The role of optimization and simplified methods in the … role of optimization and simplified...

The role of optimization and simplified

methods in the design of Thermally

Activated Building Systems (TABS) Yueting Yang 0789016

7/25/2013

[1]

Supervisor:

prof. dr.ir J.L.M. Hensen

dr. D. Costola

/ Unit Building Physics & Services

/ Built environment department

Yueting Yang The role of optimization and simplified methods in the design of Thermally Activated Building Systems (TABS)

Contents

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

1.1 Background of TABS system ................................................................................... 1

1.2 Complexity of design ............................................................................................ 1

1.3 Focus on pipe level ............................................................................................... 2

1.4 Research question ................................................................................................ 2

2. Research methodology ............................................................................................... 3

2.1 Current TABS design method ................................................................................. 3

2.2 Simulation and optimization design method ................................................................ 4

2.3 Case study ......................................................................................................... 5

3. Result and discussion ................................................................................................. 7

3. 1 Optimization ..................................................................................................... 8

3.2 Design method................................................................................................... 13

4. Conclusion ............................................................................................................ 16

Appendix .................................................................................................................. 25

5. Heat transfer theory and modeling of TABS system in TRNSYS ............................................ 27

5.1 TABS modeling in TRNSYS .................................................................................. 27

5.2 Heat transfer theory of TABS in TRNSYS .................................................................. 27

6. Case study design in current methods ............................................................................ 29

6.1 Simplified sizing by diagrams in standard [60] ............................................................. 29

6.2 Straightforward unknown but bounded method (SUB) [65] ............................................ 31

6.3 Rehva guidebook [53].......................................................................................... 32

6.4 Design manual from manufacture in USA [49] ............................................................ 34

6.5 Design manual from manufacture in Canada [55] ......................................................... 39

7. Single pipe dimension optimization ............................................................................... 41

7.1 Simulation and modeling ...................................................................................... 41

7.2 Thermal demand and pipe dimension ....................................................................... 41

7.3 Overheating hours and pipe dimension ..................................................................... 45

7.4 Pareto front in single dimension optimization .............................................................. 46



Page 1

The role of optimization and simplified methods in the design of

Thermally Activated Building Systems (TABS)

YUETING YANG‡

Thermally Activated Building Systems (TABS) are widely used because of energy saving and improved indoor comfort.

There are some simplified design methods of TABS systems including European standards, manuals from scientific

institution and manufacture guidebooks. To figure out the optimal design method, simulation and optimization are

integrated as a new method. By defining objectives as energy saving and comfort improving, 4 kinds of optimization

are investigated regarding pipe dimension design and supply water design. In a case study, the pipe dimension design

and supply water design of current simplified methods and the new simulation integrated optimization method are

shown. The corresponding building performances under each design are compared to figure out the optimal solution.

1. Introduction

1.1 Background of TABS system

Active building components are thermally heavy

parts of the building construction, which are

equipped with ducts for circulation of air or

embedded pipes for circulation of water [2] (Figure

1). Buildings equipped with thermally activated

building systems (TABS) system are heavy thermal

mass constructions with high thermal inertia, which

could absorb more heat and solar gain in and delay

the heat transfer from outside to inside [2]. In this

way, indoor temperature could be kept within a

comfortable range regardless of wide fluctuation of

ambient temperature.

TABS has been widely used in modern building

design and develops towards more energy efficient

way [3-13]. As an adaptive design, TABS has been

investigated in various environment and integrated

with numerous systems, such as heat pump ground-

coupled system [14], combined cooling, heating &

power system (CCHP) [15] and rainwater system

[16]. In this process, energy consumption could be

reduced compared with conventional systems.

Another advantage of TABS system is it can satisfy

different indoor comfort levels by low energy

consumption [17], which reduces greenhouse gas

emission [18] and allows the utilization of low grade

energy sources, such as the ground [19-20], outside

air [21] or recovered process heat [22]. As a thermal

mass integrated with the whole building, TABS

system also functions well in peak shaving and time

lag due to its thermal inertia effect [8,22-27], which

brings economic benefits when exploiting the

nighttime cheap electricity tariff[18].

There are also some potential barriers and

limitations in application. TABS is only suitable for

buildings with low heating/cooling loads (

[2]. High thermal insulation of the building

envelope and proper solar shading is a prerequisite

for application [2]. Control strategy has influence

on TABS design and performance, but there are

various ways of control which cannot be

determined at the TABS design stage. In other

words, control and design of TABS are in circular

cause and consequence.

1.2 Complexity of design

Considering the benefits and limitations of TABS

systems, there are potentials and complexities in


Page 2

the design process, which can be classified by three

levels.

Figure 1. Schematic diagram of Thermally Activated Building Systems (TABS) [28]

Building level

At building level, the designers deal with problem

related to TABS application rage and necessity.

Various building construction types [29], kinds of

climate environment and different comfort models

[30-32] should be taken into account. Once the

capacity of TABS can be decided, the necessity of

auxiliary equipment (solar panel, chiller etc.) can

also be known. The application of phase change

material also plays an important role in TABS

system [33-35].

System control level

The diverse control strategies of TABS can be

classified as water temperature control and pump

operational control (power control & energy

control). The control could be continuous or

discontinuous in a time step of one hour or one day.

Related researches cover topics including the

switching point between cooling and heating modes

[36-37], control efficiency [38-39], hydronic circuit

topologies [40-41] and integrated control with

occupant behavior [42-43].

Pipe level

There are many standards and guidebooks regarding

pipe design of TABS [44–60] which includes both

pipe dimension and supply water to pipes. Pipe

dimension design refers to sizing the pipes [61] such

as pipe diameter, pipe spacing, pipe wall thickness,

loop length and position of the pipes embedded in

the construction. Supply water design concerns

about designed heat loss, supply water

temperature, mass flow rate and pressure drop etc.

Given the heat transfer analysis and thermal

resistance model [62-63], the variables at pipe level

are directly related to the building performance.

1.3 Focus on pipe level

In most TABS design guidebooks, the supply water

design is determined based on the known pipe

dimension. The design methods discussed in this

passage come from European standard, scientific

organizations and manufactures. These current

methods are direct and straightforward, but also

less accurate and without optimal result because of

the assumptions about limited control strategies and

unstated hydronic configuration.

To set up more convincing guidelines and provide

optimal solutions, the method in this research

makes use of simulation and optimization. Modeling

and simulation have been widely used in building

performance prediction. Optimization is the

mathematical selection of a best element (with

regard to some criteria) from some set of available

alternatives to achieve defined objectives [64].

Combined optimization with simulation, a better

solution could appear in terms of TABS design.

1.4 Research question

Given the benefits of optimization, limitations of

existing design methods and more potentials of

TABS system, this research would investigate the

feasibility of optimization in design of

Thermally Activated Building Systems (TABS)

when compared with existing simplified

methods.

This passage will illustrate the research question in

the following parts. The research methodology

clarifies the current situation of existing design

methods and the integration method of

optimization and simulation. A case study has been


Page 3

introduced to investigate the quantitative analysis of

each method. The design and performance are

compared to select the optimal design method.

2. Research methodology

2.1 Current TABS design method

2.1.1 Design method from European

standard [60]

2.1.1.1 Rough sizing method

Based on the assumption of operative temperature

as 24˚C, the cooling system can be sized for 70%

of the peak cooling load. Since the inaccuracy is

around 20~30% and there is no information about

supply water temperature or pipe dimension, this

rough sizing method can only be used to size the

production unit.

2.1.1.2 Simplified method using diagrams for sizing

Within the frame of assumed operation mode,

orientation and active surface, the linear

relationship of core temperature, daily heat gain,

total thermal resistance and circuit running time has

been set up to determine the supply water

temperature. This method is based on the

assumption that both the entire conductive slab and

supply water are at constant temperatures during

the whole day. The dis-advantage lies in the

limitation of operation mode, no dynamic

consideration and no instruction on sizing pipe

dimension, which leads to 15~20% inaccuracy.

