wedge, placed just between the corner and the ground floor.

Unlike the other improvements of the linear heat loss coefficient, this will reduce the

minimal surface temperature. The reason for this is that the heat flux that previously went

through the slap is being prevented to reach the corner point. The reason why the internal

minimum temperature for the other improvements still exceeds the original temperature is

due to the overall reduction of the linear heat transmission.

The simulations of the different alterations have also shown, that it is more effective to place

the insulating layer as close to the thermal bridge as possible. It is therefore more effective to

place the insulation in between the Leca blocks, than on the outside.

4.4 Final suggestion

From the investigation of possible improvements, see Appendix C, an improved build-up is

suggested, see Figure 9. To reduce the additional heat flux through the joint the following

improvements are suggested:

Figure 9 - CAD drawing of final suggestion




The alternative build-up leads to the use of a slimmer lightweight concrete block with a

width of 100mm instead of the original 150mm. The alternative build up contributes to a

linear loss just below the requirements of 0.40 W/m*K, and a significantly rise in minimum

surface temperature.

Table 5 - Results for the final suggestion

ψ

[W/m*K]

TS

[°C]

Final suggestion 0.39 14.8

Figure 10 - Construction principle of final decision

Chapter 5 - Conclusion



5 Conclusion

In order to minimize the overall heat transmission loss, the Danish Building Regulation

states a demand of a maximum linear heat coefficient at 0.40 W/m*K. The original build-up

of the joint had a coefficient of 0.77 W/m*k which exceeded the demand greatly, and at the

same time the minimum surface temperature of 11.1°C could lead to problems related to

condensation and thereby mold issues.

Different improvements have been tested, in order to evaluate the performance on the linear

coefficient. A final suggestion has been made, which both favor the internal minimum

surface temperature and the linear heat coefficient. The alternative build-up includes external

insulation and a continuation of the wall insulation and leads to a linear heat loss coefficient

of 0.39 W/m*K and a minimum surface temperature of 14.8°C. The alternative build-up

thereby satisfies the legal requirements to the linear heat loss coefficient and issues related to

moisture are prevented.

There has been performed both steady state calculations and transient simulations, to

determine the accuracy and usability of the one compared to the other. As described in

chapter 4.1, the methods have different pros and cons. In the case, we have found that the

steady state calculation is obvious for a benchmark of different solutions, due to the low

calculation time. The transient simulation is more time consuming, however the result is

more correct, and the method should therefore be used for determination of the linear

coefficient, as also stated in the Danish Standard 418 (DS418, 2002).

Chapter 6 - Bibliography



6 Bibliography

DS418, 2002. Beregninger af bygningers varmetab, København: Dansk Standard.

EN ISO 10211-1, 1995. EN ISO 10211-1:1995, s.l.: s.n.

Energistyrelsen, 2010. Bygningsreglementet 2010. [Online]

Available at: www.bygningsreglementet.dk

International Energy Agency, 1990. Guidlines & Practice Vol. 2 - Annex 14 "Condensation

and Energy", s.l.: IEA.

Petersen, S., 2013. Lecture note on Thermal Bridges, Aarhus: Aarhus University Department

of Engineering.

Rode, C., 2001. Cold Bridges, s.l.: Department of Civil Engineering Technical University of

Denmark.

Chapter 7 - Appendix



7 Appendix

Appendix A IX-diagram ....................................................................................................... 1

Appendix B Assessment of options ...................................................................................... 3

Appendix C Attempts of improvements ............................................................................... 7




Appendix A IX-diagram

Indoor temperature: 20°C

Relative humidity: 60%

Dew point temperature: 12°C




Appendix B Assessment of options

In the following sections, measurements of the soil temperature at different depths has been

performed, compared and assessed to determine whether the chosen option is a realistic

representation of the soil temperature in a steady state calculation.

Appendix B.1 Option 1

In the following section Option 1 from Cold Bridges (Rode, 2001) is assessed regarding a

realistic representation of the soil temperature in a steady state calculation.

Far field adiabatic case Appendix B.1.1

From Figure 11 and Table 6 it is obvious that the soil temperature in every layer is below

0°C and thereby too cold to give a realistic representation of the soil temperature.

Figure 11 - Temperature plot far field adiabatic case. Source: HEAT2

Table 6 - Temperature for Far field adiabatic case

Temperature

[°C]

Below insulation -1.16

1 meter depth -2.88

3 meters depth -5.33

20 meters depth -9.21







Low depth case Appendix B.2.1

From Figure 12 and Table 7 it is seen that the soil temperature below the deck isn’t affected

by the outdoor temperature, and thereby the soil is too warm to give a realistic result.

Figure 12 - Temperature plot low depth case. Source: HEAT2

Table 7 - Temperature for low depth case

Temperature

[°C]

Below insulation 8.85

1 meters depth 8




Great depth case Appendix B.2.2

From Figure 13 and Table 8 it is seen that the soil temperature below the deck is greatly

affected by the outdoor temperature, and thereby the soil is somewhat too cold to give a

realistic result.

Figure 13 - Temperature plot great depth case. Source: HEAT2

Table 8 - Temperature for great depth case

Temperature

[°C]


3 meters depth 5.63

6 meters depth 8







Conduction VS. resistance case Appendix B.3.1

From Figure 14 and Table 9 it is clearly seen that the temperature of the soil is represented in

a somewhat more realistic manner regarding the temperature plot.

Figure 14 - Temperature plot conduction vs. resistance case. Source: HEAT2

Table 9 - Temperature for conduction vs. resistance case

Temperature

[°C]


1 meter depth 7.4

3 meters depth 8.03




Appendix C Attempts of improvements

Appendix C.1 Original construction

Ψ = 0,77 W/mK

Ts,min = 11,1°C

Comments: The linear loss coefficient does not comply with the requirements of Br10.

The surface temperature is below the dewpoint temperature of

12,0°C.

Appendix C.2 Improvement 1

45mm continuous insulations strip.

Ψ = 0,62 W/mK

Ts,min =13,2°C






0.02m insulation as cold bridges break in deck.

Ψ = 0,65 W/mK

Ts,min = 8,3 °C


The surface temperature is below the dewpoint temperature of 12,0°C


0.1m external insulation.

Ψ = 0,53 W/mK

Ts,min = 13,3 °C


Appendix C.5





0.1m external insulation, continuation of wall insulation and

Ψ = 0,34 W/mK

Ts,min = 13,1 °C

Comments: -


0.1m external insulation, continuation of 0.045m wall insulation and 0.02m insulation as

cold bridges break in deck.

Ψ = 0,39 W/mK

Ts,min = 12,8 °C

Comments: -


0.1m external insulation, continuation of 0.045m wall insulation.

Ψ = 0,39 W/mK

Ts,min = 14,8 °C

Comments: -

Heat loss through wall/slab/foundation joint for high-rise buildings

Engineering

Transcript of Heat loss through wall/slab/foundation joint for high-rise buildings