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Solar Energy 91 (2013) 1–10

A numerical and experimental analysis of the air vent management andheat storage characteristics of a trombe wall

Yanfeng Liu ⇑, Dengjia Wang, Chao Ma, Jiaping Liu

School of Environmental and Municipal Engineering, Xi’an University of Architecture and Technology, No. 13 Yanta Road, Binlin District,

Xi’an 710055, China

Received 28 May 2012; received in revised form 9 January 2013; accepted 19 January 2013Available online 27 February 2013

Communicated by: Associate Editor D. Laing

Abstract

The optimum opening and closing modes in the management of air vents has been obtained by testing and analyzing thermal perfor-mance parameters of a trombe wall installation. The parameters considered include air vent velocity, air vent temperature, the temper-ature distribution of air layer and indoor air temperature. The temperature and velocity distribution of the air layer has been obtained bynumerical calculation, together with experimental data including the heat storage and release characteristics and the influencing factorsof the trombe wall. The research results show: the optimum time to open the air vent of the trombe wall is 2–3 h after sunrise with closure1 h before sunset. On the condition of optimum air vent management mode, surface and average temperature of heat storage wall com-puter simulations were run with CFD to analyze the heat storage and release performance of trombe wall. Then, we can find out the heatstorage capacity of the trombe wall reaches its maximum value at 4 pm, its minimum value at 7–8 am. These research results provide areference base for the optimization of design and the operational management of a passive solar house with trombe wall.� 2013 Elsevier Ltd. All rights reserved.

Keywords: Trombe wall; Air vent; Optimization design; Heat storage

1. Introduction

The use of a ‘passive’ solar heating house with a trombewall is widely used in cold climates. However, it is hard tofully meet the requirements of indoor thermal environmentfor the majority of the required heating period. Thus, itneeds to be matched with an active heating system. Theheat storage and release law of the trombe wall needs tobe mastered to configure active heating system capacity.This law is directly related to the opening and closing modeof air vent. Many researches indicate that the managementmode of air vent opening at sunrise and closing at sunset isquestionable.

0038-092X/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.solener.2013.01.016

⇑ Corresponding author. Tel.: +86 29 82201514, mobile: +8613909261178.

E-mail address: lyfxjd@163.com (Y. Liu).

In 1956, solar energy collection was first used to improvethe indoor thermal environment. Felix et al. (1973a,b)came up with the famous passive solar heating pattern ofsolar collector and heat storage wall—trombe wall. Dr.J.D. Balcomb, Los Alamos National Lab., compiled theanalog computation program PASOLE to provide a com-puted foundation for the research and design of trombewall (Balcomb et al., 1977). Wang et al. (1989a,b) has useda reaction coefficient method to develop thermal calcula-tion software for passive solar house PSHDC. This canbe applied to thermal calculation of trombe wall. Chenand Liu (2004) used unsteady state numerical simulationmethod to analyze convection and heat conduction of aporous solar collector and heat storage wall. Jubran andHnardna (1991) and other scholars conducted numericalsimulation to the natural convection in the air layer oftrombe wall, to determine the relationship between

Nomenclature

as1 the absorptivity of the external surface of ther-mal storage wall

asm radiation absorptivity of external glass surfaceasn radiation absorptivity of roof external surfaceAw outdoor air temperature amplitude (�C)cp air heat capacity (kJ kg�1 �C�1)cl empirical coefficientf1, f2, fl empirical functions of turbulence Reynolds

number appearing in k � e turbulence modelg acceleration of gravity (N/kg)G the generation of turbulence kinetic energy due

to the mean velocity gradientsIsun,H solar radiation intensity of roof (W m�2)Isun,V solar radiation intensity of south wall (W m�2)k turbulent pulsation kinetic energyp pressure (Pa)Qc1g convection heat exchange of the external surface

of thermal storage wall (W m�2)Qcmg convection heat exchange amount of glass (W m

�2)Qrmg radiant heat transfer of glass (W m�2)Qrng radiant heat transfer of roof (W m�2)Qr1g radiation heat exchange between thermal stor-

age wall and glass cover-plate (W m�2)Sn internal heat source (W)tw outdoor average temperature (�C)T temperature (�C)T0 wave period of outdoor air temperature (h)

Tc temperature of reference point (�C)u velocity components in the direction of x (m s

�1)v velocity components in the direction of y (m s�1)