2.1.1.3 Simplified model based on finite difference

method (FDM)

Based on the knowledge of 24 values of the variable

cooling loads of the room and the temperature of

the air, detailed dynamic simulation for thermal

conduction in the slab via FDM has been applied to

get the related surface and supply water

temperature (inaccuracy 10~15%). The pre-

requisite of application is that the operative

temperature of the room has to be 20˚C to 25.5˚ C

as the program underestimates the temperature of

the room. The following limitations should be met

(1) pipe distance ranges from 0.15 to 0.3m, (2)

usual concrete slab structure have to be considered,

, without discontinuous light

fillings in upper or lower slabs.

2.1.1.4 Dynamic building simulation program

By taking into account of the water flow into pipes,

the heat conduction between upward and

downward surface of the slab and the pipe level,

heat conduction of each wall, mutual radiation

between internal surfaces, convection with air and

the internal balance of the air, the detailed dynamic

building-system model has been carried out.

2.1.2 Design method from scientific

organization

2.1.2.1 Rehva guidebook using diagrams for sizing [53]

There are only two types of pipe dimension

available in this method: 0.15m and 0.3m for pipe

spacing. The relationship of heat exchange rate,

thermal resistance of floor covering and medium

differential temperature has been built up and can

be read from the diagram. But the result of medium

differential temperature does not shown the exact

value of supply water temperature, return water

temperature or indoor temperature. It only reveals

the rational result of these three temperatures.

(Equation 1)


Page 4

2.1.2.2 Straight-forward unknown but bounded method

(SUB) [65]

In contrast to the conventional iterative design

method of TABS, which is based on iterative

dynamic model simulation studies, this approach is

a more straight-forward calculation process, which

is less time-consuming and enables more insight

into the potential of TABS. Based on estimated

lower and upper bounds for the heat gains, the

supply water temperature and control set-point can

be decided. It also shows the limitation of TABS

application and points out when additional auxiliary

heating or cooling devices have to be installed. The

assumption behind this method is the daily variable

heat gains has been transferred to equivalent bounds

based on a linear relationship. An outstanding

advantage of this method is that it distinguishes

ceiling and floor, heating and cooling.

2.1.3 Design method from manufacture

resource

2.1.3.1 Design and installation guide from manufacture

in USA [49]

Based on floor covering and designed heat output,

the supply water temperature and TABS dimension

can be sized. It serves for both residential and light

commercial buildings. The general diagrams are

provided for designers and installers to follow. But

it is obvious that the suggested supply water

temperature and heat output are quite high

compared with normal range.

2.1.3.2 Design and installation guide from manufacture

in Canada [55]

Similar to the design guide from manufacture in

USA, the method is also on the basis of floor

covering and designed heat output. The difference

is that flow rate in this method is an essential

variable in dimension parameters determination

instead of a result determined by dimension

parameters according to the design guide from

USA. This diminishes error propagation and

improves accuracy because there is more

uncertainty in sizing dimension than flow rate.

2.2 Simulation and optimization design method

2.2.1 Application of simulation in TABS

Over the past 30 years, the importance of building

simulation has become more and more obvious in

research about TABS system. The performance of

TABS is strongly related to the design details and

control strategy, which can be modeled in various

simulation software packages, such as ESP-r,

TRNSYS, IES VE, IDA ICE, & EnergyPlus [66]. By

means of computational simulation, design

complexities are investigated and possible

performance are predicted without time and money

wasted in uncertain construction. For example, it

was found that reductions up to 50% of the cooling

capacity for a chiller can be achieved using TABS

[25,67].

2.2.2 Application of optimization in

simulation

In order to achieve optimal system performance

under some architectural and comfort constraints,

the optimal sets of design parameters in building

envelope and HVAC system play an important role

[68-69]. In other words, optimization techniques

aim to solve problems in a systematic way by

producing a set of solutions based on predefined

objectives that are functions of design variables [70].

In the literature [71], savings of 5% to 30% in

annual energy consumption for lighting, cooling

and heating due to optimized building and HVAC

design has been reported.

The most common optimization theory is Genetic

Algorithm(GA) [72]. Its popularities comes from

the easiness of implementation since it can take into


Page 5

account discontinuous design parameters instead of

smoothing the approximating objectives. And its

population-based search has an advantage in multi-

criteria optimization decision making, which elicits

the specific optimization technique used in this

passage—multi-objective genetic algorithm

(MOGA). The obvious characteristics of this

method is to treat constraints as criteria and force

solution into desired feasible region(by penalizing

Pareto rank of infeasible solutions) [73].

2.2.3 Combined design of simulation and

optimization

In this paper, the simulation and optimization are

well combined to investigate the guidelines for

TABS designers. The methodology is shown in

Figure 2.

Figure 2 Integration schematics of optimization and simulation

A case study has been built up in TRNSYS, in which

the building with TABS system in case study has

been modeled and simulation results of energy and

comfort are available.

Optimization and simulation have been integrated

on the platform of modeFrontier. Some design

variables in TRNSYS model can be re-defined as

inputs (pipe dimension and supply water variables)

and some simulation results can be selected as

outputs (energy and comfort). The selection of

input values is made by Design of experiments

(DOE), which enables the number of designs and

the content of the sequence can be defined by the

user. The scheduler is based on the user’s sequence

defined in the DOE table. The outputs can be

related to objectives either maximize or minimize

the value. By clarifying objectives, the optimization

method—multi-objective genetic algorithm

(MOGA) is applied to help inputs selection in

purpose of driving the corresponding outputs

towards objectives.

2.3 Case study

2.3.1 Location and basic building

information

The building called Hollandsch Huys in case study

(Figure 3) is a 5-storeis multi-functional building

located in the city of Hasselt, Belgium.

Figure 3 Building in case study--Hollandsch Huys

The TABS system embedded in both floor and

ceiling for heating and cooling, which integrated

with air handling unit as the HVAC system. TABS

system has been simplified modeled using an

equivalent 1D model with one pipe instead of 3D

model, which is based on the work of (Wout Parys

and Dirk Saelens, 2001) [74]. The model is

subdivided in 12 thermal zones based on the layout

of pipes in the TABS system. The spatial indoor

comfort level is also measured by the overheating

and underheating hours in each thermal zone.

Zone 1 (Figure 4) has been selected for case study

but the whole building with system has been

modeled. It is located on the first floor of the

building and more detailed information is listed in

Table 1.

2.3.2 Control strategy


Page 6

2.3.2.1 Top level control

Top level control decides the running mode of the

system which relates to the convective heat transfer

coefficient in TABS (Table 2). According to the

average ambient temperature, three modes of

TABS can be specified including heating mode, free

running mode and cooling mode. The supply water

temperature set points depend on the average

ambient temperature during the six previous hours,

as shown in Figure 5.

Figure 4 Zone 1 in case study

Table 1 Detailed construction and system information of Zone1

Table 2 Operation mode control scheme

Figure 5 Supply water temperature control scheme in reference case

2.3.2.2 supply water mass flow rate control

As shown in Table 1, supply water mass flow rate is

decided by both water scheme and occupied area.

The hourly water scheme can be divided into two

time periods. The water is supplied to the building

in the first 10min of each hour, and the later water

scheme is decided by the temperature difference of

inlet and outlet TABS water at the 10th min. If the

temperature difference is more than 2˚C, the water

should be delivered to the building in the rest 50

minutes, otherwise TABS system would stop water

supply.

2.3.4 Simulation setting (Trnsys)

Typical week:

typical summer week: 4837~5004 hr (July)

typical winter week: 169~336 hr (January)

Time step: 2 min

2.3.3 Optimization setting (modeFrontier)

Input variables

The input variables at pipe level can be divided into

pipe dimension and supply water variables (Table

3). The supply water temperature can be a constant

value during the simulation time or follow a new

linear supply water –ambient temperature

relationship (Figure 6).

