ELAN : a computermodel for building energy design : theory and validation

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ELAN : a computermodel for building energy design : theory

and validation

Citation for published version (APA):

Wit, de, M. H., Driessen, H. H., & Velden, van der, R. M. M. (1987). ELAN : a computermodel for building energy

design : theory and validation. (1st ed. ed.) (Bouwstenen; Vol. 1). Technische Universiteit Eindhoven.

Document status and date:

Published: 01/01/1987

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L

M

7 I T

bouwstenen

M044860

1 ELAN,A COMPUTERMODEL

FOR BUILDING ENERGY DESIGN,

THEORY AND VALIDATION

MH DE WIT

H H DRIESSEN

RMM VAN DERVELDEN

faculteit

tlij

bouwkunde

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i

L ~1

8

7 I

T

B M

A

"BOUWSTENEN" is een publikatiereeks van de Faculteit Bouwkunde Technische Universiteit Eindhoven.

Zij presenteert resultaten van onderzoek en andere aktiviteiten op het vakgebied der Bouwkunde, uitgevoerd in het kader van deze Faculteit.

Bibliotheek

Technische Universiteit Eindhoven

Kernredaktie

8802874

Prof.drs. G.Bekaert,

Prof.dr.dipl.ing. H.Fassbinder Prof.ir. P.A. de Lange

Prof.ir. J.Stark

International Advisory Board Dr. G.Haaijer

American Institute of Steel Construction Chicago

Prof. ir. N.J.Habraken

Massachusetts Institute of Technology Department of Architecture

Prof. H.Harms

Technische Universität Hamburg-Harburg Fachbereich Städtebau

Prof.dr.· G.Helmberg Universität Innsbruck

Fakultät für Bauingenieurwesen und Architektur Institut fuer Mathematik und Geometrie

Prof.dr.ir. H.Hens

Katholieke Universiteit Leuven

Fakulteit der Toegepaste Wetenschappen Laboratorium Bouwfysika

Prof.dr. S.von Moos Wissenschaftskolleg Berlin Inst. for Adv. Study en

Universität Zürich

Modern and Contemporary Art Dr. M.Smets

Katholieke Universiteit Leuven

Fakulteit der Toegepaste Wetenschappen Instituut voor de Stedebouw

Prof.ir. D.Vandepitte

Laboratorium voor Modelonderzoek RijksUniversiteit van Gent

Prof.dr. F.H.Wittmann Département des Matériaux

Laboratoire des Matériaux de Construction Lausanne

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ELAN

A computermodel for building energy design: theory and validation

M.H. de Wi1

H.H. Driessen

R.M.M. van der Velden

manuscrip1 beëindigd: januari 1987

uitgegeven: februari 1987

FACULTEIT DER BOUWKUNDE Technische Universitei1 Eindhoven

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publikaties van bouwkundig onderzoek, verricht aan de

Faculteit der bouwkunde van de Technische Universiteit Eindhoven.

publications of building research at the

Faculty of Building and Architecture of the Eindhoven University of Technology.

uitgave:

Technische Universiteil Eindhoven Faculteit der bouwkunde

Postbus 513

5600 MB Eindhoven

Cl P-gegevens Konin k I i jke Bibliotheek.' s-Gra venhage

Wit. Martin de; Driessen. Henk: Velden. Noud van der

ELA"i. a computermodel for building energy design theory and validation.

Martin de Wit. Henk Driessen. Noud van der Velden

Eindhoven: Technische Universiteit Eindhoven. -111-. -(Bouwstenen: d1.1)

Uitgave van de Faculteit der Bouwkunde. Vakgroep Fysische Aspecten van de

Gebouwde Omgeving. - Met lit.opg.

ISBN 90-6814-500-2

SISO 646 UDC (681.3.02:697)+697

Trefw.: energiehuishouding; gebouwen/energiemodellen; gebouwen/computer aided design: binnenmilieu.

Copyright T.C.E. Faculteit der Bouwkunde. 1987

Zonder voorafgaande schriftelijke toestemming van de uitgever is verveelvoudig-ing niet toegestaan.

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Een klein model voor de berekening van de warmte- en koelbehoeften wordt behandeld.

Dit model is ontwikkeld voor het gebruik in een vroeg ontwerpstadium (weinig beperkingen met betrekking tot de geometrie van het ontwerp en alleen globale invoergegevens).

Uitgebreide validatie met behulp van een groot rekenmodel toont een grote betrouwbaarheid van de resultaten aan.

Summary.

A small non-stationary multi-zone model for the calculation of building heating and cooling demands is discussed. This model is meant to be used in an early design stage (few restrictions on the design schemes, only glo

-bal input data).

Extensive validatien with an actvaneed thermal model shows reliable results.

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<l> sol

L

heat flow rate

absorbed solar radiation in the room radiative part of the heat sourees convective part of the heat sourees

heat loss coefficient

heat loss coefficient in the room model between the outdoor air and air temperature node

heat loss coefficient in the room model between the resulting temperature and airtemperaturenode

heat loss coefficient in the room model between the

resulting temperature and outdoor air temperature node

heat loss coefficient in the room model bet ween the air temperature node and the capacity of the air heat loss coefficient in the room model bet ween the resulting 1empera1ure node and the capacity of the construction

T temptTalure

Tc control temperature

7?_

inside surface temperature of glazing

Tm mean radiant temperature C thermal capacily

CF convection factor

A area

U U-value

E incident solar irradiance

Vol volume

ac air change ra1e

time

SGF solar gain factor

he surface heat transfer coefficient for convection hr surface heat transfer coefficient for radiation

h, external surface heat transfer coefficient Pa density of the air

cP speciEIC heat of the air

H net radiation exchange

(W) (W) (W) (W) (WIK) (WIK) (WIK) (WIk) (W /A") (W I;..·) (oC) (oe) (°C) (°C) (J

I

A") (-) (m 2) (W !km2₎ (W fm 2₎ (m 3) (h -I) (s) (-) (W/A'm2₎ (W I f..'m 2₎ (W {km 2 ) (kg/m3) (]{kgf..') (Wtm2)