Greek symbols

b expansion coefficient of air volume (K�1)e dissipating rating of fluid pulsation kinetic en-

ergy per unitg viscosity coefficient of gas molecule (kg S�1 m

�1)geff effective diffusion coefficient (kg S�1 m�1)gt gas turbulent viscosity coefficient (kg S�1 m�1)k heat conductivity coefficient of air(W m�1 K�1)k1 coefficient of heat conductivity of thermal stor-

age wall (W m�1 K�1)km heat conductivity coefficient of glass (W m�1 K

�1)kn heat conductivity coefficient of roof material

(W m�1 K�1)q air density (kg m�3)rT empirical coefficients time (s)sg transmissivity of glass cover-plateU u, v and xwo initial phase of outdoor air temperature (rad)x velocity components in the direction of z (m s�1)

2 Y. Liu et al. / Solar Energy 91 (2013) 1–10

temperature distribution of wall surface and inclination ofglass cover-plate. The results indicate that an extremelysmall inclination glass cover-plate can also improve thethermal properties of trombe wall. Omriston andJRaithby (1986) was the first to conduct numerical predic-tion of the trombe wall system, the research finding byanalysis that the air flow interaction of the indoor andair layer is the main factor to affect air flow and heat trans-fer of trombe wall. Jaber and Ajib (2011) studied thermalenvironment and economic impact of trombe wall systemfor residential building in Mediterranean region. Theenergy performance comparison of single glass, doubleglass and a-Si semi-transparent PV module integrated onthe trombe wall fac�ade of a model test room has been car-ried out (Koyunbaba and Yilmaz, 2012). Many otherscholars have undertaken research on properties of varioustypes trombe wall (Huang et al., 1997; Burek and Habeb,2007; Ye and Ge, 2000).

In this research the thermal property of a trombe wallwas investigated by experimental and numerical calculationmethods. The solar collector parts of the wall weredesigned with the goal of coming up with the optimumopening and closing management mode of air vent andmastering heat storage and release law of trombe wall.

2. Experimental research on the air vent management mode

2.1. Experimental objectives

The experimental research used the solar energy heatingdemonstration project of the herdsman settlement which islocated in GangCha County, QingHai Province, China.The size of house is: width 3300 mm � depth3900 mm � height 2900 mm. The east, west and northwalls are constructed with 240 mm thick brick walls. Thesouth wall is trombe wall, the structure is 4 mm simpleglass, 100 mm air layer,10 mm red corrugated iron,240 mm brick wall and a 50 mm polystyrene cystosepi-ment. The absorptivity and emissivity of the brick wallexternal surface material are 0.9 and 0.3 respectively (Liu,2009). The size of air vent is 200 mm � 200 mm. Thereare two air vents on the top of the trombe wall. The dis-tance between air vent and trombe wall top edge is200 mm, and there are three air vents on the bottom ofthe trombe wall. The distance between the air vent andthe bottom edge of the trombe wall is also 200 mm. Thestructure of external window is 4 mm simple glass, 4 mmair layer, and 4 mm simple glass. The size of window is1500 mm � 1800 mm. The roof and ground structure are

Fig. 1. Live-action of test object.

Fig. 2. The interior view of the test room with measurement devices.

Y. Liu et al. / Solar Energy 91 (2013) 1–10 3

200 mm fine concrete + 80 mm polystyrene cystosepimentand 200 mm fine concrete + 50 mm polystyrene cystosepi-ment respectively. The Live-action and the interior viewof test object are shown in Figs. 1 and 2. Fig. 3 is trombewall system and testing point. Fig. 4 is physical model ofpassive solar house with trombe wall.

2.2. Test parameter and instrument

Test parameters include the solar radiation intensity ofdirect and scattered radiation of the horizontal and southelevation, the indoor and outdoor air temperature, the airtemperature of air layer of trombe wall and air temperature

and the velocity of air vent. The test instrument, type andparameters are shown in Table 1.

2.3. Test results and analysis

Solar radiation intensity and outdoor air temperature isshown in Fig. 5. The air velocity of the air vent is shown inFig. 6. The temperature distribution in the air layer isshown in Fig. 7. The average temperature of indoor airand layer air is shown in Fig. 8.