Space length, width, height 6.76m*6.95m*2.7m

Façade South/East

18.66/19.18 m2

0.205W/(m2•K)

41.27%

Adjacent wall West/North

18.66/19.18 m2

4.082 W/(m2•K)

Floor/Ceiling 46.98 m2

1.692 W/(m2•K)

weather BE_Brussels-National-64510.tm2

occupancy occupant density 10 m2/occupant

occupancy schedule Monday to Friday

8:00 am-18:00 pm

computer power 140 w

number occupant number

artificial lighting 10 w/m2

Infiltration 0.5 ACH

Solar radiation calculated from weather data

Shading devices irradiation > 250 W/m2irradiation < 150 W/m2

0.3 m

0.0266 m

0.002 m

12.6 KJ/hmK

588.77 L/h

0.00189 m2⁰C/W

0.071 m2⁰C/W

Data of room

pipe wall conductivity

supply water mass flow rate

internal thermal resistance(Rint)

circuit thermal resistance(Rcircuit)

Data of TABS configuration

loweredraised

pipe spacing

pipe outside diameter

pipe wall thickness

Internal laod

(zone 10 & 12

are zero)

Orientation

Area

Overall U-Value

Glazing fraction façade

Orientation

Area

Overall U-Value

Area

Overall U-Value

Floor Ceiling

Heating mode T_avg_3day < 13 ˚C 28.8 21.6

Free running mode 13 ˚C< T_avg_3day < 15 ˚C 0 0

Cooling mode T_avg_3day > 15 ˚C 21.6 28.8

Convective coeffient (W/m2•K)System modules Ambient temperature


Page 7

Table 3 Inputs of optimization in modeFrontier

Figure 6 Supply water temperature scheme in Linear Tsupply optimization

Optimization Method

Design of experiment (DOE)—Uniform Latin

Hypercube, number of designs: 200

Scheduler—Multi objective genetic algorithm

(MOGA-II), generations: 10

Objectives

Minimizing E_tot

E_tot indicates the thermal energy supply from

TABS, which indicates the integration of both

heating and cooling capacity of TABS system over

the simulation period.

Minimizing uncomfortable hours

Uncomfortable hours includes both overheating and

underheating hours, which generates when the

average building temperature is larger than 26 ˚C or

smaller than 19 ˚C.

2.3.4 Optimization scheme

a. Pipe dimension (including mass flow rate)

optimization

b. Constant supply water temperature optimization

c. Linear supply water temperature optimization

d. Pipe dimension (including mass flow rate) and

linear supply water temperature optimization

3. Result and discussion

The following questions have been answered in this

paper.

Optimization part

a) What is the influence of dimension

optimization in terms of energy saving and

indoor comfort?

b) What is the influence of supply water

temperature optimized as a constant in

terms of energy saving and indoor comfort?

c) What is the influence of supply water

temperature optimized with a linear

relationship of ambient temperature in


d) What is the influence of supply water

temperature optimized with a linear

relationship of ambient temperature

combined with dimension optimization in


e) Which optimization method is more useful?

Design method part

a) What are the necessary inputs and

corresponding outputs of current design

methods?

b) What is the designs of case study under

each methods?

c) What is the drawback of current design

methods?

range step

pipe spacing 0.2~0.4m 0.01m

pipe outside diameter 0.006~0.04m 0.001m

number of loops 1~23 1

specific mass flow rate 0.0028~0.007kg/(s•m2) 0.00035kg/(s•m2)

summer week 16~29 ⁰C 0.5 ⁰C

winter week 26~40 ⁰C 0.5 ⁰C

Ya 26.5~30 ⁰C 0.5 ⁰C

Yb 19~26 ⁰C 0.5 ⁰C

Yc 13~19 ⁰C 0.5 ⁰C

X2 7~20 ⁰C 0.5 ⁰C

X3 (X2<X3) 15~26 ⁰C 0.5 ⁰C

pipe dimension variables

Supply water variables

linear supply water temperature

constant supply water temperature

Ya Yb Yb

Yc

-20 -15 15 20 35 40

Sup

ply

wat

er

Tem

per

atu

re (

°C)

Ambient Temperature (°C)

X2 X3


Page 8

3. 1 Optimization

3.1.1 All dimension parameters optimization

The pipe diameter, pipe spacing, loop length and

mass flow rate in zone1 change at the same time to

achieve lower energy consumption and higher

indoor comfort. The two conflicting performance

targets are generally considered complementary but

competitive functional requirements. In winter

(Figure 7), only the energy supply from TABS is

plotted since the weekly uncomfortable hour is too

small. There are other dimension designs yielding

more energy supply than the reference design.

Figure 7 Pipe dimension optimization of a typical winter week

In summer time (Figure 8), the pipe dimension

optimization result is better than reference result

since lower energy or higher comfort could be

reached by optimization. The minimum weekly

uncomfortable hour design and minimum weekly

energy supply design are marked as B and A. By

dimension optimization, the maximum energy

saving reaches 44.52% (Figure 9) and the comfort

level improves maximally 65% (Figure 10).

Among the involved dimension design variables,

pipe spacing and diameter are two important

parameters according to the sensitivity analysis

shown in Figure 11. For larger pipe diameter, there

is more contact area and more energy supply. But

there is more uncomfortable hours since it takes

more time for heat transfer. The decreasing pipe

spacing results in longer loop length, according to

equation (Equation 2). Then the more heat will be

delivered to the building and more thermal comfort

will be achieved.

(Equation 2)

Figure 8 Pipe dimension optimization of a typical summer week

Figure 9 Energy supply boundary comparison of dimension optimization in summer

Figure 10 Uncomfortable hours boundary comparison of dimension optimization in summer


Page 9

Figure 11 Sensitivy analysis of pipe dimension in dimension optimization

3.1.2 Constant supply water temperature

optimization

Figure 12 Tsupply constant optimization in a typical summer week

Figure 13 Energy supply boundary comparison of Tsupply constant optimization in a typical summer week

To compared with existing design method, supply

water temperature is supposed to be a constant

value in a certain period of time. In summer (Figure

12), the optimization results form a Pareto front

and the reference result turns out to be a dominated

Figure 14 Uncomfortable hours boundary comparison of Tsupply constant optimization in a typical summer week

solution, which is less competitive in terms of the

two objectives. Similarly, the boundaries of

optimization are design C for minimum energy

supply (Figure 13) and design D for minimum

overheating (Figure 14).

3.1.3 Linear supply water temperature

optimization

The original control strategy of supply water

temperature is dependent on a linear relationship

with ambient temperature. Since the system works

in heating, cooling and free running mode, the

relationship can still be supposed to be linear.

According to the annual weather data, the

temperature range is -8.6 ˚C to 30.6 ˚C. So there

are 5 variables in this scheme: Supply water

temperature Ya, Yb, Yc, switching point ambient

temperature X2 and X3. The optimization process

is the re-definition of control strategy over all

operation modes and it is unnecessary to investigate

typical winter week because the typical summer

week involves all operation modes (heating, free

running and cooling).

The linear supply water temperature optimization

result is in Figure 15. The reference case is a

dominated solution compared with the Pareto

front and more optimal control strategy are

available. According to the supply water

temperature sensitivity analysis (Figure 18), supply


Page 10

water temperature Yb is most negative correlated

to energy supply from TABS and is most positive

correlated to uncomfortable hours. This is because

supply water temperature Yb involves in all

operational modes. Higher supply water

temperature Yb indicates supply water temperature

is higher in cooling mode and lower in heating

mode, which brings more overheating hours and

less energy supply. Similarly, the boundaries of

optimization are design E for minimum energy

supply (Figure 16) and design F for minimum

overheating (Figure 17).

