art-3_Dan Constantinescu

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ASSESSMENT OF THE ENERGY PERFORMANCE OF THE SOLAR

SPACE SYSTEM ATTACHED TO THE CE INCERC BUCHAREST

EXPERIMENTAL HOUSE EXPERIMENTAL VALIDATION

Dan CONSTANTINESCU*

*National Building Research Institute INCERC, Bucharest, Romania; e-mail: [email protected]

REZUMAT

de 0,60 sch / h pe durata sezonului rece, prin

Cuvinte cheie:

1. INTRODUCERE

2008 martie 2009.

ABSTRACT

The INCERC Bucharest experimental house isequipped on the Southern faade with a ventilatedsolar space. The solar space ensures theventilation of the entire building at a constant rateof 0.60 exchanges/h during the cold season, byinletting the pre-heated space in the greenhousespace. In the hot season the system ensures the

building reversible ventilation by providing thefresh air rate by air suction in the building Northernzone, a consequence of the natural draught effectensured by the solar space. This report presentsthe experiments performed in the season 2008-2009and the experimental validation of the mathematicalmodel used in assessing the solar space energyperformance in the heating season.

Key-words: energy performance of buildings,ventilated solar space, building ventilation,mathematical model for performance evaluation ofspace solar power, solar energy

1. INTRODUCTION

The use of solar energy in spaces conditioning inthe form of passive and active systems was the objectof an important national research programmecoordinated by INCERC Bucharest and carried outin the period 1972-1985. A combination of thecharacteristics of two passive solutions experimentedon the support of the 2 solar houses: CS 1 Cmpina(1974) and CS 3 Bucharest (1982) (modified Trombe

and unventilated solar space) is represented by theControlled ventilation solar space, which is the objectof this report. The solution was experimentallyvalidated on the support of the CE INCERCBucharest experimental building. The report aims topresent the calculation method proper for dimension-ing and for assessing the energy performance of theVentilated solar space as a part of a new buildingwhich is efficient in terms of energy performance. Themathematical model is detailed and its validation on

the support of the experimental building in the seasonSeptember 2008 March 2009 is presented as well.


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2. PARAMETRI TERMODINAMICI

[1]

INCERC, destinat experimentale ametodelor de calcul al Performanei Energetice aCldirilorevacuat n exterior, ceea ce permite ventilarea

Aerul preluat n totalitate din exterior, cu temperaturate

(

tss

() > te(

eratura deconfort a aerului interior, t

a(), dar n multe ore din

reducerea consumului energetic al

2. MEASURED THERMODYNAMIC

PARAMETERS

The INCERC experimental building [1], [3]

assigned to the experimental validation of theBuildings Energy Performance calculation methodsis equipped with a ventilated solar space. Thefunction of the solar space in ensuring the occupiedspace thermal comfort is reversible. In fact, in thehot season, air is taken out from the occupied spaceand exhausted outside which allows the naturalventilation of the rooms by taking over air fromoutside; in the cold season it entirely substitutes thefunction of admitting fresh air in the occupied space

by forcedly introducing pre-heated air in theoccupied space. The pre-heating function is takenover by the solar radiation collecting unit(a reinforced concrete 0.20 m thick wall) as well asby the triple and selective glazing of the collectinggreenhouse. The air flow is ensured by two venti-lators providing a constant air flow-rate whichcorresponds to a ventilation rate of 0.6 exchanges /h specific to the dwelling building, properly suppliedwith fresh air. The air entirely taken from the outside,the temperature of which is t

e

() flows along the

collecting greenhouse space height and is flown intothe dwelling space at a temperature oft

ss() > t

e().

In fact the solar space takes over a part of the heatquantity to be supplied to the fresh air to let it reachthe indoor air comfort temperature, t

a(), but in

many hours of the cold season it also ensures spaceheating, entirely or partly, replacing the conventionalheating source.

The long-term experiment (since 2005)emphasizes the important function of the solar space

in reducing the heat demand (by about 30 %),correlated with the high rate of the building thermalprotection. The solar space becomes therefore anactive-passive component (mixed) in efficiently usingsolar radiation in ventilation as well as in reducingthe building heat / cold consumption.