According to Fig. 5, the sunshine duration is 10–11 hduring the testing period in GangCha County. The averagevalues of the total solar radiation of the horizontal planeand the south elevation in sunlight are 315 W/m2 and445 W/m2 respectively. The maximum radiation on thehorizontal plane occurs at about 14:00. The maximum onthe south elevation occurs a little later, because it faces tosouth by west 15�. Direct solar radiation occupies about80–85% of total solar radiation intensity. Thus, it is clearthat solar radiation is strong in this area. It also shows thatthe solar radiation intensity of south elevation is strongerthan horizontal plane, amounting to about 1.4 times.Owing to high latitude and small solar elevation angle,the solar radiation on the south wall is more than horizon-tal plane, which provides a favorable solar radiation condi-tion for the usage of a trombe wall. And, the highest,coldest and average temperature of outdoor air in thewhole day are �10.2 �C, �28.1 �C and �20.2 �C respec-tively. It is a cold region.

It is shown from Fig. 6 that under heated pressure, nat-ural ventilation circulation among the air layer, air ventand indoor air is formed. Airflow in the upper air vent isin opposite direction to that in lower air vent. Becausethere are two air vents in upper side and three air ventsin lower side, under the same airflow, the air velocity inupper air vent is higher than that of lower air vent. Duringthe testing period the air vent was opened at 8:00 andclosed at 19:00. The testing time of air velocity was from9:00 to 18:30. Data in this figure shows that the air velocityof upper air vent was negative before 10:30. The air veloc-ity of the lower air vent is a positive value, which indicatesthat indoor air flows to the air layer from upper air ventand air in layer flows to house from lower air vent whichis a reverse cycle. It is a cooling period for indoor air. How-ever, it is a positive cycle after 10:30, which is a heatingprocess for indoor air. It can be explained as follows: atsunrise, the solar radiation intensity is relatively low. Ithas a limited heating effect on thermal storage wall andair layer. Average temperature in air layer is lower thanindoor air temperature. At about 10:30, solar radiationintensity is enhanced. The temperature of air layer isapproximate to indoor temperature. With the increase ofsolar radiation, the temperature of air layer becomes grad-ually higher that indoor temperature. The results indicatethat it is reasonable to open air vent at about 10:30, or2–3 h after sunrise. Similarly, at about 18:00, the averagetemperature in air layer is appropriate to indoor air tem-

Vent panels

Interior

Exterior

Brick wall (240mm)Polystyrene cystosepiment(50mm)

Red corrugated sheet iron(10mm)

Air layer(100mm)

Simple glass(4mm)

Glazing Vent closedGlazing

(b) Nighttime(a) DaytimeThe temperature testing point The temperature and velocity testing point

Interior

Exterior

The temperature and RH testing point

Fig. 3. Trombe wall system and testing point.

y

z

x air vent (200mm 200mm)

air layer (100mm)

heat storage wall

heat storage floor

glass

glass window

2900

mm

3300mm

3900mm

Fig. 4. Physical model of passive solar house with trombe wall.

Table 1Test instrument, type and parameter.

Test parameters Test instrument Type Accuracy Operating method

Solar radiation intensity Solar pyranometer TBD-1 ±8.789 W/m2 (All day) automatic recording every10 min

Recording meter QTS-4 —— ——Indoor air temperature Recording thermometer TR-72U ±0.2 �C (All day) automatic recording every

10 minAir layer temperature Thermocouple thermometer CENTER309 ±(0.3%rdg)+1 �C(All day) automatic

recording every 10 minAir vent wind speed Pressure/wind speed/temperature

multifunction meterSwema3000 —— (9:00–18:30) automatic recording

every 10 minUniversal micro-air velocity probe SWA03 ±1% ——

Air vent air temperature Thermocouple thermometer CENTER309 ±(0.3%rdg)+1 �C(9:00–18:30) Automatic

recording every 10 min

4 Y. Liu et al. / Solar Energy 91 (2013) 1–10

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:00-100

0

100

200

300

400

500

600

700

800

900

1000

-35

-30

-25

-20

-15

-10

-5

0

Tem

pera

ture

[]

Sol

ar r

adia

tion

inte

nsit

y [W

/m2 ]

Hour of the day

south elevation scattering horizontal scattering south elevation direct horizontal direct

Outdoor air

Fig. 5. Solar radiation intensity and outdoor air temperature.

09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Vel

ocity

[m

/s]

Hour of the day

Top vent airflow Bottom side vent airflow Bottom centre vent airflow

Fig. 6. The velocity of air vents.

