Performance Factor for Floor Heating Systems …...Performance Factor for Floor Heating Systems using New Analytical Formula Henrik Karlsson, PhD Carl-Eric Hagentoft, Professor Chalmers

Performance Factor for Floor Heating Systems using New Analytical Formula

Henrik Karlsson, PhD Carl-Eric Hagentoft, Professor

Chalmers University of Technology, Sweden

Background Floor Heating

• Water-based floor heating is commonly used in the Nordic countries, central Europe and extensively used in Korea

• One main characteristic of floor heating is that space heating is provided at a low supply fluid temperature (i.e. 25°C to 35°C) by utilizing large interior surfaces

• The control is typically provided by a heating curve (feed-forward supply water temperature) in combination with individual room thermostats (ON/OFF) at each zone


Background Floor Heating

• >=250mm thermal insulation underneath the floor heating circuits is usually sufficient in order too prevent losses in the heat distribution

• Floor materials with high thermal resistance increases the required water temperature (and increases the heat loss downwards)

• The insulation efficiency η states the fraction of supplied heat that is conducted upwards (the useful fraction)

• Floor heating with proper design has η >0.96


Background

• Low temperature water-based heating facilitate

– utilization of waste heat

– utilization of solar heat

– the COP of heat pumps

• The future nearly zero-energy buildings, and the low-energy buildings of today, may have significantly lower heat demand due too well-insulated and airtight building envelopes and energy efficient ventilation

• The combination well-designed floor heating and a building with low heat losses yields very low water temperatures in the system.


Background

• Low temperature water-based heating facilitate

– utilization of waste heat

– utilization of solar heat

– the COP of heat pumps

• The future nearly zero-energy buildings, and the low-energy buildings of today, may have significantly lower heat demand due too well-insulated and airtight building envelopes and energy efficient ventilation

• The combination well-designed floor heating and a building with low heat losses yields very low water temperatures in the system. The combination also yields a high degree of self-regulation


Self-regulation

• The supplied heat Qs is proportional to the difference between supply water temperature Ts and return water temperature Tr

Ts

Tr

rsfs TTCVQ

Vf

x


Self-regulation

• The supplied heat Qs is proportional to the difference between supply water temperature Ts and return water temperature Tr

• The amount of heat transferred from the water towards the indoor space Qup depends on:

– Ts and indoor temperature Ti

– Water flow rate Vf

– Thermal properties of the material within the floor construction and surface heat transfer properties

Tr

X, [m]

Ts

Ti

Ts

Tr

rsfs TTCVQ

Tem

pera

ture

Vf

x

Qup


Self-regulation

• What is self-regulation?

Tr

X, [m]

Ts

Ti

Ts

Tr

rsfs TTCVQ

Tem

pera

ture

Vf

x

Qup


Self-regulation


• If the is a positive perturbance within the zone:

– Indoor temperature Ti will increase

Tr

X, [m]

Ts

Ti

Ts

Tr

rsfs TTCVQ

Tem

pera

ture

Vf

x

Qup


Self-regulation




Tr

X, [m]

Ts

Ti

Ts

Tr

rsfs TTCVQ

Tem

pera

ture

Vf

x


Self-regulation




– Supply water temperature Ts is constant (feed-forward controlled)

– Return water temperature will Tr increase

Ts

Tr

rsfs TTCVQ

Vf

x

X, [m]

Ts

Tem

pera

ture Tr

Ti


Self-regulation




– Supply water temperature Ts is constant (feed-forward controlled)

– Return water temperature will Tr increase

– The upward heat flow to the indoor space Qup will decrease

– The supplied heat flow Qs from the primary system will decrease

Ts

Tr

rsfs TTCVQ

Vf

x

X, [m]

Ts

Tem

pera

ture

Qup


Self-regulation


• Self-regulation is an intrinsic negative feedback which will counteract any thermal perturbance in the zone

– Positive perturbance -> negative response

– Negative perturbance -> positive response

Ts

Tr

rsfs TTCVQ

Vf

x

X, [m]

Ts

Tem

pera

ture

Qup


Self-regulation – Dynamic Process (simulated)

• ΔEp [J] is the heat content of an arbitrary thermal perturbance

• ΔEs [J] is the net shift in supplied heat due to the perturbance

• γ [-]is the self-regulation utilization factor which quantifies the ratio between ΔEp and ΔEs

0 1 2 3 4

Time [Days]

Supplie

d H

eat

[W]

0

Qs

ref(t)

DEp

Perturbance DEs= gDEp

Qs

ref(t)+DQ

s(t)

DQs(t)

Self-regulation


Self-regulation – Dynamic Process (simulated)

• ΔEp [J] is the heat content of an arbitrary thermal perturbance

• ΔEs [J] is the net shift in supplied heat due to the perturbance

• γ [-]is the self-regulation utilization factor which quantifies the ratio between ΔEp and ΔEs

• γ close to -1 means that almost the entire heat content in any positive perturbance is utilized. The supplied heat is reduced and the indoor temperature would not rise.