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f

a c cg e g gr i,j p r s sol tot V x.y

complex decrement factor

Subscripts: air conveetien caswil gain external gain ground indices loss plant radiation stored sol ar transmission t0lal ventilation nsul1ing (-)

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Preface ... 8

Introduetion ... 9

2 Theory ... 11

2.1 The one node model ... 11

2.2 The two node model (I) ... 13

2.3 The two node model (2) ... 15

2.4 The indoor temperature control ... 18

2.5 The computer program ... 20

3 Validation of the model ... 21

4 Recommendations 23 List of references 25 A Model development ... 27

Al Heat f:lows in a room ... 27

A 1.1 The heat sourees in a room ... 27

A 1.2 The net radiation exchange of internal surfaces ... 28

A l.3 The heat balance at an interior surface ... 29

A 1.4 The heat balance of the interior air ... 30

A2 Heat f:lows through the construction ... 33

A3 The room model ... 39

A4 The salution of the network ... 41

A4.l General salution ... 41

A4.2 Control strategy ... 42

A4.3 Night set-back ... 44

B VaUdation ... 47

B.l In trod uction .. .... .. .. .. .. ... . ... .. .... ... ... . . .. . . .. . . .. . ... . . ... ... ... ... .... . 4 7 B.2 Results of the validation ... 55

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Energy use and comfort arr hidden aspects of a building design. Moreover the decisions taken in an early design stage have a major impact on the thermal performance of the final design. These facts stress the necessity of design tools to be used by designers in an early design stage. The majority

of the existing computer programmes are not suited to this purpose. For this reason manual and graphical methods, sometimes in a computer-ized form. are very popular. We thought it a challenge to develop a more

accurate and flexible method, which makes an effective use of the power of a modern microcomputer. The campromise between reliability and sim-plicity required more elfort than we had estimated.

This research was carried out by the section 'Physical Aspects of the Built

Environment'.

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Introduetion

A methad for the thermal analysis of a building in an early design stage

will only be adequate if it can meet the following requirements: the methad has to be clear and simple to handle for a non-expert, only global building data must suffice,

the methad has to be flexible in order to allow a wide variety of designs; designers are aften interested in non-conventional solutions for their design problems,

it must be possible to study many variants in a short time,

the results have to predict the right trends when changing the design

aspects.

Present available calculation methods range from simple manual ones to those whe~ large computer programmes are needed.

In large computer programmes the heat fiows in a building by conduction,

radialion and convection c<~n be modelled in a physically sufficiently correct way. They require detailed input data and can provide a detailed output.

These models are important for research and for calculations in a more or less definitive design stage.

Manual methods are essentially based on a steady state heat flow model with corrections for non-stationary thermaJ behaviour. In general these methods are designed with the help of the large computer programmes. As it is impossible to cover in a simple way a large variety of building designs and of heating and cooling control strategies they suffer severe

res-trictions: e.g. only one temperature zone in the building, only for dwel -lings, no night set-back, no cooling load, no movable insulation, no reli -abie information about overheating.

The main importance of these models is the simplicity and the insight one develops in the different quantities of heat losses and gains. As it is still

laborious to work out a manual method, it is aften implemenled on a micro-computer. In that case the limited validity of the model wil! be

easily forgotten and a mistaken confidence wil! be ascribed to the com -puter output.

The model treated in this report (ELAN) is based on a simpUfled thermal

network of a building. lt can be implemenled on a micro- or

mini-computer. We will not discuss the way the input and output can be han

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computational capacity of the micro-computer and the size of the fore-ground memory.

The attention wil! be focussed on the rhysical model, on the validation with the help of the large model KLJ (van der Bruggen, 1978, Hoen, 1987) and on the flexibility of the presented model.

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2 Theory

In order to calculate the heating or cooling needed in a room it is neces-sary to determine the different termsof the heat balance:

heat loss

+

ei>,

+

heat stored cl>s heat gains

+

cl>g

+

auxiliary heat cl>p

The heat loss consists of transmission and ventilation (infiltration) losses through the building envelope. The heat gain is caused by incident solar radiation, casual gains from people, artificial lighting, dornestic hot water and appliances.

Heat is stored and released by the building construction. Over a large time interval the total of this heat will be 0. However, the storage term has a great influence on the heat gain terms: e.g. the storage of an excess of solar energy increases the amount of solar energy that can be utilized. The auxi-liary heat is supplied or extracted by the heating or cooling plant.

2.1 The one node model

A very simple non-stationary model of a room is given by the following approximations for the heat balance terms:

heat loss where _Ltot Ltot Lt Lv Ta T, heat storage where

c

₌

=

heat gain where _cl>sol

total heat loss coefficient

Lt

+

Lv

transmission heat loss coefficient

=

ventilation heat Joss coefficient

room air temperature

cl>g

=

outdoor air temperature

dTa

C

-dt

effective starage capacity time

=

cl> sol

+

cl> cg

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cg

=

casual gains from people and appliances

Such a model can be represented in a simple way by a network, where 1/ L101 and C are analogous to resistance and capitanee in an electric net-work. Heat flow rates are treated as electric currents and temperatures as

voltages.

c

T

fig.! The one node model

With a known control strategy of the healing or cooling plant the solu-tion of this model is straigh tforward.

This model might be convenient for optimization of thermoslat control

when night set-back is applied. However, comparison of the heating loads obtained with this model and KLJ showed that the accuracy is very low.

especiaJiy when sol ar radlation is important (Hest, 1984 ).

A main reason for this is the impossibility to distinguish between

radia-tive and conveelive heat gain. ln reality the room air temperature wiJl

increase directly by convective heat gain and indirectly by radialive heat

gain. The la1ter is absorbed by the construction and will be released

slowly to the room air.

ln the one node model there is no loading or releaslog of heat from the

slorage when the room air is at constant temperature. So the model behaves like a steady state model and all heat gain is directly released 10

the room air.

On the other hand, if there is no auxiliary heating there will be too much

storage due to the large capacity on the air node.