Figure 15 Tsupply linear optimization of a typical summer week

Figure 16 Energy supply boundary comparison of Tsupply linear optimization in a typical summer week

Figure 17 Uncomfortable hours boundary comparison of Tsupply linear optimization in a typical summer week

Figure 18 Sensitivity analysis of supply water control temperature in Tsupply linear optimization

3.1.4 Pipe dimension (including mass flow

rate) and linear supply water temperature

optimization

Since both pipe dimension optimization and supply

water temperature linear optimization operation

are effective optimization methods, the

combination has been investigated to approach the

two conflicting objectives (Figure 19). Similar to

previous optimization, there are always non-

dominated solutions instead of the reference.

Similarly, the boundaries of optimization are design

G for minimum energy supply (Figure 20) and

design H for minimum overheating (Figure 21).


Page 11

To figure out the influence of dimension and supply

water temperature, a synthesized sensitivity analysis

has been made (Figure 22). The supply water

temperature B has more influence than other

parameters and its correlations with energy supply

Figure 19 Pipe dimension & Tsupply linear optimization of a typical summer week

Figure 20 Energy supply boundary comparison of pipe dimension & Tsupply linear optimization in a typical summer

week

Figure 21 Uncomfortable hours boundary comparison of pipe dimension & Tsupply linear optimization in a typical summer

week

Figure 22 Sensitivity analysis of all parameters in Pipe dimension & Tsupply linear optimization

and indoor comfort are the same as previous (-0.713 to energy supply & -0.869 to uncomfortable hours). Pipe diameter is more effective than other dimension parameters and it is positive correlated (0.381) to TABS supply energy and negative correlated (-0.196) to uncomfortable hours. Its correlation is always opposite to other dimension parameters.

3.1.5 Optimization comparison

To figure out the optimal optimization method,

there are two ways of comparison.

3.1.5.1 Pareto front of all optimization

The results of ‘pipe dimension & Tsupply linear

optimization’ are more similar to and overlapped by

the ‘linear Tsupply optimization’ than the ‘dimension

optimization’. The supply water temperature scheme

has more influence on energy and comfort than pipe

dimension. The Pareto front of all optimization

results (Figure 23) mainly come from ‘dimension

optimization’, but the boundaries still come from

‘pipe dimension & Tsupply linear optimization’ and

‘linear Tsupply optimization’. So results from the each

optimization can merely get the local optimum and

the optimization results from all optimization lead

to global optimal values.


Page 12

Figure 23 All optimization results comparison and total Pareto front

3.1.5.2 Boundary of all optimization

The boundaries of optimization indicate the

capability of each method. To investigate the

potential of each optimization, the optimal results

under single objective are shown in Figure 24 &

Figure 25.

Minimize E_tot

Compared with reference design, the energy saving

of each optimization is marked in Figure 24. ‘Pipe

dimension optimization’ and ‘linear Tsupply

optimization’ have similar energy savings. ‘Tsupply

constant optimization’ is the least effective

optimization in energy saving and ‘pipe dimension &

Tsupply linear optimization’ saves most energy.

Figure 24 Single objective comparison (Energy supply) of boundary values in each optimization

Minimize uncomfortable hours

The improved comfort of each method is shown in

Figure 25. ‘Tsupply constant optimization’ and ‘pipe

dimension & Tsupply linear optimization’ can almost

eliminate the indoor uncomfort. The collaboration

of dimension and supply water temperature has

more influence than single optimization.


Page 13

METHOD

Rough sizing peak cooling load operative temperature floor heat outputdaily heat gain orientation average core temperature

internal resistance of slab circuit resistance supply water temperature

number of active surfaces operation strategy

Simplified model based on finite difference method(FDM) all related dimension parameters supply water temperature indoor temperature

hourly heat gain façade thermal resistance supply water temperature

room air conditioning setpoint ambient temperature heat output

circuit thermal resistance internal thermal resistance

floor covering R value heat output differential temperature

pipe spacing

supply water temperature floor covering R value floor surface temperature floor heat output

total pipe length effective floor area pipe spacing pipe diameter

inside design temperature maximum allowed pipe length number of circuits actual circuit length

total water flow flow rate in single circuit

pressure drop in single circuit

floor heat output surface heat transfer coefficient floor surface temperature

effective floor area inside design temperature total water flow requirement center distance of pipe

floor construction type floor covering R value supply water temperature

differential temperature total water flow

pressure drop in single circuit

OUTPUT

Manufacture in USA

Manufacture in Canada

Simplified sizing by diagrams

Straightforward unknown but bounded method (SUB)

Rehva diagram

INPUT

Figure 25 Single objective comparison (Uncomfortable hours) of boundary values in each optimization

3.1.6 Optimization conclusion

All optimization can provide a better design than

the reference case because the energy and comfort

of reference case is a dominated solution behind the

Pareto front. Due to the conflicting objectives, all

optimization results follow the decreasing energy

and increasing uncomfort trend. The potential of

each method can be observed from boundaries.

There is one thing that all the optimization methods

share in common. Compared with reference case,

objective min_E_tot can save energy and improve

indoor comfort at the same time while objective

min_uncomfortable hours can decrease

uncomfortable level greatly but extra energy supply

is needed.

Among all optimization methods, ‘pipe dimension &

Tsupply linear optimization’ can eliminate indoor

uncomfort and save the most energy than others.

However, the Pareto front of all optimization

mainly come from ‘Pipe dimension optimization’.

Points on the Pareto front are non-dominated

solutions, which indicates the best optimization

method has to be selected on the base of design

purpose.

3.2 Design method

3.2.1 Qualitative analysis

Due to the specific assumption and simplification of

current methods, TABS designers have to acquire

specific system information and follow the

corresponding procedure. To clarify the difference

between all existing methods, a comparison of

necessary inputs and outputs has been listed here

(Table 4.).

Table 1 Inputs and outputs comparison of current TABS design methods

Page 14

3.2.2 Quantitative analysis

The dimension and supply water temperature from

all existing methods, ‘pipe dimension optimization’

and ‘Tsupply constant optimization’ have been

compared. The range value is the boundary value

fitting the TRNSYS simulation. Reference is the

design in case study.

3.2.2.1 Comparison of pipe diameter

The standard diagram method yields similar

diameter as the reference (Figure 26). The

manufacture designs and design from Rehva

guidebook are similar. From the dimension

optimization, the reference diameter is oversized

for minimal uncomfortable hours and undersized

for minimal energy supply. Smaller pipe diameter

results faster flow velocity and less contact area.

Point A is the smallest pipe diameter in range and

yields minimal energy supply. However, the

minimal uncomfortable hours needs a large

diameter instead of the largest boundary value.

Figure 26 Pipe diameter comparison of current design methods

3.2.2.2 Comparison of pipe spacing

The standard diagram method suggests a pipe

spacing similar to minimum uncomfortable hours

optimization and USA manufacture (Figure 27).

The reference case meet the requirements from

Canada manufacture and Rehva guidebook.

Compared with the dimension optimization, the

reference spacing is a medium value between the

optimization boundaries. The decreasing pipe

spacing results in longer loop length, then the more

heat will be delivered to the building and more

thermal comfort will be achieved.

Figure 27 Pipe spacing comparison of current design methods

3.2.2.3 Comparison of loop length

The designed loop length in standard diagram

method have different values in winter and

summer, which is unrealistic. The manufactures

suggest to apply a pipe length of around 90m in

light commercial buildings. The Rehva guidebook

instructs designers to apply short length loops,

which is close to requirement of the minimal

uncomfortable hours. To minimize the energy

supply, the maximum pipe length is required

(Figure 28).


Page 15

Figure 28 Pipe loop length comparison of current design methods

3.2.2.4 Comparison of specific mass flow rate

The standard diagram method suggests the maximum mass flow rate in winter, which is twice the mass flow rate in summer (Figure 29).

Figure 29 Specific mass flow rate comparison of current design methods

The reference case meet the requirements from

USA manufacture, standard diagram design of

summer and Rehva guidebook. The dimension

optimization give similar designs for two conflicting

objectives, which doubles the design in reference.