In terms of quantifying the solar space thermalresponse, it is interesting to know the temperaturevariation of the pre-heated/hot air flown into theoccupied space, the thermal flow specific to the

collector inside surface and the building heatconsumption reduction during long periods (week,month and season) in the cold season. We

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n zona peretelui captator.

de-al doilea pentru monitorizarea parametrilor

t

e() temperatura aerului exterior [C],

ta1

() camera de zi (sufragerie) [C],

ta2

() dormitor SV [C],

ta3

()

tVENT1

() temperatura aerului introdus n

ocuit prin ventilatorul 1 dormitorSV [C], t

VENT2() temperatura aerului introdus n

[C],

taS1-0,5

() - solar zona 1 h = 0,5m [C],

taS1-1,5

() temperatura aerusolar zona 1 h = 1,5m [C],

taS1-3,0

() -

zona 1 h = 3,0m [C], t

aS2-1,0()

solar zona 2 h = 1,0m [C], t

aS2-2,5()

solar zona 2 h = 2,5m [C], t

PA(0)-i()

t

PA(0,15)()

[C],

tPA(0,30) ()

[C],

emphasize that the solar space provides to asignificant rate the hot water demand in the hotseason by simply fixing a collecting area in thecollecting wall zone.

The measurement chain that is used includesthree data acquisition systems: one for monitoringthe solar space operation and the thermodynamicparameters specific to the heated space, the secondfor monitoring the indoor heating system operationalparameters and the third for measuring the relevantclimatic parameters. The measurements performedin the INCERC experimental house allow theacquisition of the following values:

Monitoring system solar space:

te() outdoor air temperature [C],

ta1

() indoor temperature of the air in theliving room (dining room) [C],

ta2

() indoor temperature of the air in theSW bedroom [C],

ta3

() indoor temperature of the air in thekitchen [C],

tVENT1

() temperature of the air flown in the

dwelling space by ventilator 1 SWbedroom [C],

tVENT2

() temperature of the air flown in thedwelling space by ventilator 2 living room [C],

taS1-0,5

() solar space air temperature zone1 h = 0.5m [C],

taS1-1,5


taS1-3,0


taS2-1,0


taS2-2,5


tPA(0)-i

() temperature of the inside surface ofthe wall facing the solar space level

0.00 m from the inside [C],

tPA(0,15) () inside temperature of the wall facing

the solar space level 0.15m from

the inside [C],

Assessment of the energy performance of the solar space system


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tPA(0,36)

()

[C],

tPA(0,46)

()

[C],

tPA(0,56)-e

(

de la interior [C],

qST

() flux termic la

[W/m].

n graficul din fig. 1medii zilnice ale temperaturii exterioare, t

e, ale

t

mVEMP,

valoarea de 3,5 5de 68C, cu valori orare de

n graficul din fig. 4 se prezint graduluide nsorire al peretelui captator din compunereasolar, pe durata anului.

3. MODELUL MATEMATIC CU PAS

ORAR

Modelarea dinamic semnificative, pe ciclul diurn, a temperaturiiexterioare virtuale, proprie mediului exterior adiacent

tPA(0,30)

() inside temperature of the wall facingthe solar space level0.30m fromthe inside [C],

tPA(0,36)

() inside temperature of the wall facing

the solar space level0.36m fromthe inside [C],

tPA(0,46)

() inside temperature of the wall facingthe solar space level0.46m fromthe inside [C],

tPA(0,56)-e

() temperature of the outside surfaceof the wall facing the solar space level 0.56 m from the inside [C],

qST

() thermal flow at the level of the inside

surface of the wall facing the solar

space [W/m].

The diagram in Fig. 1 presents the variation ofthe daily average outdoor temperature, t

e, of the

temperature of the fresh air pre-heated in theventilated solar space greenhouse, t

mVEMPand of the

daily heat consumption in the period September2008 March 2009. The sensitive effect of the solarspace and its impact on the heat consumption isclearly noticed. The diagrams in Fig. 2 and 3 presentas examples two operational details, namely the daysof 05.01.2009 and 12.01.2009 which clearly showthe pre-heating of the fresh air flown in on the sunnydays when the daily average temperature is 3,55C and that of the fresh air is 68C, with hourlyvalues up to 20C.

The diagram in Fig. 4 presents the sunlight ratevariation of the collecting wall belonging to the solarspace, during the whole year.