These problems can be overcome by a two node model where the storage

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2.2 The two node model (1)

A two node model can be represented with the following scheme:

c

T

where <PP

=

<PP 1

+

<PP 2

<Pg

=

<Pgl

+

<Pg2

Ltot

=

L1

+

L2

fi.g.2 The two node model ( 1)

<l>gl

Compared to the one node model there are two resistances and one

capaci-tance more. A lso the heat gain (ct> g ) and auxiliary heating ( <PP ) are divided.

W ith I/ L ₃

=

0 the model is i den ti cal to the one node model.

For the determination of the resistances, capac:ilances and the separation of

heat flows three different methods can be distinguished:

empirically by measurements in real buildings,

"empirically" by calculations with a large computer program or thcoretically by physical assump1 ions.

The empirica] methods were not considered. They have the disadvantage

of being complicated, because of the great number of fi.tting parameters. A

second disadvantage might be the problem of generalizing such results to a

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For the derivation of the expressions for L 1 , L 2 and L 3 a simp ie case was

studied: a room with only one external wall containing a window,

sur-rounded by rooms with the same thermal conditions as the room

con-sidered.

For this room the following approximations were made:

the walls have the same interior surface temperature, only the glazing

temperature is different,

the surface coefficients for convection and radiative exchanges are the

same for all surfaces, there is no furniture,

the thermal mass of the walls is in direct thermal contact with the

room air (no thermal resistance in the wal!),

the room has a uniform temperature.

steady state approximation for transmission heat loss.

The equations following from these assumptions were modelled by the

network of ógure 2. The temperature T 1 was the air temperature and the

temperature T 2 the average surface temperature of the opaque construc

-tions in the room.

The two node model (J) (Velden, 1985) turned out to be very successful.

However, no satisfactory salution was found for the extension to a mul

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2.3 The two node model (2)

The analogon of the two node model (2) is:

<t>p2

fig.3 The two node model (2)

Compared to the two node model (I) one capacitance and two resistances are added. More essential are the different assumptions by which the model is developed:

the room air has a uniform air temperature,

all radiation (shortwave and emitted longwave) is distributed in such a way that all surfaces absorb the same amount per unit of surface area,

the surface coefficients for convection and radiation are the same for all surfaces.

By these assumptions it is possiblc to introduce a temperature T" that together with this temperature on the other side of a wall governs the heat flow to the wal!.

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We wil! cal! Tx the "resulting" temperature. Tx depends on the air

tem-pcrature (Ta), the average surface temperature (Tm) and radiation (<'Pr)

(= radiative part of the heat gains and auxiliary heat) in the fo!Jowing way:

where hr surface heat transfer coefficient for radiation

he surface heat transfer coefficient for convection

A1 total interior area of the room

The órst term on the right hand side is similar to the environmental

tem-pcrature (Danter, 1973).

For the derivation of the different heat flow rates to the two temperature

nodes a convection factor

e

F is used to determine the convective part of

each source. By this factor the effect of the auxiliary heating system (e.g.

air heating eFP = 1) and of the window system (e.g. solar blinds)

(Cor-neth, l 984) can be estimated.

The expressions for Lv, Lg, Lxa• <'Pg1, <'Pg2, <'PP1 and <'PP2 are given in annex A3.

Two requirements are used to determine Lx,

ex

and the transmission heat

flow between two rooms, one room and outdoors (opaque walls) or one

room and the ground under a floor (<'Pxy ): a) correctness for steady state heat transfer,

b) correctness for steady-cyclic heat transfer with a cycle period of 24

hours.

The heat flow to the wal! consists of two parts:

the heat flow if the resulting temperature on the other side (TY) is

the same as in the considered room. This heat flow is zero on average

and the sum of all these heat flows to the walJs is the heat flow

from Tx to Lx and

ex.

Requirement a) is automatically fulfilled and with b) Lx and

ex

for multilayered walls can be derived (see annex

A)

the remaining part ( <'P xy ) of the heat flow to the wall depends on

Tx - Ty and the history of Tx - Ty. It can be proved that

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state requirement a) is fulfilled if :

where the summation applies to a long period of time. Uxy is the U-value of the construction.

If only va lues of Tx - Ty and xy of the previous timestep are used to determine the heat flow then it is not possible to fuifiJl require-ment b) completely. So for this heat flow we only have required that the attenuation of a steady-cyclic variation in regard to the steady state approximation is correct. Together with requirement a) that gave rise to the following expression for ..,y:

where

*

denotes the value of the previous timestep

0' a fitting parameter for a correct attenuation.

By xy all the room-modelsof a building are linked (multizone model). In the same way the air node could be used to model the ventilation heat flows between rooms. Until now we have not worked that out.

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2.4 The indoor temperature control

For the control of a heating or cooling plant any linear combination of the

resulting temperature and air temperature can be use(i. This is called the

control temperature Tc. If a certain combination of the resulting tempera

-ture and the aü ture is used Tc is equal to the operative tempera-ture (A4.2).

Concerning the control strategy three situations can be distinguished:

a. No heating or cooling:

al.- The control temperature without heating or cooling lies between the desired minimum tempera1ure and the desired maximum temperature. Jn this case the heat gains provide sufficient heat.

a2.- No heating or cooling emission system is present in the room.

b. Healing:

bi.-The control temperature is kept at the desired minimum temperature. The maximum heating load of the plant is larger than the heating demand.

b2.- The room is healed with the maximum heating load. ln this case the maximum load is less than the heating dt>mand and the control tem-perature wil! be lower than the desired minimum temperature.

c. Cooling:

cl.- The control temperature is kept at the desired maximum temperature.

The maximum cooling Joad of the plant is Jarger than the cooling de mand.

c2.- The room is cooled with the maximum cooling load. In this case the control temperature is higher than the desired maximum temperature.

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This three situations can be illustrated with the flgure below:

<Pp

t

b2

<Pmaxh~---~ where maxh c:p maxc T min T max b 1

a

I/a 2

T

max

T

min

c

1

flg.4 Tem per at ure con trol st ra tegy

maximum heating load of plant, maximum cooling load of plant, desired minimum temperature and desired maximum temperature. al.-c2. refer to the points above.