3.2.2.5 Comparison of supply water temperature

The supply water temperature in reference case is

the average value during the simulation time. By

‘Tsupply constant optimization’, reference case should

supply higher temperature in winter for both

minimizing uncomfortable hours and minimizing

energy supply (Figure 30). In summer, the

reference design should supply lower temperature

of water to relieve overheating problem. The

standard diagram design suggests similar results as

the optimization and reference. The manufacture

can only provide instruction for winter heating

period and the supply water temperature of Canada

manufacture is too high that could cause energy

wasted and overheating problem. For supply water

temperature design, Rehva guidebook can only

provide complete information in design with 0.3m

as pipe spacing, which is contrary to the dimension

design. Rehva guidebook only provide complete

information in design with 0.15m as pipe spacing in

dimension design. The design from Rehva suggests

the lowest temperature in summer and a high

temperature in winter. In other words, the

production system would be oversized. Another

design method from scientific organization—SUB

method only shows the situation in summer because

the method is used in the reverse way. In SUB

design, the supply water temperature is close to the

design in minimizing E_tot.


Page 16

Figure 30 Supply water temperature comparison of current design methods

3.2.3 Comparison of performance

The available performance of typical winter week

and summer week is shown in Figure 31& Figure

32. During the winter time (Figure 31), designs

from Rehva 0.3m spacing and Canada manufacture

are less competitive because of oversized system

and overheating. Dimension optimization design

and design from standard diagram are both non-

dominated solutions.

In summer week (Figure 32), design from Rehva

guidebook and standard diagram cannot provide a

better solution than the reference case. The design

from SUB demands less energy supply but brings

more overheating hours. The Pareto front of all

optimization represents the non-dominated

solutions.

3.2.4 Current design methods conclusion

Based on previous analysis, there are some

drawbacks of current design methods.

Limited application

Among all the design methods, the methods from

manufactures can only be used for spacing heating

in winter and the methods from scientific

departments also cannot be easily applied unless the

strict assumption has been fulfilled. For example,

the straight forward unknown but bounded method

(SUB) would have unpractical dimension results.

The design absence of some methods come from

the reverse application.

Unpractical application

The standard method gives different design

dimension parameters due to seasonal change,

which is unrealistic in practice. The dimension

optimization method suggests the same value

regardless of simulation time.

Oversized system

Due to assumption and simplification from

manufactures, the design from manufactures tend

to give oversized system suggestion. In this case,

more energy supply is needed but more

uncomfortable also exists.

4. Conclusion

This passage mainly discuss the role of optimization

and simplified methods in the design of TABS

system. TABS system have been widely used

because of the energy saving and improved indoor

comfort. The thermal inertia property functions

well in peak shaving and time lag, which brings

some economic benefits. The allowed application of

low grade energy makes TABS system an adaptive

design integrated with other systems, such as

ground-coupled HVAC system.


Page 17

Figure 31 Performance comparison of current design methods in a typical winter week

Figure 32 Performance comparison of current design methods in a typical summer week


Page 18

Considering the design complexities, several design

methods have been investigated to figure out the

optimal solution. Based on the previous simulation

results and analysis, optimization in TABS design is

important which can be illustrated in two aspects.

To begin with, there are some limitation and

drawback of existing design methods. In general,

the existing methods are over-simplified and

inaccurate. The designers cannot find out an

optimal solution to meet their special purpose.

There is no information on pipe configuration and

control strategy is limited. The design method from

manufactures assumes large heat loss and make

over-sized system to meet the promise to

customers. Some design methods cannot be easily

applied unless the strict assumption has been

fulfilled. The design of TABS includes both pipe

dimension and supply water scheme. Most of

existing methods suppose the dimension parameters

are known and the supply water design is based on

dimension design. However, there would be some

problem when these design methods are used in the

reverse way. In other words, the design of

dimension cannot be based on the known supply

water design. Due to seasonal changes, the

dimension design from some methods can be

different in different seasons, which is unpractical

since the construction cannot be changed. So the

current design methods cannot satisfy the TABS

design.

By optimization, better solutions are available. Less

energy supply and more indoor comfort can be

achieved. To investigate the role of optimization,

there are 4 types of optimization discussed in this

paper (‘Pipe dimension optimizaiton’, ‘Tsupply linear

optmization’, ‘Tsupply constant optimization’ and ‘pipe

dimension & Tsupply linear optimization). All

optimization results follow the trend of decreasing

energy supply with increasing uncomfort level.

Another common point of all optimization is that

objective min_E_tot can save energy and improve

indoor comfort at the same time while objective

min_uncomfortable hours can decrease

uncomfortable level greatly but extra energy supply

is needed. The potential of each optimization

method is different which can be observed from

boundaries. Among all optimization methods, ‘pipe

dimension & Tsupply linear optimization’ can eliminate

indoor uncomfort and save the most energy than

others. However, the Pareto front of all

optimization mainly come from ‘Pipe dimension

optimization’. Points on the Pareto front are non-

dominated solutions, which indicates the best

optimization method has to be selected on the base

of design purpose.

In conclusion, the role of optimization in TABS

design is important and current simplified methods

cannot satisfy the designers. But there is no general

conclusion about the specific optimization way since

the specific purpose of each design is different.


Page 19

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Page 25

Appendix


Page 26


Page 27

5. Heat transfer theory and modeling of TABS system in TRNSYS

5.1 TABS modeling in TRNSYS

The case study has been built up in TRNSYS, which

contains active layer in construction to model TABS

system. The active layer contains fluid pipes that

either add or remove heat from the surface and can

be characterized by 5 parameters: specific heat

coefficient of water, pipe spacing (center to

center), pipe outside diameter, pipe wall thickness

and pipe wall conductivity. For a specific wall or

floor & ceiling, there are 4 more parameters to

design the specific area including inlet mass flow

rate, inlet temperature, number of loops and

additional energy gain at the fluid level. Based on

the zone distribution, detailed specification and

control strategy of TABS system can be modeled.

(Equation 2)

In TRNSYS model, the thermal-active building

elements are used to integrate a fluid system(known

as active layer) into massive layers in the structure.

Despite as a multi-dimensional thermal conduction

problem, it could be simplified as a stationary

solution in the x-y plane of a thermo-active

construction element(Figure 33).

5.2 Heat transfer theory of TABS in TRNSYS

5.2.1 2D heat transfer at pipe level

In the basic case, the element has the same property

at each intersection along its z-axis. The equivalent

heat transfer process in x-y plane could be divided

into several steps:

a. heat convection at the interface of water and

pipe;

b. heat conduction inside the pipe, temperature

changes from to ;

c. heat conduction in the x direction, temperature

changes form to ;

d. heat conduction in the y direction, temperature

changes from to or

Figure 33. Structure of the thermo active construction

element system

5.2.2 3D heat transfer

Taken the heat loss along the pipe coil in the z

direction into consideration, the water temperature

inside pipe is not stable. Under this

circumstance, the equivalent thermal resistance is

shown in Figure 34.

Figure 34. Equivalent thermal resistance of TABS system

5.2.3 Mathematical equation of the heat

transfer process

is the total resistance ( ) between the

inlet water temperature and the pipes level

temperature determined by the Resistance Method.

can be calculated through the equation (3-7).

(Equation 3)

(Equation 4)


Page 28

(

)

(Equation 5)

(

)

(Equation 6)

(Equation 7)

—equivalent thermal resistance caused by inlet

and outlet water temperature difference

[(m²·K)/W];

—thermal resistance at the interface of water

and pipe [(m²·K)/W];

—thermal resistance inside pipe [(m²·K)/W];

—equivalent thermal resistance of pipes in star

arrangement [(m²·K)/W];

—pipe spacing(from center to center) [m];

—outer diameter of pipe [m];

—thickness of pipe [m];

—thermal conductivity of construction

[W/m•K];

—thermal conductivity of pipe shell [W/m•K];

—specific mass flow rate of pipe water

[kg/s•m2]

—loop length [m];

1.2.4 Detailed thermal resistance in

reference design

Zone 1

= 0.0035 [kg/s•m2]

(

)

[

]

[

]

According to the building components information

(Table 5) of the ceiling/floor embedded with active

layer, the thermal resistance of the whole

construction is shown in Figure 35.