3. DETAILED HOURLY STEP

MATHEMATICAL MODEL

In the phase of a new building designing, themathematical modeling of the heat transferprocesses, at an hourly pace requires to simulatethe thermal response of the solar space in the coldseason. The monthly pace modeling, the same as inthe case of space heating, proves to be a non-

recommended procedure because of the significantvariation, during the daytime cycle, of the virtualoutdoor temperature specific to the outdoorenvironment adjoining the solar space.

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0

10

20

30

40

50

60

70

80

90

-15

-10

-5

0

5

10

15

20

25

30

01.09 29.09 27.10 24.11 22.12 19.01 16.02 16.03

Consum

de caldura[kWh/zi]

TeTa

Tvent

[ C ]

Ziua

tmVENT [C] te ta med [C] CONS [kWh]

Fig. 1. Data recorded in the 2008-2009 cold season in the CE INCERC Bucharest experimental building

Fig. 2. Operation of the ventilated solar space on 05.01.2009 CE INCERC Bucharest experimental building

Heatconsumption[kWh/day]

Day /



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Fig. 3. Operation of the ventilated solar space on 12.01.2009 CE INCERC Bucharest experimental building

Fig. 4. Direct sunlight coefficient of the collecting wall of the solar space attached to the CE INCERC Bucharestexperimental building

Greenhouse sunlight [%] h hall shadow height on wall [m]

Directsunlig

htpercentage

Date /

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, care principalele ipoteze decalcul:

t(x, y, ) temperatura aerului din seracaptatoare, n care coordonatele x y,serei. Deschiderea serei se poate consideratemperaturi ale aerului att timp ct

(x, ) temperatura n interiorul pereteluicaptator care se poate considera de tip

unidimensional ca urmare a conducti- respectiv betonul armat cu valoarea=1,74W/m K.

propriu volumului de control dezvoltat pe adncimeaserei, caracterizat de temperatura medie a aerului nraport cu cota y

Avnd n vedere

(x, ):

(x,

The variation of the temperature range significantfor the solar space reveals the following functionswhich benefit from the main simplifying calculationhypotheses:

t(x, y, ) air temperature in the collectinghall, where the coordinates x and y meanthe height and the depth of the greenhouserespectively. The greenhouse span may beconsidered as not generating disturbancesof the air temperature range as long as theoutdoor air inlet is rather uniform and notpunctual;

(x, ) temperature inside the collectingwall which may be considered one-

dimensional because of the thermalconductivity of the material used forthe collecting component, namelyreinforced concrete, the value of which is=1.74W/m K.

We previously detailed the main simplifyinghypotheses substantiating the mathematical model.As concerns the greenhouse air temperature, itsvariation in the greenhouse depth is not significantbecause of the heat transfer concentration in the

boundary layer zone neighboring the two boundaries:the collecting wall and the glazing. Therefore, theproper simulation model is the one specific to thecontrol volume developed in the greenhouse depth,characterized by the air average temperature of levely. As concerns the thermally significant boundary,the solar radiation collecting wall, the most propermodel is that of the temperature uniform on thesurface with reference to the temperature distributionon the height. We emphasize that this hypothesis is

supported by the rather low intensity of the heattransfer between the area absorbing the solarradiation to air and to the glazed area.

Taking into account the elements describesabove, it results that the simulation model consistsin the following thermal balance equations:

the equation of the one-dimensional heattransfer by conduction through the collecting wall,with solution(x, ):

the equation is solved in terms of thesingleness conditions, namely the initial condition (x, = 0) which will be represented by a



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0

fluxului termic la frontierele elementului de

t();

v().

n fig. 5

a.

Fig. 5. Ventilated solar space calculation concept

)]()([)()](),([)( +==+ vcvpapcvepa ttStcGtxStcG (1)

i a energiei interne a aerului din volumul de control. Cotax se refer la grosimea peretelui captator.

b.

vvevvvcvpvpr SRttSttStx =+=1

)]()([)]()([)](),([ (2)ia temperaturii medii a aeruluit(

random value 0, taking into account the

ergodicity characteristic of the heat parabolicequation as well as the boundary conditionsexpressing the thermal flow continuity at the

boundaries of the collecting component,expressed by the III-rd rank boundarycondition;

the equation of the greenhouse air globalthermal balance on the control volume determinedby the greenhouse depth, height and span, withsolution t();

the glazed area thermal balance equation,with solution

v().