Situation b2 where the heating demand is higher than the maximum load can occur after a period of night set-back.

In ELAN a routine is used to start heating up the room earlier to avoid that the control temperature is lower than the desired minimum tempera-ture at the desired moment in the morning.

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2.5 The computer programme

The model ELAN was the starting point for a computer program or the

same name. As the model is almost irrespective of the geometry of a room

only global input data are needed:

the total area for internal walls, Boors, external waHs and roofs, the total area, orientation and slope for glazing .

For each surface the user has to specify a certain construction which can

be selected from an existing data-base.

Other input data (casual gain and ventilation regimes, control strategy for

the heating or cooling plant, use of shutters and solar protection) are

optional but of course necessary for certain calculations.

The model offers the opportunity to specify zones consisting of more than

one room. This reduces the total number of input items and will also

reduce the time needed to calculate the healing or cooling loact of a

build-ing.

Of course it is necessary to keep in mind that one should only join several

rooms into one zone if the tbermal properties for the different rooms are

more or less identical. lf for example a room facing south (high percentage

of glazing) and anotber room facing north ( low percentage of glazing) are

joined results cao be inaccurate.

The user can specify which output data are needed. These range from:

only lotal healing or cooling loads,

to:

peak loads for heating or cooling.

hours of overheating,

the values of the air-, rtsulting- or control temperature for each

hour,

the number of hours the heating or cooling plant is on,

the number of hours minimum or maximum temperatures are

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3 Validatien of the model

The main purpose of the model is to achieve in a simpJe way reJiable

information about the relation between the heating or cooling load and design changes. An extensive validation of the model with measured data is difficult to realize as many measured data of buildings and their vari-ants should be at hand. Moreover the user behaviour and a lot of parame-ters of the building are unpredictable.

For these reasoos a comparison with data obtained by a sophisticated

thermal model (KLI) was assessed.

As it is important for a designer to know if and when an excess in tem

-perature wil! occur in the building this excess quantity was validated too.

The variants considered can be divided into two groups:

variants with only one room and variants with two rooms.

In both groups one variant with two facades with glazing (north and

south) was chosen as a reference. The glazing percentage of the facade to the north for all variants is 5 %.

The heating Joad was calculated for the one-room reference (20 % glazing

south) and this referencr with the following modifications: higher glazing percentage,

three facades with glazing,

without solar radiation, higher level of insulation and

less thermal mass (light construction).

For two rooms the chosen examples consisted of the two-room reference and this reference with:

higher glazing percentage,

one room with no temperature controL

the same but with more ventilation in the unheated room and the same with an insulated upper floor.

Cooling loads were calculated only for two variants, a one-room and a two-room scheme with 70% glazing.

Temperature excess quantities were calculated for the one-room and two

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The calculation of the heating and cooling load turned out to be

sufficiently accurate for design purposes (see table B.5).

The results for cooling are less accurate than for heating. The mean reason is the overestimation of absorbed solar radiation in the room. This can easily be improved in the future.

The accuracy of the calculation of hours of overheating turned out to

improve the Jonger the period of calculation. Jt can be a good indication whether the reduction of these hours with solar blinds can be obtained.

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4. Reeommen <ia ti ons

Using the model and the results of the validatien made clear that there is

a need for further investigations.

Some items for research on small models are:

determination of La and Ca in such a way that more accuracy is

obtained,

modelling air flow between zones,

modelling the apparant solar absorptance of a room,

actdition of passive solar systems (sunspace, air collector to preheat

ventilation air etc.),

a more accurate method to calculate heat losses of the groundfioor.

In relation to building design the actdition of other features would make a

small model more desirabie to use:

impact of shadow and external shadow devices,

capita! costs versus recurring costs,

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List of references.

1. Bruggen, R.J.A. van der

Energy consumpt ion for heating and caoling in relation to building

design.

Thesis, Eindhoven University of Technology. 1978.

2. Corneth, P.

Raamsysteem en zonwering.

Report, Eindhoven University of Technology, 1984. 3. Danter, E.

Heat exchanges in a room and the definition of room temperature.

IHVE symposium, 1973. 4. DJN 4701

Regel11 für die Berechnung des Wärmebedarfs von Gebäuden.

1959.

5. Hest, J.L.A. van

Energiebehoeften van woonwij ken.

Report, Eindhoven University of Tcchnology, 1984.

6. Hoen, P.J.J.

Energy consumpt ion and indoor environment in residences.

Thesis, Eindhoven University of Technology, to be published May 1987.

7. Pipes, LA.

Matrix analysis of heat transfer problems.

J.Franklin Institute 623, 195-206, 1957.

8. Velden, R.M.M. van der

ERn hoU\vkundige computertoepassing voor energiebewust omwerpen.

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A Model development A I Heat flows in a room

A 1.1 The heat sourees in a room The heat sourees consist of: heat supply cl>P casual gains cl> cg

solar heat gain <l>sol

The solar heat gain of each window is:

<l>sot = SGF (Ag E) where SGF Ag E

=

solar gain factor glazing area incident irradiance

The incident irradiance depends on orientation, slope of the glazing area and the shadow factor. The total <1>₅₀₁ is simply found by actdition of the different contributions of each window.

The heat sourees have a radiative and a convective part. The convective fraction wiJl be denoted by the convection factor CF.

So the radiative part is:

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A1.2 The net radiation exchange of internal surfaces

In actdition to the radiation coming from the different sourees there is radiation emitted by each surface. The total surface radiation is equal to:

LJAj €0

T/

where _Ai = surface area of j -th surface

f. = emissivity (assumed equal for all surfaces)

a = Boltzmann constant

Ti = absolute temperature of each surface j

The calculation of the amount of radiation each surface will receive, demands a great number of data about geometry, reflectivity etc. and is not suited for our purpose. Therefore an approximation of the physical reality is needed in order to reduce the required data considerably.