0 1 2 3 4

Time [Days]

Supplie

d H

eat

[W]

0

Qs

ref(t)

DEp

Perturbance DEs= gDEp

Qs

ref(t)+DQ

s(t)

DQs(t)

Self-regulation


Analytical Formula by Karlsson and Hagentoft 2010

• The self-regulation utilization factor γ can be quantified by an analytical formula

• Kup [W/K] is the thermal conductance between Ts and Ti

– High values of Kup is found when:

– Low thermal resistance in the floor cover material

– Small distance between the embedded pipes

– High water flow rate Vf

• Ke [W/K] is the total heat loss (transmission and ventilation)

01,

g

gupe

up

KK

K



• The utilization factor γ will be exceptionally high for:

– Well-insulated buildingspreferably with air-to-air heat recovery

– A floor heating system design in such way that the supply temperature is low (high Kup)

– High insulation efficiency η 01,

g

gupe

up

KK

K



• A detached single-family “passive house” (according to Swedish specification) would result in a self-regulation efficiency γ in the range of 0.85-0.9.

• Multi-level residential houses with concrete floors may have γ >0.9.The heat is transferred both upwards and downwards which increases the thermal conductance between pipe inlet and indoor temperatures.

• Buildings with higher heat losses and inadequate floor heating design may yield γ in the range of 0.5-0.6

01,

g

gupe

up

KK

K



• If the heating system and building show a high degree of self-regulation:

– The heat supply will be robust, heat can not be transferred to the space whenever the indoor temperature is “high”

– The intrinsic self-regulation effect can entirely replace the room controls

– Hence, the control system can be made much simpler and more cost-effective (both material and installation costs can be reduced)


Experimentally validation of the self-regulation utilization factor

• The validity of the utilization factor formula γwill be tested experimentally

• For this purpose, a test room is prepared where the self-regulation process will be measured

The utilisation factor γ has been determined in three different lab tests:

• Analytical solution based on measured system and building properties. The utilisation factor calculated according to formula. Input data are measured properties

• Step-response test. Measuring the stationary shift in heat supply due to the introduction of a stationary thermal perturbance.

• Pulse-response test. Measuring the heat content of the shift in heat supply due to a thermal perturbance in the shape of a pulse.


Test room during winter conditions

• Uavg = 0.29 W/m2K

• Ventilation air flow rate 10 l/s

• Heat recovery, ηt ≈ 0.78

• Afloor= 11.15m2

• Heat demand: 12-13 W/m2

• Supply water temperature: 25.3 - 27.2°C

• The supply air is carefully supplied along the surface of the ceiling with a low air velocity

• Both test room and secondary chamber situated in a large lab hall

• >100 temperature measurement points in the test room

Supply

Retu

rn

3.6 m

3.2

m

Water

temp.

controlQs(t)

Te = -12.5

Tlab(t) ≈ +20

Ti(t)


Test room during winter conditions

• Heat is emitted from thin electrical resistance wires in order to generate a thermal perturbance

• The temperatures at surfaces, in the air volume, the supply and exhaust air is measured continuously with thermocouples

• Air temperatures Ti is measured in 9 locations and at 3 heights. Total 27 measurement points

• The supply and return water temperatures are measured with PT100 sensors (within the water flow)

ΔQp


Floor heating systems

• Three different floor heating systems will be considered in the experiments:

– Lightweight system CC 300

– Embedded heavy concrete systems CC 300 (pipes in the lower part of a 104mm thick slab)

– Embedded heavy concrete systems CC 200 (pipes in the upper part of 104mm thick slab)

CC300 Embedded

PEX Pipe

EPS insul.300mm

EPS insul.

Aluminum

conduction plates

PEX Pipe

CC300 Lightweight

Floor heating systems

• A thin rubber mat covers the top of the slab, or the aluminum plates before top wooden layer is applied

• A 12mm wooden board is applied as top floor cover material


Analytical solution based on measured system and building properties

Lightweight

CC300

Embedded

(low)

CC300

Embedded

(high)

CC200

η Insulation efficiency [-] 0.89 0.85 0.89

Transmission heat loss [W/K] 16.2 16.2 16.2

Ventilation heat loss [W/K] 2.5 2.5 2.6

Ke Total Heat loss [W/K] 18.7 18.7 18.8

Kup [W/K] 19.2 19.6 27.9

Vf Water flow rate [l/h] 89.9 92.4 155.9

Calculated Self-Regulation

Utilization γ [-]

