Data analysis

Summing up on unwanted heat flows between deck/room and guard

In this section the unwanted heat losses between deck and guard and room and guard have been investigated. An estimated maximum value of each of the unwanted heat losses has been given based on a worst-case situation.

A combined accuracy of the mock-up has not been found. Firstly, the accuracy in an actual case depends on the relevant heat flows in that case. For instance an energy balance for the upper deck will not be influenced (directly) by the unwanted heat loss through the inner walls.

Secondly, since the mock-up has not been finished with the guard wall being installed, the accuracy will depend on the temperature in the laboratory, which is different for all

measurement series – and therefore a new estimation of the accuracy is, in principle, needed for each measurement. Considering only the upper deck, it may actually be an advantage that the guard is not finished, since the unwanted heat loss from the floor surface will be smaller since the surrounding temperature in the laboratory is normally lower than in the room.

An assessment of the maximum unwanted heat loss from the deck to the guard has shown that the maximum value is found to be 40W (30W from the ends and 10W from the sides). This is based on a guard temperature which is higher than the room air temperature, which is not the case for the measurements where the guard temperature is typically 1K-2K lower. A

correction of 40W is equivalent to 2W/m² floor surface, since the room is 21.6m². As the cooling capacity of the deck in the measurements is between 30W/m² and 60W/m² an error of 3%-7% is the maximum expected value. However as this value is based on maximum

expected values, the unwanted heat loss will be lower than given here.

∆Tfloorcovering

q_up

q_down

q_pipe Measurement area

Guard Guard

q_guard

Figure 6.29 Heat flows in upper deck

Eq (6.7) is the main energy balance for the deck assuming steady-state conditions.

guard down

up

pipe q q q

q = + + (6.7)

The individual heat flows can be found as described below.

The heat flow between pipe and concrete deck, qpipe, is given by the basic relationship between flow and temperature difference between supply and return temperature.

(

supply return

)

p

pipe m c T T

q = &⋅ ⋅ − ^(6.8)

The heat flux through the floor surface, qdown, is found from:

ing floorcover ing

floorcover

down T

q = R 1 ⋅∆

(6.9)

The thermopile is placed directly across the plywood layer in the floor construction. The thermal resistance of the floor covering is therefore the resistance of the plywood plate. The thermal resistance of the plywood plate is well-defined, which means that the measurement of the heat flow based on this thermal resistance will also be well-defined.

The unwanted heat loss from the ends and sides of the deck to the guard, qguard, can be estimated based on simulations using the actual measurement conditions as input. This has been described above in section 6.3.2. In general, the heat loss is a function of geometry and temperatures in room, guard and deck (based on the fluid temperature pipe).

(

room guard fluid

)

guard f geometry T T T

q = , , , _(6.10)

In this investigation, no corrections of the heat flow from the deck to the guard will be made.

Notice, that in section 6.3.2, a maximum expected unwanted heat loss of 3%-7% of the total energy balance of the deck is found.

Based on Eq. (6.7) to Eq. (6.10) it is possible to find, q_up, which expresses the cooling capacity of the ceiling surface.

This set of equations is equally applicable to both decks, though the upper deck is the most interesting when the decks are used for cooling the room. Notice that the heat flow through

the ceiling surface of the lower deck will not be realistic compared to the upper deck due to the proximity of the floor in the laboratory – especially for radiation.

Heat flows in the room

The heat flows in the room are generally more difficult to measure than in the deck alone.

Therefore, the measurement accuracy is expected to be poorer than for the deck alone.

Figure 6.30 shows the heat flows in the room

Room

q_pipe1

q_room q_wall

q_up1

q_pipe2 Upper

deck

Lower deck

q_up2 q_down1

q_down2 q_χ

q_ψ

Figure 6.30 Heat flows in room.

Again, an energy balance equation can be set up for the conditions – in this case for the room:

χ

ψ q

q q q

q

q_room = _up1 + _down2 + _wall + + (6.11)

Where:

qroom Heat load in the room

1

qup Heat flow from room to the upper deck through the ceiling surface

2

qdown Heat flow from room to the lower deck through the floor surface qwall Unwanted one-dimensional heat flow from room to guard qψ Unwanted two-dimensional heat flow from room to guard qχ Unwanted three-dimensional heat flow from room to guard

The heat flows through the wall, qwall, is a function of the temperature in the wall and guard and the thermal transmittance of the wall.

(

room guard wall

)

wall f T T U

q = , , (6.12)

The heat flows through the assemblies and corners, qψand qχ, are as the wall heat transfer a function of the temperature difference between room and guard. The line and point heat transfers can be calculated in for instance Heat2 and/or Heat3, which are used to predict the unwanted heat loss. These two are shown in Eq. (6.13) and (6.14).

(

geometryTroom Tguard Tfluid

)

f

q_ψ = , , , (6.13)

(

geometry Troom Tguard Tfluid

)

f

q_χ = , , , _(6.14)

Notice, that the fluid temperature is also included in the equations, even though it is not directly a part of the heat transfer between room and guard. However, the temperature in the decks will have an influence on the line and point losses from the room to the guard.