It is assumed that the sum of absorbed and transmitted radiation ( the Jatter only for shortwave radiation through the glazing) per unit of sur-face area is equal for each surface. As each surface also emits radiation the net radiation exchange is:

In a linearized form:

=

surface heat transfer coefficient for radiation total interior area

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Al.3 The heat balance at an interior surface

The heat balance at an opaq ue surface is

heat flow directed to the wall

Hi net radiation exchange

Ta air temperature of the room Ai surface area

The surface heat transfer coefficient he is assumed to be 2 WIm 2 K for all surfaces. The air temperature is the same near all surfaces. (This is a similar approximation as the one for radiation).

The heat flow <l>x can be written as:

where

hr

LJ

A j Tj

+

<Pr

+

he At Ta A1 (hr

+

he)

For each surface the resulting temperature Tx has the same value. Tx is similar to the concept of 'environmental temperature' (Danter, 1973). If a surface is not opaque the reflected solar radiation coming from the room surfaces is partially transmitted. lf this solar radiation is assumed to be transmitted completely the heat flow through the glazing is:

Ag x i

=

Ag (he

+

hr )(Tx - Tg) - (I - CFsoi ) sol

A

(30)

Al.4 The heat balance of the interior air

The heat balance of the air is:

where Ca heat capacity of the air

Lv ventilation heat loss coefficient

T. external air temperature

c

a

=

Pa CP Vol

where _Pa density of the air

CP specinc heat of the air

Vol volurne of the air

Lv Pa CP ac Vol 3600

where ac air change ra te (h-1 )

Elimination of the surface temperature with the expression for Tx leads

to the following equation:

where

The equation for the 'resulting' temperaturenode with the sameheat flow

from Tx to Ta is easily derived from the expression for Tx:

or:

L}

<l>xj

+

Lxa (Tx - Ta)

=

(I

+

~

c

)<l>r

(31)

The equations for the air point node and the 'resulting' air node can be represented by a thermal network:

L

<f> xy

(32)

A2 Heat flow through the construction

From Al it follows that the unidirectional heat flow through the

con-struction depends on the 'resulting' temperatures on both sides of the

construction and its thermal properties (including surface coefficients). The resulting temperatures outdoors wiJl be the air temperature for

glaz-ing, the sol-air temperature for opaque walls and weighted average of soil

temperature and external temperature for the ground floor.

The calculation of the heat flow is simplified by demanding correctness

only for:

steady state transfer ( mean heat transfer)

steady-cyclic transfer with a cycle period of 24 hours.

For sinusoirlal variations the temperatures and heat flow cycles can be

linked by use of matrix algebra (Pipes, 1957):

where fx.

fy.

and ifx ,

ijy

are the cyclic variations of the

temperature and heat flow density on both sides of

the partition.

Mxx, Mx~·. Myx. MY>' are complex coefficients.

The derivation of Mxx. Mxy, Myx and Myy for a multilayered

construc-tion is a standard technique and wiJl not be 1reated bere.

lt can be proved that the determinant of de matrix always equals I so:

By manipulating the system of equations one can derive for the heat

flows:

+YxyTx

+

Uxyfxy(Tx

-YyxTy

+

Uxyfxy(Tx

where Yxy, i'yx

Yxy

=

admittance

(33)

-=

=

Mxx - 1 M:xy

U-value of lhe construction complex decrement factor

I

The flrst term on the right hand side represents the heat flow if there were no ( thermal) differences bet ween either side of the wall. In the

steady state approximation this part is zero.

The second term represents the transmission. For a steady state approxi-mation

f

xy

=

1.

The total heat flow to the surrounding envelope is:

cf>1

=

L,AyYxyTx

+

L,AyUxyfxy(Tx Ty)

}' y

If a zone consists of more rooms the admittances of the partitions within the zone can be added to the flrst term on the right hand side. The second term wil I be zero for these partitions as Tx

=

Ty. The same holds for furniture in a room.

The órst trrm can conviently be represrnted by a simple flrst order ther-mal network that also mrets the strady state requirement:

(34)

The conductance L, and capacitance Cx can simply be formed by equat-ing the real and imaginary parts of the followequat-ing equation:

_I_+

-Lx j wC x L,Ay Yxy y where w

21T

24.3600 )2 - I

The second term cannot be represented in a simple way by a thermal

net-work. Compared with the heat flow for

f

xy = 1 (stationary) the heat flow cycles will be delayed (the phase shift can be more than 90°) and

attenuated. This term also links all rooms and makes a simple solution

impossible.

To solve this problem we choose a standard delay time of one time step

and required the correct attenuation for 24-hour cycles. The expression

used to calculate <P xy is as follows:

where

r;'

r;.

<P;y are the values at the preced

-ing timestep

G' a factor to account for the atlenuation

This expression obeys the requirement that for steady state the heat flow

is given by:

<f>xy

=

UxyCTx - Ty)

The factor G' can be determined by the next equation:

Ie i w& - (I - G') I

=

Q' I

f

I

where wD.t l f I

;~

( if the timestep is hour)

(35)

1T t:,2

With 1 - cos()=

-2 the solution is:

12 1 4 _6.₂₎₂ _1:::.₂

D.C---

4

+

CY= I

f

1 2 2 2 -I

f

12

For the heat loss through the ground floor some extra approximalions are

necessary as:

the heat flow is not one-dimensional. One can distinct two

com-ponents: the heat loss to the zone of constant temperature (e.g. -5 m

and 10 °C) and the edge losses to the adjoining ground.

the heat capacity of the ground is very large. So the heatflow will

depend very much on the initia! conditions.

As the risk that the initia! conditions are not accurate is very great we

calculated Lx, Cx and I

f

I ror the ground fioor with only a smal! slab of ground beneath (0.2 m).

The steady state heat loss can be approximated by:

where Ay the area of the ground floor,

Uxgr U-value of the jjoor including 5 m of soil.

=

U-value for the edge losses,

constant ground ternperature (JO 0

c )

,

temperalure of the ground near the edge.

