Nikola Kaloyanov, Borislav Stankov, Georgi Tomov, Nina Penkova

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EFFICIENCY OF TRANSPARENT STRUCTURES IN TROMBE WALLS

Nikola Kaloyanov1, Borislav Stankov1, Georgi Tomov1, Nina Penkova2

ABSTRACT

The Trombe wall is a passive solar design solution suitable for buildings in temperate and warm climates. The transparent units, which constitute the external boundary of the structure, are among the most important factors for its energy performance. This paper presents an analysis of the energy performance of unvented Trombe walls using two of the most commonly encountered types of glazing – single glass and double insulting glass units (IGU). The analyses are based on physical measurements obtained at a test site and numerical simulations of the heat transfer processes in the system. In addition to the energy performance assessment, a thermal load analysis is performed for the more efficient solution, i.e., the double glazed unit, to predict the influence of the occurring heat transfer processes on the mechanical behavior and reliability of the construction.

Keywords: Trombe wall, solar gains, efficiency, thermal loads, modelling, numerical simulation, test site.

Received 05 December 2017Accepted 15 June 2018

Journal of Chemical Technology and Metallurgy, 53, 6, 2018, 1157-1166

1Technical University of Sofia, 8 Kliment Ohridski, 1756 Sofia, Bulgaria2University of Chemical Technology and Metallurgy 8 Kliment Ohridski, 1756 Sofia, Bulgaria E-mail: nina@uctm.edu

INTROdUCTION

The term “Trombe wall” refers to a category of external walls which are integrated in sun-facing build-ing facades to function as indirect-gain passive solar systems. They consist of a thermal storage mass (which typically has some type of a coating on the external surface, i.e. an absorber), a transparent unit and an air gap between them. As in most passive solar systems, the control of the solar heat gains is usually accomplished by moving a component that regulates the amount of solar radiation admitted into the structure, i.e. by manually or automatically controlled shading devices [1].

Trombe walls are designed in two basic configura-tions: unvented and vented (Fig. 1). In unvented units the absorbed solar energy is transferred to the building interior via conduction through the thermal storage mass and convection and radiation from the internal wall surface to the indoor environment. The thickness and the thermal diffusivity of the storage mass determine

the thermal inertia of the construction. Therefore, the thermal mass is designed to store solar energy and shift the heat gains to the most appropriate time of day. Vented Trombe walls can be used in several modes to provide more immediate heat gains – via convective heat transfer between the thermal mass and the transparent unit – by natural or fan-assisted ventilation.

The Trombe wall construction plays a crucial role for its energy efficiency. Its design should maximize the absorption of solar heat and minimize heat losses from the absorber back to the outdoor environment. The storage mass is usually built of solid non-porous materials of a high heat capacity, such as concrete or ceramic bricks. The absorber should have a very high solar absorbance (e.g. black paint) and preferably a low infrared emissivity (e.g., black chrome).

The purpose of the transparent element is to trans-mit as much solar radiation as possible and to reduce heat losses from the absorber. It is composed of clear glass layers or alternative transparent materials, e.g.,

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lightweight polycarbonate panels filled with nanoporous aerogel insulation [2]. Single glass or double insulating glass units (IGU) are typically used. The optical and thermal properties of the glazing used influence signifi-cantly the energy performance of the system.

A joint research project is carried out by the Tech-nical University of Sofia (TUS) and the University of Chemical Technology and Metallurgy (UCTM) aiming to investigate the effect of the glass units on the efficiency of unvented Trombe walls in view of the heat transfer processes in the construction and the associated thermal loads of the glass elements. The study continues a pre-vious research on energy performance of Trombe walls with single and double-glazed units presented in ref.[3,4].