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:00

-20

-10

0

10

20

30

40

50

Tem

pera

ture

[]

Hour of the day

The top layer The middle layer The bottom layer

Fig. 7. Temperature distribution of air layer.

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:00

-20

-10

0

10

20

30

40

Tem

pera

ture

[]

Hour of the day

Average temperature of the air layer Indoor air temperature

Fig. 8. The average temperature of indoor air and layer air.

Y. Liu et al. / Solar Energy 91 (2013) 1–10 5

perature. After this time, the average temperature in airlayer is lower than indoor air temperature, which is alsoa negative cycle. Thus, it is reasonable to close air vent at18:00 or 1 h before sunset.

According to Fig. 7, the temperature of the air layer is ofobvious layered effect. The daily average temperature ofupper, middle and lower measure point are 2.0 �C,

�3.7 �C and �9.6 �C respectively. During the optimumopening time (10:30–18:00), which are 28.3 �C, 22.5 �Cand 5.6 �C respectively. The temperature differencebetween upper and lower point can reach 22.7 �C, Itprovide a favorable temperature difference condition fortrombe wall to conduct heat convection to improve ther-mal environment of room during the daytime.

In Fig. 8, the relationship between the average tempera-ture of air layer and indoor temperature is given. The opti-mum opening and closing mode of the air vent is given bythe view of the airflow direction in the vent. Thus, the lawof temperature in this figure visually explains this point: theaverage temperature of air layer is appropriate to that ofindoor air temperature at 10:30 and 18:00, amounting to�3.7 �C and 3.5 �C respectively. The average temperatureof air layer is higher than the indoor air temperature from10:30 to 18:00. In this time range, the air vent should beopened. To be conclude, it is optimum efficiency to openair vent 2–3 h after sunrise and close it 1 h before sunset.

3. Numerical research on heat storage and release of trombe

wall

3.1. Assumed condition

The physical model of numerical simulation is shown inFig. 4. In the research on the heat storage and the releaselaw of trombe wall, the heat convection of indoor air andair layer of trombe wall and heat-transfer process in ther-mal storage wall need to be analyzed, which is the couplingthermal process between convection and heat conduction.In the research on air current distribution in the air layer,the Boussinesq assumption is thought to be right (Tao,2011), and a low Reynolds number k � e model is used.Indoor air is assumed to be free convection of three-dimen-sional unsteady state. The following assumptions are alsomade:

(1) Air in the air layer is a single-phase incompressiblefluid.

6 Y. Liu et al. / Solar Energy 91 (2013) 1–10

(2) The buoyancy caused by temperature difference istaken into consideration, disturbance to air currentdistribution caused by air infiltration from the doorand windows and personnel activity are ignored.

(3) No other heat source exists in room.

3.2. Governing equation

3.2.1. Equation of continuity

@q@tþ @ðquÞ

@xþ @ðqmÞ

@yþ @ðqxÞ

@z¼ 0 ð1Þ

where q is air density, kg/m3, x and y is horizontal direc-tion and z is the vertical direction and u, v and x are veloc-ity components in the direction of x, y and z respectively.These are measured in m/s.

For an incompressible gas, density is a constant. Theequation of continuity can be abbreviated to be:

divðUÞ ¼ 0 ð2Þ

3.2.2. Equation of momentum

General equation of momentum in x, y and z directionis:

@ðqUÞ@s

þ @ðquUÞ@x

þ @ qmUð Þ@y

þ @ðqxUÞ@z

¼ @

@xgeff

@U@x

� �þ @

@ygeff

@U@y

� �þ @

@zgeff

@U@z

� �þ SU

when U is u, v and x, source item SU are:Source item (u)

Su ¼ �@p@xþ @

@xgeff

@u@x

� �þ @

@ygeff

@m@x

� �

þ @

@zgeff

@x@x

� �ð3Þ

Source item (v)

Sm ¼ �@p@yþ @

@xgeff

@u@y

� �þ @

@ygeff

@m@y

� �þ @

@zgeff

@x@y

� �ð4Þ

Source item (x)

Sx ¼ �@p@zþ @

@xgeff

@u@z

� �þ @

@ygeff

@m@z

� �

þ @

@zgeff

@x@z

� �þ qgbðT� T cÞ ð5Þ

The last item of Eq. (5) is the buoyancy caused by tem-perature difference, applying Boussinesq hypothetical cor-rection item. Because the research object has a low Renumber, the effective diffusion coefficient geff should includea turbulent diffusion coefficient and a molecular diffusioncoefficient.