The calculation of Uxgr is straightforward. For Uxed extra data are needed

like the perimeterlengthof the floor (DIN 4701. 1959).

We did not ónd a good solution for fe yet. So far i1 was estimated by:

So ónally <P XJ can be calculated in the sa me way as for other construc-tions, with:

(36)

U:xy

=

U:xgr

+

Uud

T

=

Uxgr Tgr

+

Uxed

f

.

y UX)'

We did nol validate the heat loss through the ground floor until now. A problem is that also large computer programmes like KLJ make crude

approximations for this heat loss.

The resulting temperature for opaque walls is:

where he = 25 W

/m

2 ,

U'

=

absorptivity for solar radiation of the wal!. Up to now only the value cv

=

0 is used in the ELAN model.

The heat flow through the glazing can be approximated by the steady state U-value. In the network representation:

Te Ag U' Ag (he +hr) Tx

o~--~~~~A-

· ~

·

· ~

· ~1~--o

--

sol

Ar

flg.A.3 The network for a window (I)

This is equivalent to the network:

Lg

... ..:, ... : .. ,:,::, ... .:.:,,

.

.,~

fig.A.4 The network fora window (2)

AgUg

(37)

=

The factor Fg in the above expression is only a crude aproximation as

absorption of solar radiation in the window sys1em is neglected and also

the fraction Ag I A1 is doubtful. A better expression wilt be derived in the

(38)

A3 The room model

Combination of the results (AJ.l. Al.4 and A2) for one room leads to

the ELAN network:

where:

<l> g I

L

V

=

_:_P:::..a c..J:.P_a_c Vol

3600

(39)

If shutters are used Ug is the U-value including shutters. The thermal capacitance of the air is:

Ca

=

PaCp Vol

The resistance I/ La is added for future developments. In the model tested up to now liLa

=

0.

(40)

A4 The solution of the network

A4. J General so1ution

The model can be described with four equations: - Heat balance at the air temperature node;

Lxa(Ta- Tx)

+

Lv(Ta- Te)+ a

=

p2

+

g2

- Heat balance at the resu!ting temperature node;

Lg (T, - Te )

+

Lxa (Tx - Ta )

+

x

- Heat flow to the air capacity;

Ca d a dTa

-

+

=

c

-La dt a a dt

After Crank-Nicolson discretisation:

where (Y a

=

Up to now only the value 0'₀

=

1 is used in the ELAN model.

- Heat flow to the construction capacity;

dTx

c

-x dl

After Crank-Nicolson discretisation:

where

( 1)

(2)

(3)

(41)

1 Cx

+

-2 Lx Ö.l

Jn eq.(3) and eq.(4) vatues having superscript

*

are the known quantities of the previous timesteps.

Substituting eq.(3) in eq.( 1) and eq.(4) in eq.(2) and solving the system of linear equations leads to the general solution for Ta and T, :

Ta

=

al

+

h1<l>p

Tx

=

a 2

+

h2<l>P

A4.2 Con trol strategy

(5) (6)

In ELAN any linear combination of the air temperature Ta and the resulting temperature Tx can be used for control of the healing or cooling plant. So:

Jf the air temperature is used for the control then:

8=1

If the "operative' temrerature (0.5(Ta

+

Tm

+

<l>r !hrA1 ) ) is used:

Tm is the mean radiant temeperature:

With eq.5 and eq.6 this leads to:

where a 3 = Oa 1

+

(

1 -

0

)a 2

h 3 = ob 1

+

(I - 0 )h 2

(7)

(42)

At the beginning of a timestep control criteria are needed. These criteria

are formulated with the help of three temperatures:

Control temperature with no heating or cooling, <PP

=

0 :

Control temperature with maximum heating capacity, P

=

<Pmaxh

Control temperature with maximum cooling capacity, <PP

=

<Pma.xc

Now the criteria are:

Tee ?-T max p

=

<'~>maxc _, Tc

=

Tee

Tco?-T max> Tee Tc

=

T max p

T max-Tco

_,

₌

b3

T max> Tco> T min p

=

0

_,

Tc

=

Tco

Tch > T min?-Tc 0 Tc

=

T min p

=

T min-Tco

_,

b3

(43)

A4.3 Night set-back

If night set-back is applied the minimum control temperature is lowered

(Tminnight) and raised again in the morning (Tminday ). lf this is done at a

fixed moment it offers no extra problem for the model, but it can offer a comfort problem in the real situation. This can be avoided by heating up earlier to arrive at the desired control temperature at the desired moment

in the morning.

In order t.o calculate the heating up of a room the air ca;.>acity is

neglected. Th is leads to a first order model. The analytica! sol ution for this first order model can easily be found and is:

- with respect to Ta:

(9)

- and with respect to Tx:

( 10)

where:

( IJ )

(12)

( 13)

As T,=oTa+(J-8)1~ the first hour Tc(M) is below Tminday heating up

(44)

T

t

Tco

T

minday 1----.

T

minnighr - - - ~o::---f ...

....

- -

-

;"

-~-- / /

/

(45)

B Validation

B.I Introduetion

As mentioned in chapter 3 ELAN has been validated with a large

compu-termodel named KLI.

The validatien has been carried out for three different geometries, in

which the percentage of glazing, the amount of insulation, the thermal

mass of the building and the air change rate are varied. Heating and

cool-ing loads and the effect of overheating calculated by ELAN and KLI have

been compared.

The elirnatic data that have been used are part of the THE reference year

for heating and cooling. Calculations have been made for typical winter

conditions CJanuary, February and March, ng.B.l and B.2) and typical

summer conditions Oillle, July and August, ng.B3 and B.4).

Daily heating loads are calculated from day 1 (I January) till day 90 (3I

March). Daily cooling loads are calculated from day I52 (I Jillle) til! day 243 (3I August). Overheating is calcuiated over a period of one month (July ).