ANALYSIS OF THE THERMAL BEHAVIOUR OF THE TROMBE WALLTest site measurements

A Trombe wall test module built at TUS (Fig. 2) equipped with temperature and air velocity measurement systems is used to obtain detailed information on the temperature and velocity fields in the construction of a typical Trombe wall. An adjacent weather station is used for measuring the pertinent weather parameters. The transparent element consists of double insulating glass units (IGU) with uncoated glass panes and air in the her-metically sealed space. The units are fixed to the façade through a PVC frame. The distance between the wall and IGU is 10 cm. The thermal storage wall is divided into two halves made of different materials (clay bricks and concrete bricks), both coated with a black paint. Due to the different thermal diffusivities, the temperatures of the

absorber in each of the halves are different. The construc-tion of the test module and the placement of the sensors are described in detail in refs. [3, 4]. The measurements of the following parameters are carried out for a period of six months (one heating season):

l the temperature at several locations on the ab-sorber;

l the temperature and the relative humidity of the outdoor air;

l the total and diffuse horizontal solar irradiance on a surface and the total solar irradiance on the verti-cal south-facing surface (aligned with the test module);

l the wind speed and the direction;l the soil temperature at 30-cm depth.The measurements are used to determine the bound-

ary conditions of the models described below. The heat flows are calculated for the average temperature of the sensors placed on the absorber (on both halves of the

Fig. 1. Different types of Trombe walls.

Fig. 2. A Trombe wall test module (right).

Nikola Kaloyanov, Borislav Stankov, Georgi Tomov, Nina Penkova

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thermal storage wall), excluding the sensors placed on the peripheral sections behind the frame of the glazing unit.

Modeling and numerical simulation Computational Fluid Dynamics (CFD) analysis

Detailed information on the temperature, the veloc-ity and the pressure fields in the Trombe wall can be obtained by coupled numerical solution of the following system of partial differential equations: A fluid domain (gas cavities in Trombe wall):

l a continuity equation;l momentum equations;l an energy equation;l a turbulence model;l a boundary layer model.The gases can be modeled as ideal and uncompressible.

Solid domains (thermal mass, spacers, seals, solid elements in the window system):

l heat conduction (Fourier-Kirchhoff) equation.The absorption of solar energy by the solid media

can be modeled as a heat source (a heat generation rate) in the energy equation. The radiation heat exchange in the infrared spectrum between the surfaces enclosing the gas cavities can be computed by the “Surface to surface radiation” methods considering the view fac-tors between the finite volume surfaces. The boundary conditions reflect the heat exchange by radiation and convection between the external surfaces and the ambi-ent environment, as well as between the internal surfaces and the room.

Such CFD analyses are possible using advanced software tools implementing a finite difference, a finite volume or a finite element model. However, they are very time-consuming when modeling the conjugate heat transfer under transient conditions. Therefore, CFD simulations are performed for a small set of observations to analyze in detail the temperature field and the thermal loads in the glass under extreme conditions. Meanwhile, a simplified model of the heat transfer processes in the construction is implemented in MATLAB to investigate the energy performance of the Trombe wall over the whole period of measurements. The MATLAB model described in section 2.2-2.5 provides the computation of the following parameters based on inputs from the test site measurements:

l average temperatures of the internal and external glass panes;

l convection and radiation heat transfer coefficients in the enclosure between the absorber and internal glass;

l convection and radiation heat transfer coefficients between the glass panes;

l convection and radiation heat transfer coefficients between the external glass and the outdoor environment;

l an overall coefficient of the heat transfer from the absorber to the outdoor environment, i.e., an external heat loss coefficient.

Since the heat transfer coefficients are temperature-dependent, an iterative solution through successive substitution is used.