geff ¼ gþ gt ð6Þ

where g is viscosity coefficient of gas molecule, kg/(S m), gt

is gas turbulent viscosity coefficient, kg/(S m), b is expan-sion coefficient of air volume, 1/�C and Tc is temperatureof reference point, �C.

gt ¼ cljfljqk2=e ð7Þ

fl ¼ exp�2:5

1þRet=50

� �ð8Þ

Ret ¼ qk2=ðegÞ ð9Þ

where cl is empirical coefficient, k is turbulent pulsation ki-netic energy and e is dissipating rating of fluid pulsation ki-netic energy per unit mass.

3.2.3. Energy equation

@ðqT Þ@s

þ @ðquT Þ@x

þ @ðqmT Þ@y

¼

@

@xgeff

@T@x

� �þ @

@ygeff

@T@y

� �þ @

@zgeff

@T@z

� �þ ST

ð10Þ

where,

geff ¼kcpþ gt

rT¼ g

Prþ gt

rTð11Þ

where g/Pr is caused by molecular diffusion, gt/rT is causedby turbulent pulsation, k is heat conductivity coefficient ofair, W/(m K), cp is air heat capacity, kJ/(kg �C) and rT isempirical coefficient.

Source item ST includes internal heat source Sn and dis-sipative function of converting mechanical energy into heatenergy caused by sticky function. Internal heat source is 0.

then

ST ¼ geff 2@u@x

� �2

þ @m@y

� �2

þ @x@z

� �2" #

þ @u@yþ @m@x

� �2(

þ @u@zþ @x@x

� �2

þ @m@zþ @x@y

� �2)

ð12Þ

Introduce the Boussinesq assumption. Then, the key tocalculate turbulence flowing is to determine gt. Jones andLaunder (1972,1973) introduced low Re number k � eequation and gave the calculation equation of gt. Withthe introduction of two variables k and e, this equation isunclosed. Thus, in order to make this equation closed (toresolve), a partial differential equation including pulsationkinetic energy k and dissipation rating of pulsation energye should be given.

3.2.4. k � e EquationGeneral formula of pulsation kinetic energy k and dissi-

pation rating of pulsation kinetic energy e equation is:

Y. Liu et al. / Solar Energy 91 (2013) 1–10 7

@ðqUÞ@s

þ @ðquUÞ@x

þ @ðqmUÞ@y

þ @ðqmUÞ@z

¼ @

@xCU

@U@x

� �þ @

@yC@U@y

� �þ SU ð13Þ

Source item (k)

Ck ¼ gþ gt

rk

Sk ¼ gtG� qe� 2g@k1=2

@y

!2������

������G ¼ 2

@u@x

� �2

þ @m@y

� �2

þ @x@z

� �2" #

þ @u@yþ @m@x

� �2

þ @u@zþ @x@x

� �2

þ @m@zþ @x@y

� �2

Source item (e)

Ce ¼ gþ gt

re

Se ¼ek

c1jf1jgtG� qc2

e2

kjf2j þ

2ggt

q@2x@z2

� �2�����

�����G ¼ 2

@u@x

� �2

þ @m@y

� �2

þ @x@z

� �2" #

þ @u@yþ @m@x

� �2

þ @u@zþ @x@x

� �2

þ @m@zþ @x@y

� �2

f2 ¼ 1� 0:3 expð�Re2t Þ

Based on Jones and Launde’s research on low Re num-ber k � e model, the value of the coefficients in k � e equa-tion are shown in Table 2.

3.2.5. Boundary condition and initial condition

Thermal boundary condition of external glass surfaceand roof external surface are given by:

�km@ts;m

@y¼ asmIsun;V þ Qrmg þ Qcmg y ¼ y1

�kn@ts;n

@z¼ asnIsun;H þ Qrng þ Qcng z ¼ z1

where y = y1 is external glass surface of south wall, z = z1is roof external surface. km and kn are heat conductivitycoefficient of glass and roof material respectively, W/(m K), asm and asn are the solar radiation absorptivity ofthe external glass surface and the external surface of theroof respectively, Isun,V and Isun,H are the solar radiationintensity of south wall and the roof respectively, W/m2,

Table 2The coefficient of Jones–Launde low Reynolds number k � e model.

f1 cl c1 c2 rT rK re

1.0 0.09 1.44 1.92 (0.9–1.0) 1.0 1.3

Qrmg and Qrng are the radiant heat transfer of the glassand the roof respectively, W/m2 and Qcmg and Qcng arethe figures for the convective heat exchange of glass androof respectively, measured in W/m2.