Figure 35 Thermal resistance model of floor/ceiling construction


Page 29

Table 5 Construction information of floor/ceiling embedded with active layer

Layer (inside to outside)

Thickness Type Conductivity (kJ / h m K)

Capacity (kJ / kg K)

Density (kg/m3)

Thermal resistance (m2•K/W)

CARPET 0.005 massive 0.216 1.3 200 0.0064

FINISHING 0.09 massive 3.96 1.1 1900 0.0063

XPS 0.005 massive 0.1224 1.45 35 0.0114

CON_TOP_BOTM 0.05 massive 9 1 2400 0.0016

ACT_LAYER_CAL 0.12 massive 13.32 1 700 0.0025

ACTIVELAYER

active

ACT_LAYER_CAL 0.12 massive 13.32 1 700 0.0025

CON_TOP_BOTM 0.06 massive 9 1 2400 0.00186

6. Case study design in current methods

6.1 Simplified sizing by diagrams in standard [60]

6.1.1 Supply water temperature design

(Forward design)

Inputs

2 active surfaces

= 0.0035 [ ]

Internal resistance

Circuit resistance

Orientation: South & East

Energy entered in the design cooling/heating day(including solar gain, wall transmission, coupling, internal gain, heating, cooling, ventilation and infiltration)

Operation strategy: 4 hour

The operation time of water supply is determined by the temperature difference of supply water and return water at the 10th minute of each hour. The control strategy is designed for 24 hours, but the actual water supply time depends on the water temperature difference. The equivalent operation time is 4 hour since it is the real time of water supply during the simulation period.

Calculation procedure & outputs

Calculate average core temperature

Since the simplified sizing by diagrams in standard method is based on the linear relationship to get the coefficient, the new coefficient of operation 4 hour can be derived by linear extrapolation from data in Table 6 .


Page 30

Table 6 Coefficient for average temperature calculation of the slab

Calculate the supply temperature for removing

cooling energy or supplying heating

energy

6.1.2 Dimension design (Reverse design)

Inputs

In reverse design, the supply water temperature come from the average value during simulation time in the reference design.

Internal resistance

Orientation: South & East


Operation strategy: 4 hour


Calculate average core temperature

Calculate the circuit thermal resistance

Calculate the pipe dimension and specific mass flow rate

The dimension and specific mass flow rate can be calculated by equations (3-7). However, the calculation is not direct because the 5 variables are integrated in these five equations. By the range setting of each variable, the calculation can be done in modeFrontier (Table 7).

Table 7 Dimension design of standard diagram

6.1.3 Building performance of designed

TABS system

By setting the designed system in TRNSYS, the building performance are available by simulation (Table 8).

outputs unit range summer winter

pipe diameter m 0.006-0.04 0.030286 0.030286

pipe spacing m 0.2-0.4 0.23 0.22

pipe length m 6.8-156.6 146.6133 96.68

mass flow rate kg/(s m2) 0.0028-0.007 0.00384 0.00748

Rz m2•K/W 0.031002 0.015915

Rw m2•K/W 0.002287 0.001829

Rr m2•K/W 0.001482 0.001418

Rx m2•K/W 0.008742 0.007941

Rt m2•K/W 0.043513 0.027103

Rt m2•K/W 0.0435 0.0271


Page 31

Table 8 Building performance from standard diagram design

6.2 Straightforward unknown but bounded method (SUB) [65]


(Forward design)

Inputs

= 0.0035 [ ]

Internal resistance

Circuit resistance

Resistance of façade

According to the building components information

(Table 9) of external wall, the thermal resistance of

façade is

Outdoor average temperature

Room heating/cooling set-point



Supply water temperature

For heating

( )

For cooling

( )


Inputs

Internal resistance

Resistance of façade

Outdoor average temperature

Room heating/cooling set-point



In reverse design, the supply water temperature come from the average value during simulation time in the reference design.

For heating

For cooling

summer 0.625 30

winter 0.634 0.33

summer 0.394 0

winter 0.771 0.067

Supply water

design

Dimension

design

weekly supply

energy (kJ/m2)

weekly uncomfortable

hours (hr)

Design

method


Page 32

Table 9 Construction information of the facade

Layer (inside to outside) Thickness

(m) Type

Conductivity (kJ / h m K)

Capacity (kJ / kg K)

Density (kg/m3)

Thermal resistance (m2•K/W)

1GYPSONBOARD 0.013 massive 0.9 0.84 950 0.004012346

1CAVITY50 0.05 massive 1 1 1.2 0.013888889

1OSB 0.012 massive 0.468 1.3 650 0.007122507

1CELLULOSEINSULATION 0.184 massive 0.18 1.3 50 0.283950617

1WOODFIBERBOARD 0.018 massive 0.198 2.1 260 0.025252525

1CAVITY65 0.065 massive 1.3 1 1.2 0.013888889

1EXTERNALBRICKWORK 0.115 massive 4.86 0.84 1700 0.006572931

Calculation procedure & outputs Circuit resistance

The circuit thermal resistance is different in different seasons, which is not practical. For every dimension design, the calculated value is out of the range (Table 10). So the straightforward unknown but bounded method (SUB) cannot be used in the reverse way.

Table 10 Dimension design of straightforward unknown but bounded method (SUB)

range summer winter

Circuit resistance

( )

0.449 8.321

pipe diameter (m) 0.006-0.04 0.877 25.53

pipe spacing (m) 0.2-0.4 2.532 31.43

pipe length (m) 6.8-156.6 0.384 0.0117

mass flow rate

( ) 0.0028-0.007

0.00039 0.0000183


TABS system


Table 11 Building performance from straightforward unknown but bounded method (SUB)

6.3 Rehva guidebook [53]

The Rehva guidebook uses several supposed cases (Figure 38) to make diagrams for TABS design. Based on the dimension and supply water design in reference case, the Rehva guidebook can only be used in supply water temperature design (forward design).


(Forward design)

Inputs

= 0.0035 [ ]

summer 0.3007 49.43

winter 0.0714 0

summer / /

winter / /

Dimension

design

Design methodweekly supply

energy (kJ/m2)


hours (hr)

Supply water

design


Page 33

Figure 36 Heat exchange as the function of water temperature and floor covering (pipe spacing T= 150mm)

Figure 37 Heat exchange as the function of water temperature and floor covering (pipe spacing T= 300mm)


Page 34

Heat exchange rate 37 [ ]

Floor covering resistance 0.0064

Figure 38 Sketches of calculated cases for capacity diagrams (thickness of structure layers, position of pipes)

Calculation procedure & outputs Pipe spacing

or

According to Figure 36 & Figure 37, the medium differential temperature can be decided.

For winter

For summer

For winter

For summer


According to the definition of the medium differential temperature (Equation 1), the supply water temperature is related to return water temperature and indoor operative temperature. The determination of supply water temperature has to be acquired by simulation in TRNSYS

(Equation 1)

For winter (no appropriate value)

For summer

For winter

For summer


TABS system

By setting the designed system in TRNSYS, the

building performance are available by simulation

(Table 12)

Table 12 Building performance from Rehva guidebook design method

6.4 Design manual from manufacture in USA [49]

There is only design for winter in this manual.


(Forward design)

Inputs

Heat output ⁄

Indoor design temperature

Floor covering resistance The floor covering is carpet and the thermal resistance is 0.0064 in model. But in consideration of safety factor, the resistance is supposed to be 1 , which is decided by thickness of carpet.

range winter

pipe diameter (m) 0.006-0.04 0.017 0.017 0.017

pipe spacing (m) 0.2-0.4 0.15 0.3 0.3

pipe length (m) 6.8-156.6 13.05 13.05 13.05

0.0035

Circuit resistance

(m2K/W)0.05294 0.07137

mass flow rate

(kg/(s m2))0.0028-0.007 0.0035 0.0035

weekly supply energy

(kJ/m2)weekly uncomfortable

hours (hr)

1.64 0.97 1.79

0.37 22.70

summer

0.0714


Page 35

Figure 39 Output chart of manual from manufacture in USA

Calculation procedure & outputs Floor surface temperature

According to Figure 39, heat output and indoor design temperature decide the floor surface temperature . The floor covering resistance is 1 , the supply water

temperature is .