Heat transfer in the air gap between the absorber and the internal glass

The space between the absorber and the internal surface of the glass unit is a narrow vertical rectangular enclosure, where the heat transfer occurs via natural convection and radiation. The average convection heat transfer coefficient is determined through the following correlations of MacGregor and Emery [5]:

-0.30.25

L L4 7

L

H10 40HNu 0.42Ra LL 10 Ra 10

< < = < <

(1)

1/3L L

6 9L

H10 40L

Nu 0.046Ra 1 Pr 2010 Ra 10

< <= < < < <

Lc,i

NuhLλ

= (3)

where NuL is the Nusselt number, RaL is the Raleigh number, Pr is the Prandtl number, H is the height of the enclosure (m), L is the width of the enclosure (the distance between the absorber and the internal glass) in m, λ is the thermal conductivity of air (Wm-1K-1), while

ich , is the convective heat transfer coefficient (Wm-2K-1).All air properties required for Nu, Ral and Pr

determination are evaluated at the mean temperature between the absorber and internal glass based on the data provided by refs.[6, 7].

For consistency, the radiant heat transfer can be represented by the radiation heat transfer coefficient analogous to the average convection heat transfer coef-ficient [5]:

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3r,i eff mh 4 Tε σ= (4)

where irh , is the radiation heat transfer coefficient (Wm-

2K-1), εeff is the effective emissivity, Stefan-Boltzmann constant σ =5.67x10-8 Wm-2K-4; while Tm is the mean absolute temperature (of the absorber and internal glass) in K.

The effective emissivity is calculated following the procedure applied to infinite parallel plates:

eff

gl abs

11 1 1

ε

ε ε

=+ − (5)

where εgl is the emissivity of the glass surface, while εabs is the emissivity of the absorber.

The heat flux at the internal glass surface is calcu-lated as:

( )( )gl,i c,i r,i abs gl,2q h h T T= + −

(6)

where gl,iq is the heat flux (Wm-2), Тabs is the average surface temperature of the absorber (К), while Тgl,2 is the temperature of the glass (К). It is used as a function of the internal glass surface temperature Tgl,s in case of CFD analyses of the heat transfer in UGU:

(7)

where Tair is the average temperature of the air in the cavity (К).

Heat transfer in the glazing unitThe convection and the radiation heat transfer

coefficients between the two parallel glass panes can be calculated by the correlations above using the tem-peratures of the glass panes. These temperatures are also dependent on the amount of absorbed solar energy. Considering the solar ray tracing between two identical clear glass panes, the total absorbances of the external and the internal glass layers 1A and 2A are:

21 1ˆ

RTRAAA−

+= and 2 2

TAA1 R

=−

(8)

where A, R and T are the solar absorbance (0.154), reflectance (0.071) and transmittance (0.775) of clear glass. The solar heat fluxes absorbed by the external and

the internal glass layer are:

sgl, IAq 11ˆ= and sgl, IAq 22

ˆ= (9)

respectively, where Is is the total solar irradiation on the glass pane (Wm-2).

Heat transfer at the external glass surfaceThe heat losses from the external surface to the

outdoor environment are due to natural and forced convection to the outdoor air and radiant heat exchange with the ground and the sky. The convective heat transfer is calculated according to the MoWiTT model (on the windward side), which can be applied to very smooth vertical surfaces (such as glass) in low-rise buildings [9]:

( )2 21/3 0.89

c,se gl,1 0 wh 0.84 T T 3.26v = − + (10)

where c,seh is the convection heat transfer coefficient (Wm-2K-1), Tgl,1 is the temperature of the external glass (K, To is th temperature of outdoor air (K), while vw is the local wind speed (ms-1).

The radiation heat transfer between the external glass and both, the ground and the atmosphere, is calculated [9] via the combined radiation heat transfer coefficient r,seh :

( ) ( )( )

4 4 4 4gnd gl,1 gnd sky gl,1 sky

gl 4 4sky gl,1 0

r,segl,1 0

F T T F T T

F (1 ) T Th

T T

βε σ

β

− + − + + − − =

−

(11)

)cos1(5.0 φ−=gndF (12)

)cos1(5.0 φ+=skyF (13)

)cos1(5.0 φβ += (14)

where Fgnd and Fsky are the view factors for the glass/ground and glass/sky pairs, correspondently, ϕ is the slope of the glazing unit (90°), Tgnd is the ground sur-face temperature (K), while Tsky is the apparent sky temperature (K).