Boundary velocity condition: ux = uy = uz = 0Thermal boundary condition of thermal storage wall:

�k1

@ts;1

@y¼ as1sgI sun;V þ Qr1g þ Qc1g y ¼ y2

where y = y2 is the external surface of thermal storage wall,k1 is coefficient of heat conductivity of thermal storagewall, W/(m K), as1 is the absorptivity of the external sur-face of the thermal storage wall to solar radiation, sg istransmissivity of the glass cover-plate, Qr1g is the radiationheat exchange between the thermal storage wall and theglass cover-plate, W/m2 and Qc1g is convection heat ex-change of the external surface of thermal storage wall,W/m2. Hence,The boundary velocity condition:ux = uy = uz = 0.

The boundary condition of external surface of east, westand north wall:

@t@y¼ 0 y ¼ y3

@t@x¼ 0 x ¼ x1

@t@x¼ 0 x ¼ x2

ux ¼ uy ¼ uz ¼ 0

where y = y3, x = x1 and x = x2 are in central position ofnorth, east and west interior wall.

The boundary condition of floor bottom:

@t@z¼ 0 z ¼ z2

where z = z2 is lower surface of floor.

ux ¼ uy ¼ uz ¼ 0

The boundary conditions of other interior surfaces, orsurfaces exposed to the indoor air cannot be pre-deter-mined. (This is limited by the interaction between the fluidand wall surface.) At this stage of the calculations, both theboundary temperature and the heat-flow density are partsof numerical calculation result, which will not be deter-mined. This kind of thermal boundary condition is deter-mined in the exchange process of quantity of dynamicheat, which belongs to coupling heat-transfer and cannotbe pre-determined (Burek and Habeb, 2007).

Initial condition:

s ¼ 0 t ¼ const ux ¼ uy ¼ uz ¼ 0

Meteorological condition:Law of outdoor air temperature:

twðsÞ ¼ tw þ Aw cos2pT

sþ wo

� �

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:004

8

12

16

20

24

28

32

36

Tem

pera

ture

[]

Hour of the day

Trombe wall average temperature (vent open) Trombe wall average temperature (vent close)

Fig. 10. The average temperature of thermal storage wall under closingand opening working condition of air vent.

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:000

5

10

15

20

25

30

35

-300

-200

-100

0

100

200

300

400

500

600

Inst

anta

neou

s he

at s

tora

ge c

apac

ity

[W/m

2 ] Trombe wall average temperature

Tem

pera

ture

[]

Hour of the day

Unit area trombe wall

Fig. 11. Instantaneous heat storage and release of thermal storage wallper unit area and the average temperature of thermal storage wall.

12

16

m2 ]

Heat storage Heat release

8 Y. Liu et al. / Solar Energy 91 (2013) 1–10

where tw is average outdoor air temperature, �C, Aw is theamplitude of outdoor air temperature, �C, wo is the initialphase of outdoor air temperature, rad and T is period ofoutdoor air temperature, h. The value of tw, Aw, wo andT are �19.5 �C, 9.4 �C, 59 rad and 24 h respectively.

The solar radiation intensity is calculated according tothe Solar Calculator DO radiation model of FLEUNT,which can achieve automatic tracking of solar elevationangle and azimuth angle.

3.3. Numerical calculation results and analysis

3.3.1. Law of air temperature

The indoor air temperature and average temperature ofair layer under the opening and closing working conditionof air vent is shown in Fig. 9.

According to Fig. 9, when air vent is opened, the aver-age temperature of the air layer and the indoor air temper-ature is 2.6 �C and 5.1 �C respectively. When the air vent isclosed, they are 7.6 �C and 4.2 �C respectively. It can beseen that the closing of air vent increases layer air temper-ature and decreases indoor air temperature. The averagevalue of the layer air temperature and the indoor air tem-perature in daylight (10:00–18:00) is 13.6 �C and 8.7 �Crespectively when air vent is opened. When the air vent isclosed, it is 26.7 �C and 6.7 �C respectively. The closingof the air vent in daylight increases blanket air temperatureand decreases indoor air temperature to improve indoorthermal environment.