Fig. 5 presents the calculation concept.

Control volume

a. Greenhouse air thermal balance

equation:

Equation (1) is expressed according to thehypothesis of the air incompressibility andoverlooking the inner energy of the air in the controlvolume. Level x refers to the collecting wallthickness.

b. Glazing thermal balance equation

which provides the expression of the air averagetemperature t() according to the temperatures of

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)()(),()( 321 ++== evp tAtAxAt (3)

Intr3)conduce la determinarea expresiei temperaturii

)(),()( 21 +== epv tBxBt (4)

)(),()( 21 +== ep tCxCt (5)

c.

x = a peretelui captator

+==++

=

)](),([)]()1()([)(),(

txSSIcIcSx

xppcvvdsTsp

x

&

)](),([ =+ vppr txS (6)

=p

v

S

S.

)](),([)]1()1([),(

11 =+=

=Esprcv

x

ptxBC

x

x(7)

expresia:

+

+

+

+= )()(

)1()1()(

2211

22e

rcvrcv

rcvEs tI

BCBC

BCt

& (8)

cu:

)()1()()( += dsts IcIcI

n care coeficientul css-a utilizat conform fig. 4.

a III-a la cota x = .

d.cota x

)],0()([),(

0==

=xtx

xpii

x

p

(9)

the control volume thermodynamic outline and tothe outdoor temperature:

Relation (3) introduced in the balance equation(1) allows us to define the greenhouse glazing surfacetemperature:

Equations (3) and (4) are processed andgenerate as follows:

c. The III-rd order boundary condition at level

x = of the collecting wall generates the followingthermal balance equation:

=p

v

S

Sis marked.

The processing of equation (6) generates the

following relation:

where the equivalent outdoor temperature has thefollowing expression:

where:

where coefficient cs

was used according to thediagram in fig. 4.

Relation (7) represents the III-rd rank boundarycondition at level x = .

d.The III-rd order boundary condition at levelx = 0 is expressed by the following relation:



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C

)1()1( 11 BC rcve +=& ;1i& =

mmi

+1

(10)

n care m este indice pentru straturile din com-caracterizate de capacitate termic redus, alteledect per(elementul structural din BCA la carese stratul de termic)

==

==

=

=

)](),([),(

)],0()([),(

0

Espe

x

p

pii

x

p

txx

x

xtx

x

&

& (9)

(10)

la structura peretelui captator.

[2]. In

x

)]1()([exp]1)([exp)(exp)0(),0( 112

21

1

11 +++=== MM

M

NM

M

NMqxq ii (12)

Expresia temperaturii peretelui captator la cotax=,

p(x=,

)Bi1()()]()([Bi

Bi)(

Bi

)Bi1(Bi1),1( 1

1

++

+

++== iiEsi

e

ei

e

iep Rqtt

nRq

nx& (13)

n care

= xx& .

Grosimea a elementului de captare, precumade generare a structurii omogene echivalente [1].

++++

=+

=

++=

+++

=

112

3

2

1

2

1

Bi50,0)Bi()1(

)Bi1(Bi1Num;

Num

BiBi

Num

)Bi()1(

Bi

;Num

Bi

)]1(Bi1[

i

e

iee

e

e

e

e

ie

nn

n

na

M

nnM

n

Bina

M

(14)

The following notations are used:

wherem indicator for the layers forming the solarradiation collecting unit, characterized by a lowthermal capacity, others than the reinforced concretecollecting wall (the structural component made ofBCA autoclaved lightweight concrete plus thethermal insulation layer); the two boundary conditionsbecome as follows:

and are associated to the heat parabolic equationwith reference to the collecting wall structure.

An acceptable solution of the problem of theheat transfer through the solar radiation collectingunit may be provided by the heat conduction integralequation [2]. The heat transfer intensity at level

x = 0 (adjoining the occupied space) is determinedby the following relation:

The expression of the collecting wall tempe-rature at level x=,

p(x=,) is determined

by the following relation:

where

= xx& .