The left side of Eq. (6.11) can be found by measuring the heat loads in the room, which comes from the electrical heaters in the room. The relationship between heat loads and control signal has been defined in Figure 6.26 and Eq. (6.6).

(

heatloads

)

f

q_room = (6.15)

Cooling capacity

The cooling capacity of the ceiling surface of the upper deck can found based on Eq. (6.7) to Eq. (6.10), using steady-state measurements. In this section the method is applied to the measurement conditions and further, the cooling capacity coefficient is defined.

In brief the method is to find the heat flow through the ceiling surface and divide the heat flow by the temperature difference between the fluid and the room.

The heat flow through the ceiling surface, q_up, is found from Eq. (6.16)

guard down

pipe

up q q q

q = − − (6.16)

That is, the heat flow through the ceiling surface is the heat flow in the pipe minus the unwanted heat flows to the guard through the sides and ends of the deck and to the guard through the floor covering.

The heat flow from the fluid is found from Eq. (6.8) while the heat flow through the floor covering is found from Eq. (6.9).

Therefore, the cooling capacity coefficient, U_cc,ceiling, can be found from the following relationship:

(

room fluid

)

deck up deck

up ceiling

cc A T T

q T

A U q

−

= ⋅

∆

= ⋅

, (6.17)

Here the fluid temperature, T_fluid , is defined as the average value of the supply and return temperature, or:

(

supply return

)

supply supply return

fluid T T T T

T = ⋅ − = + ⋅∆ ₋

2 1 2

1 (6.18)

The room temperature is more difficult to define, as this depends on both position in the room and the fact that the air and surface temperatures are different. An approach, which is used for guarded hot box measurements for finding the thermal properties of windows using ISO 12567-1 (ISO, 2000), is to calculate the environmental temperature, which is the average of

the air and radiant temperatures weighed by the surface heat transfer coefficients for convection and radiation respectively.

rad conv

rad rad air room conv

h h

T h T T h

+

⋅ +

= ⋅ _(6.19)

The radiant temperature, T_rad, is found as the average temperature of measured surface temperatures on the inner walls and floor surface and the air temperature, T_air, is found as the average of the measured temperature in 0.7m and 1.1m height. Notice, that the room air temperature is stratified in the room, such that the air temperature is higher in the top of the room than in the bottom.

The radiative heat transfer between two surfaces is given by the following relationship taking the view factors and emissivity of the surfaces into account. (Mills, 1992).

(

4 2 2⁴

)

^{, 0 1}

1 1 2 , 1

12 = ⋅F ⋅ ⋅T − ⋅T ≤F ≤

q σ ε ε (6.20)

By assuming that all surfaces (except for the ceiling) have the same temperature, and all surfaces have the same emissivity as well as linearizing the temperature difference, Eq. (6.20) can be simplified to:

( ) ( )

(

room ceiling

)

rad

ceiling room

m

T T

h

T T

T q

−

⋅

=

−

⋅

⋅

⋅

⋅

= ³

12 σ ε 4

(6.21)

Here T_mis the average value of all surfaces in the room. In all cases the radiant heat transfer coefficient will be around 5.5m²K/W.

The convective heat transfer coefficient depends greatly on the actual temperature conditions and is difficult to accurately calculate. Therefore, the convective heat transfer coefficient will be based on the actual measurement data, where it is assumed that that the actual measured heat flow between the cooled surface(s) and the room, q_up, is equal to the sum of the convective and radiative part of the heat transfer:

(

_{air sur}

)

_rad

(

_{rad sur}

)

co

up h T T h T T

q = ⋅ − + ⋅ − (6.22)

Eq. (6.22) has only one unknown, namely the convective heat transfer coefficient. Using Eq.

(6.19) through Eq. (6.22) therefore yields the environmental temperature, T_room. Based on this, the cooling capacity of the ceiling surface of the deck can be calculated.

The influence from the floor surface on the cooling capacity from the lower deck can be included by making a similar calculation to Eq. (6.17) thereby finding the cooling capacity coefficient for the floor, where instead the heat flow through the floor covering, q_downis used.

(

room fluid

)

deck

down deck

down floor

cc A T T

q T

A U q

−

= ⋅

∆

= ⋅

, (6.23)

Again the same calculations can be used for finding the heat flow and temperature difference.

Therefore a combined cooling capacity coefficient for the ceiling surface of the upper deck and the floor surface of the lower deck can be found by the following relationship, summing the two cooling capacity coefficients to give a combined cooling capacity coefficient of the decks towards the room.

ceiling cc floor cc room

cc U U

U _, = _, + _, (6.24)

To check the results from the calculation of the cooling capacity of ceiling and floor surface, an alternative calculation can be made where the room heat load is used in stead of the fluid heat flow in the decks.

(

room fluid

)

floor

internal room

cc A T T

U q

−

= ⋅

, (6.25)

Where,

exf inf wall room

internal q q q

q = − − _/ (6.26)

That is, the cooling capacity of the deck is equal to the heat load in the room minus the unwanted heat losses through wall and from infiltration/exfiltration. Both of these unwanted heat losses are kept small. The same method for finding the room temperature as described in Eq. (6.19) can be used again.

In document Modelling building integrated heating and cooling systems (Sider 172-177)