3.3.2. Characteristics of heat storage and release of thermal

storage wall

The average temperature of the thermal storage wallunder the closing and opening working conditions of theair vent is as shown in Fig. 10. Instantaneous heat storageand release of the thermal storage wall per unit area andthe average temperature of thermal storage wall is shownin Fig. 11. The total heat storage and release of thermalstorage wall per unit is as shown in Fig. 12.

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:00

-30

-20

-10

0

10

20

30

40

Hour of the day

Tem

pera

ture

[]

Outdoor air Indoor air (vent close) layer air (vent close) Indoor air (vent open) Layer air (vent open)

Fig. 9. Comparison between indoor air temperature and average temper-ature of layer air of trombe wall.

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 00:00-12

-8

-4

0

4

8

Tota

l hea

t qua

ntity

[M

J/

Hour of the day

Fig. 12. Total heat storage and release of thermal storage wall per unitarea.

According to Fig. 10, it can be seen by comparing theaverage temperature of the thermal storage wall that theaverage temperature under the opening working condition

Y. Liu et al. / Solar Energy 91 (2013) 1–10 9

of air vent is higher than that under the opening workingcondition of air vent, the difference of which is relativelysmall in daytime, and almost the same at night. The open-ing and closing of the air vent is of little effect on the aver-age temperature of thermal storage wall.

Fig. 11 shows that the negative value of instantaneousheat storage and release of thermal storage wall per unitindicates heat release. The passive value indicates heat stor-age. A balanced heat storage and heat release is achieved atabout 7:30. At this moment, the instantaneous heat storageand release equals to zero. The average temperature of thewall achieves its minimum 6.6 �C. After 7:30, with theenhancement of solar radiation, the wall begins to storeheat. At about 11:30, the instantaneous heat storage of wallachieved its maximum 470 W/m2. After 11:30, the instanta-neous heat storage gradually decreases but the total heatstorage still increases. The average temperature of wallgradually increases. At 16:00, the instantaneous heat stor-age of wall has reached a minimum, the total heat storagehas reached its maximum. The average temperature of wallreaches a maximum 29.8 �C. After 16:00, the instantaneousheat release gradually decreases. The total heat releasegradually increases, which causes the fall in temperature.At about 7:30, balance is achieved again and a recycle isfollowed.

Fig. 12 shows the total heat storage and release of ther-mal storage. At about 7:30, the thermal storage wall beginsto store heat. As time progresses, heat storage graduallyincreases. At about 16:00, the heat storage of the wallreaches its maximum. The maximum heat storage of thethermal storage wall per unit is about 10.6 MJ/m2. After16:00, the thermal storage wall begins to release heat. At7:30 on the next day, the heat release reaches its maximum,amounting to about 10.4 MJ/m2. It can be seen that thetotal heat storage and release are different, amounting to0.2 MJ/m2, which is stored in the wall and participates inthe heat storage and energy release of the next day.

4. Conclusions

Optimization research on the opening and closing modelof trombe wall has been conducted by using experimentalresearch and numerical calculation. The heat storage andrelease laws of the thermal storage wall have been ana-lyzed. Several conclusions are obtained. These are asfollows:

(1) In order for the thermal environment of the solarhouse with trombe wall to be maximized, the opti-mum opening and closing mode of the air vent hasbeen proposed: it is to open the air vent 2–3 h aftersunrise and close air vent 1 h before sunset.

(2) A comparison between the opening and closing modeof the air vent of the trombe wall under the conditionof the air vent closed (or no air vent for the improve-ment of the thermal environment of solar house) is

obviously poorer than that with the air vent open,and the closing of the air vent is of little effect onthe heat storage and release law of trombe wall.

(3) At 7:30 in morning, the heat storage of trombe wall isfully released. Temperature at this moment reachesits minimum. At 16:00, the heat storage achieves itsmaximum, as does the temperature.

The first two conclusions above are appropriate formost of the trombe wall heating system. However, onlythe structure of the trombe wall is similar with the objectin this paper, the last conclusion is appropriate.

Acknowledgements

We extend our gratitude to the Funds supports of Na-tional Natural Science Foundation of China (Project No.51078302). And also express my thanks for the grant ofthe Creative Research Groups of China (Project No.50921005).

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