The collecting unit thickness as well as thethermal diffusivityaare determined by the procedureof generating the equivalent homogeneous structure[1]. The following notations were used:

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=

+

=

1

10

1

32

321 )(

jj

j

jj

EE

Ei

EE

tt

MN

ttMtt

MN

(15)

(orare) . Indicativul jtervalul decalcul curent, iar j1 intervalul anterior decalat cu .

Temperatura medie a aerului din volumul decontrovaloarea

p(x = ,

te

(

)](exp1[)](),([)(),( aytxtyt epe =+= (16)

,t(), permite identificarea coeficientului a:

aH

aH

tx

tt

ep

e )(exp11)(),(

)()( =

= 1)

(17)

n care t( cu5).

odei este cavaloarea a = ct. la orice moment .

:

)](),([)(),()( =+=== txaHtHytt petas (18)

Un alt element de identificarei de consisten

a (12) a integrale a cldurii l coeficientul numeric n al splinecare temperaturii n grosimea

peretelui captator, ( )), x . Valoarea acestuiatrebuie s fie constanti independentde momentul. Determinarea valorilor a i n se face pe caleexperimental prin aplicarea procedurii de validarea modelului matematic prezentat, particularizatpentru constructiv a serei captatoare dincomponena solar.

1)

)(),(

)(),(

=

==

ep

p

tx

tx ,aH

aH)(exp1 =

Relations (12) and (13) can be used by meansof the recurrence procedure in finite (hourly) time-lags,. Identifier j defines the current calculationinterval and j 1, the previous interval modified by .

The average temperature of the control volumeair is determined by relation (5) according to value

p(x = , ), determined by relation (13) and by

the outdoor temperature te

(). The air temperaturevariation along the control volume height (of thecollecting greenhouse) may be expressed by thefollowing relation:

The expression of the greenhouse heightaverage temperature, t() allows the identificationof coefficient a:

where t() is determined at each moment byrelation (5).

The consistency condition of this method is thatvalue a = ct. at any moment.

Thus is determined the temperature value ofthe air exhausted in the occupied space at eachmoment :

Another item used in identifying the verifying

the consistency of solution (12) of the heat integralequation is the value of the numerical coefficient nof the spline function which represents thetemperature variation in the collecting wall thickness, (x, )). Its values should be constant andindependent of moment . Values a and n areexperimentally determined by the procedure ofvalidating the mathematical model presented,particularized for the constructive solution of thecollecting greenhouse belonging to the solar space.



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4. VALIDAREA EXPERIMENTA MODELULUI MATEMATIC PE

SUPORTUL SPALCE INCERC Biarna 2008-2009

caracterizate de debitele volumice de 44,5m3/h3/h, n total 102,1m3/h. n raport cu

3, debitul

S1) 01.10.2008 10.10.2008 15 zile

(232 ore)2) 15.11.2008 25.12.2008 41 zile

(976 ore)3) 13.01.2009 04.03.2009 51 zile

(1217 ore)

n total 107 zile (2425 ore), interval semnificativ

pentru validarea metodei de calcul.

t

as-m(

tas-t

(), (18),difere

)]()([)( tttGcQ easpavss = (19)Conform celor , o particularitate a

de determinarea cu caracter de identificare aexponentului ncaptator opac. Validarea presupune ca pe toaten.Valoarea n

4. EXPERIMENTALVALIDATION OF

THE MATHEMATICAL MODEL ON

THE SUPPORT OFTHE CE INCERC

BUCHAREST SOLAR SPACE

winter 2008-2009

The experiment was performed in the 2008-2009 cold season; in this period the solar spaceoperated and thus contributed in providing the freshair rate to CE INCERC Bucharest.

The two ventilators supplying pre-heated freshair in the solar space greenhouse are characterizedby volume air-flows of 44.5m3/h and 57.6m3/h,a total of 102.1m3/h. Compared to the building

total volume of 167.8m3, this flow-rate represents0.61 exchanges / h.

The following validation periods were selected:1) 01.10.2008 10.10.2008 15 days

(232 hours)2) 15.11.2008 25.12.2008 41 days

(976 hours)3) 13.01.2009 04.03.2009 51 days

(1217 hours)

a total of 107 days (2,425 hours), a significant period

for the validation of the calculation method.