The ground surface temperature is calculated on the ground of the soil temperature measured at a depth of 30 cm by a ground temperature sensor in view of the heat balance at the ground surface:

Nikola Kaloyanov, Borislav Stankov, Georgi Tomov, Nina Penkova

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gndgnd 0 gts

gtsgnd

gndgnd

gts

h T TD

Th

D

λ

λ

+=

+ (15)

where gndh is the heat transfer coefficient at the ground surface (Wm-2K-1), λ gnd is the soil thermal conductiv-ity equal to 1.5 Wm-1K-1, Dgts is the depth of the soil temperature sensor amounting to 0.3 m, while Tgts is the temperature measured by the sensor (K).

The apparent sky temperature is calculated accord-ing to the Aubinet cloudy sky model [10]:

sky w t oT 94 12.6 ln(p ) 13K 0.341T= + − + (16)

where pw is the partial pressure of the water vapor (Pa) at the measured dry-bulb temperature, relative humidity and barometric pressure [11], while Kt is the sky clear-ness index defined as a ratio of the global horizontal ir-radiance to the corresponding extraterrestrial irradiance:

βsino

tht I

IK = (17)

where Ith is the total horizontal irradiance on the ground (Wm-2), I0 is the extraterrestrial solar irradiance incident on a surface normal to the sun’s rays (Wm-2), while β is the solar altitude angle (°) [1].

The extraterrestrial solar irradiance is approximated with the application of the following equation [12]:

−

+=365

3360cos033.011367 nIo (18)

where n is the number of the day of the year.The heat flux between the external glass surface and

the outdoor environment is described as:

( )( )se c,se r,se gl,1 oq h h T T= + − (19)

where Tgl,1 is the temperature of the external glass (K), while To is the outdoor air temperature (K).

The heat flux is presented as a function of the external glass surface temperature Tgl,se and the mean radiating temperature of the outdoor environment Tr,m :

(20)where:

( )1/ 44 4r,m gnd o sky skyT F T F .T= + (21)

Thermal balance

The temperatures of the internal and the external glass panes are defined by the system of equations given below. It is obtained on the ground of the thermal bal-ance of the glazing unit assuming negligible conduction thermal resistance of the glass panes:

( ) ( )( )

( ) ( )( )

c,i r,i c,gl r,gl gl,2 c,gl r,gl gl,1

c,i r,i abs 2 s

c,gl r,gl c,se r,se gl,1 c,gl r,gl gl,2

c,se r,se 0 1 s

h h h h T h h T

ˆh h T A I 0

h h h h T h h T

ˆh h T A I 0

+ + + − + −

− + + =

+ + + − + −

− + + =

(22)

where glch , and glrh , are the convection and the radia-tion heat transfer coefficients between the glass panes (Wm-2K-1), respectively.

The external heat loss coefficient, representing heat losses from the absorber to the outdoor environment [3], can be roughly approximated as:

e

c,i r,i c,gl r,gl c,se r,se

1U 1 1 1h h h h h h

=+ +

+ + +

(23)

ENERGY PERFORMANCE ANALYSIS

The external heat loss coefficient Ue is a primary factor determining the energy performance of Trombe walls. It strongly depends on the absorber coating type and the glazing unit. Values of Ue used with the simpli-fied model presented in ref. [3] are obtained from results of the dynamic simulations with TRNSYS. The range of values (excluding outliers) is shown in Fig. 3. The median values for each group can be considered as a representative of a wide range of unvented Trombe wall configurations. The importance of the glazing unit is considerable, especially if the absorber is not selective, because in that case the radiant heat exchange is much higher. In such configurations the median value drops by more than 35 % when double glazing is used instead of single one. The values of the external heat transfer coefficient of the test site module obtained according to the MATLAB model presented above are lower than the median value of the respective group presented in Fig. 3

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(black paint, double glazing). However, the inhomogene-ity of the thermal mass and averaging of the temperature over both halves, made of different materials, do not provide a direct comparison of the values. Also, the ac-tual coefficient would be increased if all imperfections in the construction are considered. The more significant results of the analysis concern the calculated convection and the radiation heat transfer coefficients as well as their effect on the external heat loss coefficient.