-0.54 -0.55 -0.64

eup

up

KK

K

g


Step-response test - Lightweight system

• Initially the system is in steady-state condition. Indoor temperature 20.2°C

• The perturbance ΔQp = 68.5W is activated at time zero

• The response in the suppled heat Qs is very fast for the lightweight system

• The shift in supplied heat ΔQs is -35.4W

• γ is found as the ratio: ΔQs / ΔQp = -35.4/68.5 = -0.52

60

70

80

90

100

110

120

130

140

150

160

-360 0 360 720 1080 1440

Po

wer,

[W

]Time, [min]

Supplied Heat, Qs

Perturbance, ΔQp

ΔQs


Step-response test - Lightweight system

• Initially the system is in steady-state condition. Indoor temperature 20.2°C

• The perturbance ΔQp = 68.5W is activated at time zero

• The response in the suppled heat Qs is very fast for the lightweight system

• The shift in supplied heat ΔQs is -35.4W

• γ is found as the ratio: ΔQs / ΔQp = -35.4/68.5 = -0.52

25.5

26

26.5

27

-360 0 360 720 1080 1440

Tem

pera

ture

, [°

C]

Time, [min]

SupplyTemperature, Ts

ReturnTemperature, Tr


Step-response test - summary

Lightweight

CC300

Embedded

(low)

CC300

Embedded

(high)

CC200

Initia

l

co

nd

ition

Ts Supply water temperature [°C] 26.92 27.17 25.26

Tr Return water temperature [°C] 25.52 25.70 24.34

Vf Water flow rate [l/h] 89.9 92.4 155.9

Qs Supplied heat [W] 147.1 156.7 163.4

Afte

r new

ste

ad

y-

sta

te

Ts Supply water temperature [°C] 26.92 27.17 25.26

Tr Return water temperature [°C] 25.85 26.01 24.62

Qs Supplied heat [W] 111.2 123.3 115.5

ΔQp Perturbance[W] +68.5 +68.3 +68.6

ΔQs Shift suppliedheat[W] -35.9 -33.3 -47.9

γ Self-regulation utilization [-] -0.52 -0.49 -0.70


Pulse-response test: Embedded CC200 system

0

20

40

60

80

100

120

140

160

180

-1440 0 1440 2880 4320 5760 7200 8640 10080

Effe

kt,

W

Tid, minut

Pulsexcitering - Absoluta effekter

Effekt Golvvärmeslinga

Effekt varmtråd

Pow

er, [

W]

Qs

ΔQp



0

20

40

60

80

100

120

140

160

180

-1440 0 1440 2880 4320 5760 7200 8640 10080

Effe

kt,

W

Tid, minut



Effekt varmtråd

Pow

er, [

W]

Qs

ΔQp



0

20

40

60

80

100

120

140

160

180

-1440 0 1440 2880 4320 5760 7200 8640 10080

Effe

kt,

W

Tid, minut



Effekt varmtråd

ΔEs = -4.5kWh

ΔEp = 6.6kWh

Pow

er, [

W]

Qs

ΔQp



0

20

40

60

80

100

120

140

160

180

-1440 0 1440 2880 4320 5760 7200 8640 10080

Effe

kt,

W

Tid, minut



Effekt varmtråd

ps EE DD g

γ = -0.68

Pow

er, [

W]

Qs

ΔQp

ΔEs = -4.5kWh

ΔEp = 6.6kWh


Summary of experimental validation

Method Lightweight

CC300

Embedded

(low)

CC300

Embedded

(high)

CC200

γ Analytical solution based on

measured properties

-0.54

±0.016

-0.55

±0.016

-0.64

±0.019

γ Step-response test [-]-0.52

±0.06

-0.49

±0.06

-0.70

±0.09

γ Pulse-response test [-]-0.68

±0.09

uncertainty (k=2)


Discussion

• The self-regulation ability is not so significant in any of the tested systems, compared to our cases in current low-energy buildings in Sweden

• This can be explained:

– The form factor of the test room is not beneficial for an energy efficient building in general; the heated floor area is small in comparison to the total envelope of the test room (including walls towards the lab hall)

– The isolated measurements of the conductive heat losses Kc reveals that the test chamber has some major thermal bridges

– The thermal conductivity of the slab is considerably lower than a regular concrete slab (the slab in the test room is made of plastic reinforced cement screed)


Conclusion

• The low self-regulation utilization factors can be explained

• We have found a good agreement between calculated self-regulation utilization factor γ and direct measurements in the test room by means of step- and pulse-tests

• With a proper floor heating design and a suitable building (i.e. low heat losses) the self-regulation utilization will be significant. Control equipment can be eliminated and a more cost-efficient solution can be made, without jeopardizing thermal comfort or energy consumption for space heating.


Documents

Performance Factor for Floor Heating Systems …...Performance Factor for Floor Heating Systems using New Analytical Formula Henrik Karlsson, PhD Carl-Eric Hagentoft, Professor Chalmers