The validation indicators used include besidethe analysis of the hourly differences between theexhausted air temperature, measured, t

as-m() and

the exhausted air temperature determined bycalculation t

as-t(), (18), the differences during the

above mentioned periods between the solar spaceenergy performance determined theoretically and thecalculated one:

According to the elements mentioned above, acharacteristic of the heat integral equation solutionis represented by the determination, meaningidentification, of thenexponent specific to the splinefunction which describes the space variant of thetemperature in the opaque collecting wall thickness.The validation implies the fact that during all thesupport periods, the same value n should bepreserved. Value n does not influence the result in

terms of energy performance. The only influence isnoticed on the amplitude of the oscillation of thetemperature of the air exhausted from the solarspace.

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4.1.este n=0,65. Fenomenul fultat. n graficul din fig. 6

)())((

nft

t

as

as =

(20)

na (17)conduce la valoarea a

H=3,106, valoare care

0,00575

0,005875

0,006

0,006125

0,00625

0,006375

0,0065

0,006625

0,00675

0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1

n

ab.

med.patratica/temp.medie.teor.[-]

Fig. 6. Determination of exponent n value period 01.10.2008 10.10.2008

(Determinarea valorii exponentului n interval 01.10.2008-10.10.2008)

2

2

(conf

n graficul din fig. 7tas-t

(), tas-m

(), te() pentru intervalul analizat. Prin

Ct tas = 1,28 , Ct mas = 3,27 .

4.2.Cel de al doilea interval cuprins ntre

14.11.2008-aHn=0,60. n graficul

din fig. 8 se prezinf(n) (20), dinn = 0,60.

4.1. The optimum value for the first period isn = 0.65. As the phenomenon is the same, theother periods should also lead, theoretically, tothe same result. The diagram in Fig. 6 presents the

function:

which confirms value n= 0.65 as the optimum value.For the period of time under analysis, equation (17)provides value a H=3.106; both values have tobe confirmed in the under periods of time underanalysis.

In terms of the Energy Performance criterion,

the specific values are 3.66kWh/m2

(according tothe measurements) and 3.92kWh/m2 (accordingto the theoretical model) respectively, whichgenerates a global deviation of 7.26 %which isconsidered acceptable. The diagram in Fig. 7 presentsthe hourly variations t

as-t(), t

as-m(), t

e() for the

period of time under analysis. Values Ct tas = 1.28 ,

Ct mas = 3.27 result from averaging.

4.2. The second time-lag, 14.11.-25.12.2008

confirms the preservation of value a H =3.106and the reaching of value n = 0.60. The diagrame inFig. 8 presents the variation of function f(n) (20),which provides n = 0.60.

squarestand

arddeviation/theoreticalaveragetemp



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6

10

14

18

22

26

30

34

38

42

46

0 10 2 0 30 40 50 6 0 70 80 90 100 110 1 20 13 0 140 150 160 1 70 180 190 200 2 10 22 0 230

momentul [h]

t.vent.m,t.vent.t,te[C]

te

t-vent.m [C]

t-vent.t [C]

Fig. 7. Temperatures specific to the operation of the ventilated solar space 01.10.2008-10.10.2008

(232 hours) CE INCERC Bucharest

0,00527

0,00528

0,00529

0,0053

0,00531

0,00532

0,00533

0,00534

0,00535

0,00536

0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1

n

ab.med.patrati

ca./temp.medie.teor.[-]

Fig. 8. Determination of exponent nvalue period 15.11.2009-25.12.2008 (Determinarea

valorii exponentului n interval 15.11.2009-25.12.2008)

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Fig.VI.5 Temperaturi caracteristice functionarii spatiului solar ventilat 15.11.2008 - 25.12.2008(976 ore) CE INCERC Bucuresti.

-4

-2

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0 48 96 144 192 240 288 336 384 432 480 528 576 624 672 720 768 816 864 912 960

momentul [h]

t.vent.m,t.v

ent.t,te[C]

t-vent .m [C]

t-vent.t [C]

te [C]

Fig. 9. Temperatures specific to the operation of the ventilated solar space 15.11.2008-25.12.2008(976 hours) CE INCERC Bucharest

valorile specifice sunt de 9,53kWh/m2, respectiv9,83kWh/m2

modelului de calcul.n graficul din fig. 9alorile orare

tas-t

(), tas-m

() pentru intervalul analizat. Prin

Ct tas = 7,11 , Ct mas = 5,11 .