For this validations the following assumptions were made:

the resulting temperature for external walls is not the sol-air tem

-perature as mentioned in A2 but the outdoor air temperature, so

there is no absorption of solar radiation by the walls,

the resistance 1 I La bet ween the air tem per at ure node and the heat

capacity of the air is set to 0,

the factor a a in eq.3 in A4.1 is set to 1, so the heat flow to the air

capacity does not depend on the value of a previous timestep,

oniy geometries which have no groundfioor were tested,

the factor Fg in A2 is set to 0.

Table B.l shows the different variants that have been compared with their

properties, table B.2 the different temperature regimes, table B.3 the air

(46)

, ~ ... o· :.;; f--0

(\

I

IJ

~

/11

~i

!

I

I~

i

11

I

I ~

t~

_~

~\

I I

1\

V\

~

I A

\

I

J\

VI\

/1

(1

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~\

I I

\I

J

' i

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/\\~/I

I

, I

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(

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i

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V

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i ! I I i I ' I I

i

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I ! I _I ' I I

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_I

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I I I i 21 31 4~ 5! 6: 7~ - -> QRi ~ûMBEA ii - 1 JR~û19i)

fig.B.I Outside air temperature (winter)

\

(\

\/

t

I

i

I

i

!

I I

I

81

~

I

l

i

!

' ' 9:

!

(47)

I

g

I

~

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~

1 \

1C.C:.87t lfj@)l::!l.i

i

tU)

I

I ! ;

~

i

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--+

~

--~

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--~--~~~+--~

~

---~

~~

~

--,

~-+

~

--

-

~,

!

:

--

m-

--

+-

-+j

rl

~.

~

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-r!

~/

1 ~

z

I

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:::g

i I

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f\

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t---1

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-+.

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_________._!

-:--

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----i

j

-+-

1 +--.--\

I

i\

/ . . - - - ' 1

1-~

-I

\

-;-!i

--t-

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: - - + \ , . _ "' ;

~.

· :

·

'!

j'i''

I I I ~~

i

\I l

I

I~ i \ ! ' ~~+---~--~~~*4*-~+-~44~4-~4

~

I

i

\i, I_ ,.1: ,1,,1 : \

l

I

~

jl :

!

1

\

1 '\

I

\

!1\

I

;\\

~

1 I

i\

I

~Î!

l

-

I

i

\ ,

1 \

/

!

\

I

' ,1

~

,.

~

I

!

,,

''

1'1,/

'

!!!I //,1.1,1 !.l· 'I I

I

!

1

'!

!

N

\.

'Cl \

I

1 1!

· ~

j

,

--.

~

· \/\\

1.t~

..

~

1\

i'

· ,

I

l'\

~

I

en

~

,

\

,

!

\i!

1!:

I

Lv__'./1/ l

~

I

Ij~

,

Vi!/11'\J

Ij~~

~

\

V

~

!