The obtained temperatures of the internal and the external glass panes are plotted in Fig. 4 for the month of February. The external heat loss coefficient obtained for the same period is plotted in Fig. 5.

A statistical summary of the convection and the ra-diation heat transfer coefficients over the whole period of measurements is shown in Table 1. The variation of the equivalent total thermal resistances is shown in Fig. 6.

All median values in Table 1 and Fig. 6 are of the same order of magnitude. The external surface coefficients are higher (while the thermal resistance is lower, respectively) as expected, but they are also the least dependent on the glazing unit type and are largely determined by other factors. On the other hand, the choice of the glazing unit can significantly affect the other coefficients.

The external heat loss coefficient is plotted versus

Fig. 3. A box plot of the external heat loss coefficient for different constructions.

Fig. 4. Internal and external glass panes temperature.

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the temperature difference between the absorber and outdoor air in Fig. 7. There is a moderate correlation which indicates that the value increases by ca 30 % at a temperature difference of 50 K.

The highest data points concentration is in the range of а temperature difference from 10 К to 20 K, where the external heat loss coefficient remains concentrated mostly in the range of 1.3 Wm-2K-1 to 1.6 Wm-2K-1.

THERMAL LOAd ANALYSIS OF THE INSULAT-ING GLASS UNITS

The transient temperature fields in IGU result in positive or negative gauge pressure in the hermetically sealed gas space and a subsequent deformation of the glass panes – they can be deformed in different directions within the day and the year. The input value for these pro-cesses estimation refer to the so called isochoric pressure:

1is 2 metp C T C H p∆ = ∆ + ∆ + ∆ (24)

where C1 = 0,34 kPaK-1 and C2=0,012 kPam-1. ∆H [m], ∆pmet [kPa] and ∆T [К] are the changes of the altitude, the atmospheric pressure and the gas temperature, cor-respondently. They are related to the respective values at IGU manufacturing.

The prediction of these processes is important for the choice of proper IGU type in order to prevent con-struction failures [13]. The stresses due to the internal loads, in combination with the thermal stresses due to temperature gradients and temperature expansion/com-pression of the glass (brittle material), can lead to cracks and breaking of the pane. The terms in Eq. (24) referring to changes of the altitude and the atmospheric pressure can be predicted according to the location where IGU is

Fig. 5. A variation of the external heat loss coefficient.

Heat transfer coefficient Mean Median Max Median absolute deviation

Between absorber and internal glass

Convection 1.04 1.06 1.39 0.095 Radiation 2.44 2.35 3.70 0.148

Between internal and external glass

Convection 1.05 1.03 1.47 0.086 Radiation 2.23 2.18 3.30 0.134

Between external glass and outdoor environment

Convection 3.00 2.52 11.06 1.701 Radiation 19.40 8.97 – 3.250

Overall external heat loss coefficient 1.48 1.45 1.93 0.096

Table 1. A statistical summary of the heat transfer coefficients, Wm-2K-1.

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used. The pressure difference due to the gas temperature change depends on the boundary conditions of the heat transfer and can be computed by modeling and numerical simulation. There are well recognized rules and practices to prevent problems in classical IGU constructions in transparent building envelopes [14]. But the heat transfer boundary conditions in a Trombe wall are different from those valid for conventional building facades.