4.3.

valorile n=0,55, aH=3,106, 2kWh/m26,15=mq ,

2kWh/m84,15=tq , %63,3= , ceea ce repre-

Ct tas = 5,12 Ct mas = 2,12

n graficul din fig. 10f(n), iar n

graficul din fig. 11 valorile tas-t

(), tas-m

(), te().

n

In terms of energy performance, the specificvalues are 9.53kWh/m2 and 9.83kWh/m2

respectively, which generate a global deviation inthe time-lag of 3.16%, confirming the validity of

the calculation model.The diagram in Fig. 9 presents the hourly values

tas-t

(), tas-m

() for the analyzed time-lag. ValuesCt tas = 7.11 , Ct mas = 5.11 are provided by

averaging.

4.3. The third case is characterized by values

n=0.55, a H=3.106, 2kWh/m26.15=mq ,

2kWh/m84.15=tq , %63.3= , which represent

a clear validation. Values Ct tas = 5.12 andCt mas = 2.12 also attest the very good estimation

by the theoretical model.The diagram in Fig. 10 presents f(n) and the

diagram in Fig. 11 values tas-t

(), tas-m

(), te().

This analysis shows that the hourly calculationmodel used for the temperature of the air exhaustedin the occupied space provides results allowing theirinclusion in the calculation algorithm of the thermalresponse of the entire building, if the average valuen = 0.62 is used (an average rated with the



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68 Nr. 1 / 2010

Fig.VI.7 Temperaturi caracteristice functionarii spatiului solar ventilat 13.01.2009 - 04.03.2009 (1217

ore) CE INCERC Bucuresti

-8

-4

0

4

8

12

16

20

24

28

32

36

40

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

momentul [h]

t.vent.m,t.vent.t,te[C]

te

t-vent.m [C]

t-vent.t [C]

Fig. 11. Temperatures specific to the operation of the ventilated solar space 13.01.2009-04.03.2009 (1217 hours), CE INCERC Bucharest

Fig.VI.6 Determinarea valorii exponentului "n" - interval 13.01.2009 - 04.03.2009

0,00768

0,00769

0,0077

0,00771

0,00772

0,00773

0,00774

0,00775

0,00776

0,00777

0,00778

0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1

n

ab.med.patratica/temp.med.teoretica[-]

Fig. 10. Determination of nexponent values period 13.01.2009-04.03.2009

(Determinarea valorii exponentului n interval 13.01.2009-04.03.2009 )

squ

arestandarddeviation/theoreticalaveragetemp

D. Constantinescu


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69 Nr. 1 / 2010

Material Thickness [m] [W / mK] [kg / m3] c [J / kgK] a [m3 / s]Mat. 1 1 1 1 C1 a1

Mat. 2 2 2 2 C2 a2

Mat. 2 2 3 3 C3 a3

.. . ... ... ... ... ...

Mat. n 1 n 1 n 1 n 1 Cn 1 an 1

Mat. n n n n Cn an

captatoare.

5. S

5.1. Determinarea structurii omogene

echivalente a elementului de

5.1.1. face de la interior la exterior) (Tabelul1)

5.1.2. Determinarea valorii i

E

TRrcvi

S

SF += ; )6(2,0

iPRNF =

5.1.3. e& (10)

5.1.4. termice)

=

+

+

=n

k kei

R1

11&

5.1.5.

M),M

cM.

measurements durations) as well as the direct sunlightcoefficients resulted from the analysis of the sunlightcoefficient of the solar radiation collecting surface natural and artificial obstacles and from the glazing

rate of the collecting greenhouse front surface.

5. METHODOLOGICAL SYNTHESIS

It requires considering the solar radiationcollecting unit as a homogeneous flat plate withmaterial geometrical and thermo-physicalcharacteristics which are determined as follows:

5.1. Determination of the equivalent

homogeneous structure of the solar

radiation collecting unit

5.1.1. Real component structure, thermo-physical characteristics, thermal resistance (the layersare marked from the outside to the inside) (Table 1).

Table 1.