Dimension design

Table 13 Pipe dimension and heat output chart

The pipe dimension can be decided by heat output (Table 13). The corresponding tube size of heat output can be 3/8'', 1/2'' and 3/4 ''. According to the system design guideline, the recommended pipe dimension for this residential building is 3/8''

Pipe diameter 0.01 [m]

Pipe spacing 0.23 [m]

The recommended length can be get by Table 14.

Table 14 Recommended tube length from manufacture in USA

Table 15 System design guideline from manufacture in USA

Number of circuit

=total pipe length/recommended pipe length


Page 36

pipe length=total pipe length/number of circuit

=188.5/4=47.125 [m]

Mass flow rate

⁄

Pressure drop

The calculated supply water temperature is .

However, the minimal supply water temperature in

chart (Table 16 & Table 17) is . Supposed

the supply water temperature and head loss is linear

relationship , the pressure drop can be decided.


Inputs

Supply water temperature (from reference case)

Floor covering resistance 1

Indoor design temperature

Calculation procedure & outputs Floor surface temperature

According to Figure 39, heat output and indoor design temperature decide the heat output

⁄ .

Dimension design

The pipe dimension can be decided by heat output (Table 13). The corresponding tube size of heat output can be 3/8'', 1/2'' and 3/4 ''. Compared with the forward design, the heat output is lower. So according to the system design guideline, the recommended pipe dimension is 1/2''

Pipe diameter 0.013 [m]

Pipe spacing 0.3 [m]

The recommended length can be get by Table 14.

Number of circuit

=total pipe length/recommended pipe length

pipe length=total pipe length/number of circuit

=143.6/2=71.8 [m]

Mass flow rate

⁄

Pressure drop

The calculated supply water temperature is

. However, the minimal supply water

temperature in chart (Table 16 & Table 17) is

. Supposed the supply water temperature

and head loss is linear relationship , the pressure

drop can be decided.


Page 37

Table 16 Head loss when supply water temperature at 100


Page 38

Table 17 Head loss when supply water temperature at 120


Page 39


TABS system


Table 18 Building performance from TABS design manual of manufacture in USA

6.5 Design manual from manufacture in Canada [55]

There is only design for winter in this manual.

6.5.1 Supply water temperature and

dimension design (Forward design)

Inputs

Heat output ⁄

Area 6.76m * 6.95m =

Temperature difference of supply and return water

Floor covering resistance The floor covering is carpet and the thermal resistance is 0.0064 in model. But in consideration of safety factor, the resistance is supposed to be 1 , which is decided by thickness of carpet.

Calculation procedure & outputs Pressure drop

=2.22 GPM

According to the relationship of flow rate and heat output (Figure 40), there are several choices for dimension design (Table 19).

Table 19 Distance on center and flow rate

Distance on center(inch) Flow rate (GPM)

6 1.1

9 1.6

12 2.2

To meet the requirement of pressure drop, the

distance on center has to be 12 inch.


By heat loss and resistance of floor covering, the

supply water temperature can be decided (Figure

41).

Dimension design

The pipe dimension and pressure drop has to fit the

following relationship (Table 20). The requirement

of this system is 2.2, the possible dimension designs

are listed in Table 21.

Table 20 Pipe dimension and pressure drop relationship

Table 21 Possible dimension designs at total pressure drop 2.2 GPM

range

pipe diameter (m) 0.006-0.04 0.01 0.013

pipe spacing (m) 0.2-0.4 0.23 0.3

pipe length (m) 6.8-156.6 47.125 71.8


hours (hr)0.17 4.37

Supply water

design

Dimension

design

mass flow rate

(kg/(s m2))

0.0028-

0.0070.0035 0.0021


(kJ/m2)0.8 1.34

winter

Circuit resistance

(m2K/W)0.061 0.092

1 2.2 3 1'' 506 600-750

3 1'' 253 600-750

1.7 3/4'' 253 500-600

1.3 5/8'' 253 325-500

3 1'' 169 600-750

1.7 3/4'' 169 500-600

1.3 5/8'' 169 325-500

1 1/2'' 169 250-325

Tube

size

Loop length

(ft)

Recommended

loop length (ft)

2

3 0.7

1.1

Flow rate

(GPM)

Number

of circuit

Max flow

rate


Page 40

Figure 40 Flow rate and heat output chart at 10 supply/return temperature differential

Figure 41 Water supply temperature for 12 inch on center


Page 41

All the designed pipe length are not in the range of

recommended loop length. So there are two

possible designs which are most close to the range

of recommended loop length: 3/4''& 5/8''.


TABS system

By setting the designed system in TRNSYS, the

building performance are available by simulation

(Table 22).

Table 22 Building performance from TABS design manual of manufacture in Canada

7. Single pipe dimension optimization

7.1 Simulation and modeling

TRNSYS model

The simulation in MODEFRONTIER is integrated with the basic ‘only building’ TRNSYS model. The indoor environment of building is only controlled by the TABS system without other heating or cooling equipment. The supply water temperature of TABS is controlled by the ambient temperature and supply water flow rate is controlled by the temperature difference of supply and return water(TABS outlet) temperature at 10th minute of each hour. The air handling unit(AHU) is responsible for the ventilation and the boiler works as a supplement in heating mode.

TRNSYS simulation time

4837-5004hr, a typical summer week in July

Input variable

According the thermal resistance model, there are pipe sizing related parameters: pipe diameter, pipe distance, deepness of embedded pipe and specific mass flow rate.

-pipe diameter of active layer, which ranges from 0.006m to 0.04m with a step of 0.0005m

-pipe spacing between pipe centers, which ranges from 0.2m to 0.4m with a step of 0.01m

--pipe deepness, which ranges from 0.09m to 0.13m inside original active layer(from the pipe position to the outside covering) with a step of 0.01m

Optimization Method

Design of experiment(DOE)—Uniform Latin Hypercube, number of designs: 200

Scheduler—Multi objective genetic algorithm(MOGA-II), generations: 10

Objectives

Minimizing E_tot:

E_tot indicates the thermal demand of building, which includes both heating and cooling capacity of TABS system.

Minimizing Overheating:

Overheating is the weekly overheating hours which generates when the average building temperature is larger than 26 ˚C.

7.2 Thermal demand and pipe dimension

According to Figure 42, Figure 43 & Figure 44, the thermal demand increases when pipe diameter or pipe deepness increases and decreases when pipe spacing increases. Thermal demand is the integration result of thermal capacity of TABS over the simulation time.

a. The thermal capacity of TABS system is

determined by both temperature difference of

supply and return water, and the water mass

flow rate (Equation 8).

pipe diameter (m) 0.006-0.04 0.022 0.019

pipe spacing (m) 0.2-0.4 0.3 0.3

pipe length (m) 6.8-156.6 28 28


(kJ/m2)5.04 5.13


hours (hr)49.9 49.93

Circuit resistance

(m2K/W)0.042 0.042

mass flow rate

(kg/(s m2))0.0028-0.007 0.008 0.008

winter

3/4'' 5/8''range


Page 42

b. According to the simulation data (Figure 45 &

Figure 47), the temperature difference is not

large, so the determinant factor is water mass

flow rate, which increases with the pipe

diameter growth (Figure 46 & Figure 48).

( )

(Equation 8)

Return flow rate

( )

(Equation 9)

c. And the specific mass flow rate is determined

by the temperature difference at 10 minute of

supply and return water as shown in (Equation

9), which is described in the TRNSYS

model(Every hour, water circulates for the first 10

minutes. Then, calculate temperature difference of

supply and return water at 10th minute, If

temperature difference is higher than 2°C, the water

will circulate for the next 50 minutes; If temperature

difference is lower than 2°C, the water pump stops for

the next 50 minutes).