o

~~~~

~

!

ill;

--k-

1/

i

'

I 1:

l

t

'-!

i

(

,Aj

,

'

~

~Jr

'

~!lrvf ~

u

.~

"

"'

..

i

I

~ ~~>

'"

"

"BE"

" •

'

~

"

'

"'"

I

L

----

--

----

--

----

--

~

(48)

/

I

~

(49)

10.1.81

0

_{+--'---+-"---+----1-~-i----'--t---'----+---''--+---'--t-="rr1C}

_'

_4C

~

"' _{~+---+--~-~~-~--~--+--+--~--~}

tU3

l62 172 l82 l92 2C2 212

oe;~ NLI:1EE'1 ll = l JRNURR:J

1 I

l .

I

\

1 \

A (\ i

I

l I 1

r

I

i

(50)

fig. 8.8 B.9 B.IO B.ll B.l2 B.l3 8.14 8.15 8.16 8.17 8.18 8.19 B.20 8.21 8.22 8.23 8.24 8.25 B.26 variant (1) (2) (3) (4) (5) (6) (7) (8)

•

A20 0.91 20 1 - 1 - 1 - WH A20ZZ 0.91 20 I - I - I - WH A70 1.5 I 70 1 - I - 1 - WH A70ZZ 1.51 70 I - I - I - WH A20NA 0.91 20 2 - I - I - WL A20S'C 0.57 20 1 - 1 - 2 - WH A20Ll 0.91 20 I - 1 - 1 - WH A70EN 1.51 70 I - 1 - 1

-

WH A70K 1.51 70 I - 1 - 1 -

se

A20KT 0.91 20 4 - 1 - 1 - ST A20KTZW 0.91 20 4 - 1 - 1 - ST 820 0.82 20 I 1 1 1 1 I WH B20MV 0.82 20 1 3 1 I I I WH B20MV2 0.82 20 I 3 1 3 2 3 WH 820MV2F 0.82 20 1 3 1 3 2 3 \\'H C20 0.91 20 I 1 1 I 1 1 \\'H C70 1.51 70 I I 1 I I I WH C70K 1.51 70 1 4 I I 1 I SC C20KT 0.91 20 4 4 1 1 I I ST

(I) average U-value (W /m 2_A.')

(2) % glazing sou th

(3) _t_{emperature regime}_room I

(4) tem per al ure regime room 2

(5) casuaJ gains room I

(6) casual gains room 2

(7) ven ti la ti on regime room

(8) ventilation regime room 2

*

WH winter healing load

SC summer cooling Joad

ST summer temperature

**

zz

without solar gains EN 20 % glazing north & east

WB with solar blinds

JU insolated upper floor

***

H double brick

L timber

The narnes of the variants refer to fig.B.5, B.6 and B.7.

tab Je B. J Nam es and properties of the variants.

• •

•••

-- H

zz

H -- H

zz

H -- H -- H -- L EN H -- H -- H \\'8 H -- H -- H -- H IU H -- H -- H -- H -- H

(51)

I

T min

I

nr.

i

0-Bh 8-!8h 18-24h 0-24h

I

I '

I

₂

I

3

I

4 20 20 20 5 20 20 5 5 5 20 20 20 table B.2 Temperature [°C

1

0-Bh 1 0.5 8-18h 1 0.5 18-24h I 0.5 2 2

table B.3 Air change ra te

I

h-l ]

I

nr.

I

0-Bh 8-18h 18-24h

I 7 7 7

2 7 0 0

3 0 7 7

table B.4 Casual gains

I

W Im 2 ] 25 25 25 free

All the variants have only a north and south external wall and 5 % glaz

-ing on the north facade, except one which has a window on the north, east and sou th wal!.

The construction consists of double brick with cavity for external walls, concrete for internal walls (0.1 m l and floors (0.2m), except for one vari-ant with a light construction: tim ber for external and internal walls. Walls are insuialed with 5 cm insulation, variant A20SU with 15 cm. Variant B20MV2F has an insulated (5 cm) internal floor between the two rooms.

(52)

The three geometry modules are:

A.- One room. w

*

l

*

h

=

6

*

5

*

3 ( m ).

I

1/

i/

A

V

I

6 flg.B.5 Geometry module A.

B.- Two rooms, one above the other, each 6

*

5

*

3 (m).

I

n

I

~

I

V

6

óg.B.6 Geornetry mod 11le B.

C.- Two rooms, one a long the other. each 6 * 5

*

3 ( m ).

I

/V

VI!

vv

c

Vv

3

V

óg.B.7 Geometry module C.

(53)

B.2 Results of the validation.

Table B.S summarises the results of the validation and fig.B8 to B.26

show the results for the different variants.

I

_Variant _{Heating or cooling load} _{Peak load}

I

ELAN KLJ diff ELAN KLJ diff I

I

_[kWh) _[kWh] _[%] _[W) _[W] _[%]

I

A20 1440 1429 0.8 1631 1639 -0.5

I

A20ZZ 1786 1788 -0.1 1718 1739 -1.2 1 A70 1388 1375 0.9 2034 2028 0.3

I

A70ZZ 2422 2434 -0.5 2304 2312 -0.3 A20NA 1260 1272 -0.9 2428 2516 -3.5

I

A20SU 491 481 2.1 812 807 0.6 A20LJ 1439 1421 1.3 1854 1760 5.3 A70EN 1861 1823 2.1 2535 2504 1.2 A70K -860 -838 2.6 -2269 -2152 5.4 B20 2925 2934 -0.3 3139 3183 -1.4

I

B20MV 1891 1871 1.1 3112 3203 -2.8

!

B20MV2 2190 2170 0.9 4271 4119 3.7 I 1 B20MV2F 1770 1758 0.7 4132 4317 -4.3 1 C20 2128 2113 0.7 2532 2553 -0.8 1 C70 2084 2069 0.7 2934 2955

_-o.1

1 C70K -844 -831 1.7 -2619 -2534 3.4 1

(54)

ïf.T::asi ~ •\5 I Cl c:: u f,

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_I

L

[];1S!

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t~

I _' ! :.; ! I

_:

!

1\

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--

-!

! I

'

_!

! i _i

i

' I i I j

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fl

I _I i

_!

_I

-

--n

l

_! I _i ' I I

l

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_'

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I

I i

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I

i

!

_

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\ ' i !

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·-

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LL

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' _i i _!

-

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-1

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11'

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: ' I / I _! ' I I I

_jJ_

i _! : I I I

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;

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'

j

r- -' I ' . ' 1(T " ' I

i

I 1\ . I I . i

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i

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: ' ' ' 2. 31 " 51 6, 1 91

---> oq-; I:JMBF.9 d = i JA•;Jq9: I

L___ ____________________________________________ ~

5g,R8 Variant A20

Calculated: Winter heating load ( J JanUäry - 31 March). (--) Heating load according to KLJ

(-) Heating load according 1o ELAN

Difference

1429 ( kWh ).

1440 ( kWh ).

0.8 ( % ).

(55)

il.il. ! g,cJ I ~ I

I

i

I

~

I

t~

I

I ~ "' "' I I I I ! ' ' a I "'

~~

I

I _I ' i ' I i

I

I i I

I

;~ I I 1:.: I !....::.::!.1'1

;uN

~(

_:I

I '

fÎ'v!J

1

I I

I~

_i+-R

1

A

i

.

ik

I~ !t.:)g I \

/i\;

•z

.

'I \

I

\;JN

;h

1

-~~ J~ ~;\i

i

I :e:

~\

Iu.; ., '

'\71

vy

I

h

-

·r'V

I

\ I _; i: I _!

i

' I _! ' ~ !

I

! I I

i

:

_I

i

! ! I !

i

i i I . "' I _I I

I

I I I I

I

ai 11 21 31 41 51 61 71 BI 91

---> _DRY NUMBER l1 = 1 JRNURRY;

ilg.B.9 Variant A20ZZ

Calculated Winter heating Joad ( 1 January - 31 March) without solar radiation.

( --) Heating load according to KLI (-) Heating load according to ELAN

Difference

1788 ( kWh ).

1786 ( kWh ).

(56)

g g,~ I

n

- -- - - -- -- --lï.'iT."!SI

<;it---'---;---

1 ..._____._

,

~I

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---> OR~ Nu'18E9 ,J ; l JRNUqRr;

ng.B.IO Variant A 70

Calculated : Winter heating load ( l January - 31 March ).

(--)Healing load according to KLI

(- )Healing load according to ELAN

Difl'erence

1375 (kWh ).

1388 (kWh ).

(57)

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---> ORI NUMBE"I ll = i JANLJqR~ J

óg.B.II Variant A 70ZZ

C:alculated Winter heating load (I January - 31 March) without solar radiation.

(--) Healing Joad according to KLJ (-) Heating load according 1o ELAN Difference

2434 ( kWh ).

2422 ( kWh ).

-0.5 ( % ).

(58)

-f

l i 21 31 41 Sl 6! 71 81 91

·-·-> DA~ NJMB"9 i l l JRNJ'I'1~')

~---~ fig.B.12 Variant A20NA

CaJcu1akd Winter heating load (J January - 31 March) with night

set-back.

( --) Ht>ating load according to KLJ

(-) Healing 1oad according to ELAN Difference

1272 ( kWh ). 1260 ( kWh ). -0.9 ( % ).