CFD simulations are performed to analyze the tem-perature fields in IGU and their effect on the mechanical behavior of the glass layers of the Trombe wall investi-gated. The window frame is neglected: it is verified that it does not significantly affect the temperature fields in IGU [15]. Numerical simulations are performed for the moments with expected maximum positive and nega-tive gauge pressure during the period of the test site measurements (Table 2). The boundary conditions at

the external and the internal glass surfaces are modeled according to Eq. (7), (9) and (20) and the heat transfer coefficients in Table 1.

The visualizations of the temperature fields in IGU are shown in Figs. 8 and 9. A relatively high average temperature of the internal glass is observed for the investigated moment in April due to the radiation heat exchange between the glass and the absorbing wall. The temperature of the uncoated glass would be lower in the same IGU if it is a part of a conventional south oriented façade in Sofia [16]. Therefore, the temperature expansion of the glass and subsequent thermal stresses are expected to be higher if IGU is a part of an unvented Trombe wall.

The results concerning the internal loads are given in the last two rows of Table 2. The vacuum pressure in the cold days and the positive gauge pressure in the hottest day

Fig. 6. A box plot of the thermal resistances. Fig. 7. An external heat loss coefficient vs. temperature difference dependence.

Fig. 8. A temperature field in IGU at 8:00 AM on 1st of January, 2015.

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are nearly two times higher in comparison with an IGU unit in a conventional south-facing building façade at the same location. But the values of Δp in Table 2 are higher than the resultant internal load when the glasses are deformed. It is established in previous investigations that the stresses due to the internal load are several times smaller than the maximal permissible value for the glass [14]. Therefore, the internal loads at the investigated construction are not hazardous for the glass layers. That is a fact.

CONCLUSIONSDouble insulating glass units improve the energy

performance of Trombe walls. The heat losses to the outdoor environment are lower in comparison with a single glass alternative by:

35 % on average in case of an absorber with a non-selective coating;

20 % on average in case of an absorber with a selec-tive coating;

Table 2. Conditions for numerical simulations defined according to the test site measurements.

Internal and external conditions

Parameter

Lowest external

temperature

Highest external

temperature

Highest temperature of the

absorbing wall

Highest ΔT between the wall and the

outdoor environment Date 1.1.2015 16.4.2015 3.2.2015 18.2.2015 Time 8:00 17:00 15:00 15:00 Indoor temperature, °C 4.1 27.3 21.5 19.5 Outdoor temperature, °C -14.5 24.5 5.5 0.3 Temperature of the absorber, °C 2.1 53.9 75.4 70.6 Temperature of the internal surface of the wall, °C 3.3 35.8 34.8 32.8 Average temperature of air in the gap between the IGU and the absorber, °C -1.4 53.3 58.7 54.4 Solar irradiation, Wm-2 0 405.3 840.9 852.9 Convection heat transfer coefficient ich , Wm-2K-1 1.3 0.7 1.5 1.5

Results Temperature of air in the hermetically sealed space, K 264 310 308 303 Isochoric pressure at temperature change Δp, kPa -9.86 5.78 5.1 3.4

Fig. 9. Temperature field in the IGU at 5:00 PM on 16th of April, 2015.

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The most effective case refers to a combination of an absorbing wall with a selective coating and double insulating glass units.

Changes in the weather conditions result in a variation of the thermo-mechanical behavior of the glass in IGU of the investigated Trombe wall. The internal gauge pressure, due to deviations of the gas temperature in the hermetically sealed space from that at the time of production, varies from positive to negative. Subsequent glass deflections are expected in different directions if IGU is produced at an altitude near that of the Trombe wall location. These processes, in combination with the change of temperature and temperature gradients in the glass, can contribute to IGU elements fatigue and construction unsealing.

Acknowledgements This work was supported by the National Science

Fund of Bulgaria under project DFNI E 02/17 ”Para-metric analysis for estimation of the efficiency of trans-parent structures in solar energy utilization systems”.

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