7.2.1 Pipe diameter optimization and

thermal supply

In this sense, the probability of temperature difference at the first 10th min of each hour is larger than 2°C increases with the growth of pipe diameter, as shown in Figure 49. The temperature difference of return water and supply water at 10th of ceiling in zone1 is plotted, and larger the pipe diameter, more dots are over the boundary of 2˚C. All the points indicate either pipe diameter has more water supply opportunity than the other one. So the more dots over the 2˚C boundary, the more possibility of water supply.

This is because the heat transfer determinant depends on the specific situation. With smaller pipe diameter, the velocity in pipe is faster and the contact area is smaller. In this sense, heat transfer is

less sufficient because of fast velocity so the temperature difference of supply and return water is not so large. While in the case of larger pipe diameter, the velocity in pipe is slower and more contact area is available. It takes more time for heat transfer and the temperature difference is larger, but the average temperature difference is smaller because of more sufficient heat transfer.

Figure 42 Pipe diameter optimization and weekly thermal supply

Figure 43 Pipe spacing optimization and weekly thermal supply

Figure 44 Pipe deepness optimization and weekly thermal supply


Page 43

Figure 45 Temperature and mass flow rate in TABS outlet (pipe diameter)

Figure 46 Mass flow rate and pipe diameter

Figure 47 Temperature and mass flow rate in TABS outlet (pipe spacing)

Figure 48 Mass flow rate and pipe spacing

7.2.2 Pipe spacing optimization and thermal

supply

When there is a larger pipe spacing, the probability of temperature difference at first 10th min of each hour is decreasing (Figure 50). The temperature difference of return water and supply water at 10th of ceiling in zone1 is plotted, and smaller the pipe spacing, more dots are over the boundary of 2˚C. All the points indicate the water supply schemes of two pipe spacing systems are different from each other. So the more dots over the 2˚C boundary, the more possibility of water supply. And the smaller pipe spacing has more water supply opportunity than the larger ones. This is because the decreasing pipe spacing results in longer loop length, according to equation 2. Then the more heat will be delivered to the building and more thermal comfort will be achieved.

7.2.3 Pipe deepness optimization and

thermal supply

There is not much difference in thermal supply for both ceiling and floor cases when pipe deepness changes. This is because the determinant outlet water temperature and mass flow rate do not change much as well. The changeable range of deepness is quite narrow because of the characteristics of active layer. According to the TRNSYS manual, there are several rules for active layer design (Figure 52).

a. For entering the layers of the floor heating

system start with a thickness of the later

adjacent to the active later with a

thickness≥0.3*pipe spacing.

b. Define an active layer. Automatically, a new

layer with the same properties of the layer

above the active layer is added below.

c. Enter an insulation layer with a resistance of at

least 0.825 .

d. The thickness of the layer between the active layer and the insulation layer≥1/2* outside pipe diameter.


Page 44

Figure 49 Temperature difference of supply and return water at 10th minute of ceiling in zone1 (pipe diameter)

Figure 51 Temperature difference of supply and return water at 10th minute of ceiling in zone1 (pipe deepness)

Figure 1 Temperature difference of supply and return water at 10th minute of ceiling in zone1 (pipe spacing)


Page 45

In this case, the possible range of pipe deepness is quite limited, which indicates the pipe deepness is not a determinant factor for optimization (Figure 51).

Figure 52 Scheme of active layer in TRNSYS

7.3 Overheating hours and pipe dimension

7.3.1 Pipe diameter optimization and

overheating hours

As shown in Figure 53, weekly overheating hours decreases when pipe diameter increases. This could be explained by the declining return water temperature in pipes with the increase of pipe diameter, shown in Figure 54. The temperature of supply water is controlled by outdoor ambient temperature. The temperature difference is decreasing, which indicates TABS system absorbing more heat. In this case, a more comfortable indoor environment and less overheating hours would be achieved.

Figure 53 Pipe diameter optimization with weekly overheating hours

Figure 54 Pipe water temperature, indoor air temperature and pipe diameter

7.3.2 Pipe spacing optimization and

overheating hours

As indicated in Figure 55, more overheating hours results from larger pipe spacing. This is because the return water temperature grows larger in larger spacing system (Figure 56). The larger pipe spacing, the smaller output is. Then the TABS system absorbs less heat and results in higher indoor temperature in the case of larger pipe spacing.

Figure 55 Pipe spacing optimization and weekly overheating hours

Figure 56 Pipe water temperature, indoor air temperature and pipe spacing


Page 46

7.3.3 Pipe deepness optimization and

overheating hours

Figure 57 Pipe deepness optimization and overheating hours

There is not much difference in overheating hours for both ceiling and floor cases when pipe deepness changes (Figure 57).

7.4 Pareto front in single dimension optimization

Considering the two conflicting objectives: low thermal demand and high thermal comfort, the multi-objective genetic algorithm is applied to solve the problem. To compare with energy and comfort standard, the annual results of some points are also indicated. Unfilled dots are the dominated solutions and the filled ones are a set of optimal trade-offs(all objectives are equally important), which is called the non-dominated solution or PARETO FRONT. The Pareto front of pipe diameter and pipe spacing optimization are shown in Figure 58 & Figure 59.

Since there are restrictions on both objectives, the selected solutions can be determined by the specific purpose of the TABS system designers.

a. According to Energy Benchmarks Codes &

Standards, the annual thermal demand for low

energy consumption office building is

40kWh/m2•yr and 15kWh/m2•yr for passive

office buildings. Compared with this code, the

designers for TABS system could get an

appropriate range of pipe diameter for specific

building types. For example, there are some

disadvantages for a passive house, such as

system running noise and high overheating hour

risk. In this case, the annual thermal demand

should be more than 15kWh/m2•yr to avoid

the drawbacks of passive house.

b. Given the standard from the Government

Buildings Agency and the Government

Occupational Health Agency in the

Netherlands, a good thermal indoor climate had

to comply with the limitations:

25˚C may not be exceeded during

maximally 100 hours a year;

28˚C may not be exceeded during

maximally 10-20 hours a year;

In the case of TRNSYS model, the overheating set point is 26˚C, and it is obvious that all the annual overheating hours exceed far higher than the standard limit. The whole building is suffered from severe overheating problem. As for the energy demand, this building is in a quite energy-saving way.


Page 47

Figure 58 Energy demand and thermal comfort of a typical summer week in July with PARETO FRONT (pipe diameter)

Figure 59 Energy demand and thermal comfort of a typical summer week in July with PARETO FRONT (pipe spacing)

700 800 900 1000 1100 1200 1300 140020

21

22

23

24

25

26

27

28

Weekly thermal demand from TABS[kJ/m2.week]

Weekly

overh

eating h

ours

[hr]

Energy demand and thermal comfort of a typical summer week in July

3mm

10mm

17mm

24mm

31mm

38mm

45mm

weekly simulation result

pareto front

ORIGINAL PIPE DIAMETER 0.0266m

Annual overheating hours 785hr

Annual thermal demand 22.51kWh/m2

PIPE DIAMETER 0.006m

Annual overheating hours906hr

Annual thermal demand18.42kWh/m2

PIPE DIAMETER 0.04m


Annual thermal demand23.35kWh/m2

950 1000 1050 1100 1150 1200 1250 1300 1350 1400 145018

19

20

21

22

23

24

Weekly thermal demand from TABS[kJ/m2.week]

Weekly

overh

eating h

ours

[hr]

Energy demand and thermal comfort of a typical summer week in July

20cm

22cm

24cm

26cm

28cm

30cm

32cm

34cm

36cm

38cm

40cm

weekly simulation result

pareto front

Pipe spacing 20cm



Pipe spacing 40cm

Annual overheating hours 821.6hr


ORIGINAL pipe spacing 30cm



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