5.1.2. Determination of value i

5.1.3. Value e& is determined by relation (10).

5.1.4. Thermal resistance (the thermal bridgesare excluded)

5.1.5. Random values of the density and of the

mass specific heat of the single material (M) areselected selected, namelyM

andcM.



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70 Nr. 1 / 2010

5.1.6.

M:

2

=

k k

k

k MMk

k

Mca

5.1.7. omogene echivalente, pe fiecare strat n parte:

50,0

=MM

kk

k

MkM

c

ck

5.1.8.

=k

MM k

5.1.9.

MM

MM

ca

=

structurii echivalente:

M

M

ei

R

+

+

=&

11

p

v

S

S= ; 1111 = Vcv RA ;

cv

vcvr RA

++=

11

2 ;11

3 = vcv RA

])1([

)]1([

222

1111

AAAcg

AAAcgB

cvpa

cvpa

++

+=&

&;

])1([

)1()1(

222

332

AAAcg

AAcgB

cvpa

cvpa

++

++=&

&;

1211 BAAC += ; 2232 BAAC += ;22

1BC

Drcv +

=

&;

M

Mii

=Bi ;

M

Mee

= &Bi ;

n

M1, M2, M3, 14).

5.1.6.The equivalent thermal conductivity is

5.1.7. The thickness of the equivalent homo-geneous structure is determined for each layer:

5.1.8. The total equivalent thickness isdetermined:

5.1.9. The equivalent thermal diffusivity isdetermined:

5.2. The equivalent structures thermal

resistance is determined:

(equal to the real structure thermal resistance).

5.3. The following numerical coefficients

are determined:

n = 0.62 (for the solution of the CE INCERCBucharest solar space)

M1, M

2, M

3, Num, according to relation (14).

determined,M:

D. Constantinescu


19/19

tE():

)]()1(1,1)([)()(22

++

+= dsTs

rcv

eE IcIc

BC

tt&

(deoarece C2 = 1 C1; B2 = 1 B1).

5.5.N1, N

2(conform (15))

dinamice sunt:

qi(x = 0, ) conform (12)

p

(x =M

, ) conform (13)t() conform (5)tas

() conform (18)

Dintre acestea qi(x = 0, t

as() sunt para-

6. CONCLUZII

1.

solar ventilat s-a elaborat un model propriu regimuluivariabil de transfeavnd ca.

2.suficient pentru a valida statistic rezultatele.

3.

4.

BIBLIOGRAFIE

[1] * * *

contextul prevederilor directivei europene 2002/

91/EEC[2] Constantinescu, D. .

, Vol. 1 Fundamentare, Ed. AGIR, 2008

5.4. The equivalent temperature tE() is

determined:

(as C2 = 1 C1; B2 = 1 B1).

5.5. N1, N

2are determined (according to 15)

The calculation relations necessary in deter-mining the thermal flows and the temperaturesrequired by the dynamic simulation are:

qi(x = 0, ) according to (12)

p

(x = M

, ) according to (13)t() according to (5)tas

() according to (18)

Of these, qi(x=0,) and t

as() are the

parameters required by the dynamic simulation ofthe main zone of the building, which is equipped witha ventilated solar space.

6. CONCLUSIONS

1.Taking into account the ventilated solarspace of CE INCERC, a model specific to the hourlypace heat transfer transient conditions was carriedout, the object of which is the modeling of thedynamic process of pre-heating the air exhausted inthe building.

2.The experimental validation tests coveredthree periods of time totalizing 104 days, a numbersufficient for statistically validating the results.

3. The parallel analysis was focused on thetemperature variation of the hot air exhausted in theheated space and on the thermal flow supplied tothe ventilated solar space by a convective effect.

4. The errors between the measured and thecalculated values range between 3-8 % which con-firms the satisfactory accuracy of the mathematicalmodel specific to the ventilated solar space.

BIBLIOGRAPHY

[1] *** Impact of the modern solutions of the energyupgrading of the existing buildings on their energyand economic performance, in the context of theEuropean Directive 2002/91/EEC, Contract 6B02Amtrans, Phases 3 and 4/ 2004

[2] Constantinescu, D., Heat Engineering Treatise Heat Engineering in Construction, Vol. 1, Ed. AGIR,Bucharest, 2008


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