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CFD modeling to evaluate the thermal performances of window frames in accordance with the ISO 10077
Energy 111 (2016) 430e438
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CFD modeling to evaluate the thermal performances of window frames in accordance with the ISO 10077 Maria Malvoni, Cristina Baglivo, Paolo Maria Congedo*, Domenico Laforgia Department of Engineering for Innovation, University of Salento, 73100 Lecce, Lecce, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 October 2015 Received in revised form 30 May 2016 Accepted 1 June 2016
The main goal of the EPBD (Energy Performance Buildings Directive) is the improvement of the energy performance of the European buildings. The internal comfort is critically dependent on the envelope that plays a key role in the thermal balance of the entire building. In particular, the windows are one of the most critical elements in terms of solar gains, heat losses and thermal bridges; therefore, the design of high efficiency frames is requested, both in cold and warm climate, but with different peculiarity. The UNI EN ISO 10077-2 provides a methodology to evaluate the frame thermal behaviour and it proposes the criteria to validate the numerical model. This paper presents a two-dimensional numerical method for the thermal behaviour evaluation of the frame sections using GAMBIT 2.2 and ANSYS FLUENT 14.5 CFD code. The results have been validated in accordance with the UNI EN ISO 10077-2. The standard ISO replaces the air gas with a fictitious material “air solid” into the cavities. Besides the simulation carried out with ideal gas entails higher internal surface temperature than the air solid case. Therefore, the standard ISO imposes preventive computational conditions. The proposed numerical method can be implemented for several frame profiles with different features in terms of geometry and materials, representing a valid support in the design of new high thermal performance frames. © 2016 Elsevier Ltd. All rights reserved.
Keywords: CFD Thermal break Window Frame 10077 EPBD
1. Introduction In order to address the current global warming trend due to greenhouse emissions, the European Union (EU) is involved to develop strategies to reduce the negative effects on climate change [1e3]. The renewable source integration in power systems [4e6] and the home automation are some of the adopted solutions for the energy-saving and to guarantee high-energy performance in the buildings [7e10]. It has been noted that the building sector is responsible for about 40% of the energy requirement [11]; therefore, the Energy Efficiency Directive [12] aims to improve the level of the energy performance and to reduce the energy consumption and environmental impact [13]. In order to obtain high efficiency buildings, several studies show how it is possible to reach, keeping costs down, a decreasing in terms of primary energy consumption and CO2 gas emissions. Studies [14e19] present a methodology based on the comparison of
* Corresponding author. E-mail address: [email protected] (P.M. Congedo). http://dx.doi.org/10.1016/j.energy.2016.06.002 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
several energy efficiency measures to identify the cost-optimal solutions for buildings located in a warm climate. The buildings performances are also investigated in cold areas as Estonia [20], Unit States and China [21]. Multi-objective analyses have been carried out in several studies [22e26], to optimize the thermal performance of the building envelope; such an analysis allows to identify a set of optimal external wall configurations in order to reduce winter energy consumption and to increase summer thermal comfort. The multi-layer wall system reduces heating energy consumption of 27%e38% respect to single-layer wall system [27]. Once designed a highly efficient envelope, to ensure the comfort to the end-users it is necessary to evaluate other physical factors such as heat, light and sound [28]. A numerical study presented in the [29] show a comparison between the behaviour of double, triple and quadruple pane windows in order to demonstrate that the heat loss through the transparent elements can be reduced by increasing the number of panes especially in cold climate areas. Several thermal benefits can be reached by adopting of the multi pane window solutions considering that they cause around 30e50% of the losses by transmission across the building envelope [29].
M. Malvoni et al. / Energy 111 (2016) 430e438
Hence, the window design is strategic to reach the highest performance and reduce the overall energy demand for heating and cooling [30,31]. The thermal performance of the window depends on the thermal and geometrical characteristics of the framework and the interaction effects between its components. The thermal transmittance is evaluated by International Standard ISO 10077. In particular, the first part of the ISO 10077 [32] specifies a simple calculation method for a set of fenestration. The main disadvantage is that the calculation procedure does not take into account the effects of solar radiation and the heat transfer caused by air leakage and does not consider the ventilation and the condensation phenomena. In addition, it does not consider other additional elements, as gaskets, inserts, etc., that can be introduced to reach high performance solutions. Therefore, it can be used for a first estimation of the thermal transmittance. The second part of ISO 10077 [33] details a method for the calculation of the thermal transmittance of frame profiles Uf and of the linear thermal transmittance of their junction with glazing or opaque panels L2D f , providing information about the input data useful for the calculation. Also, it provides the criteria to validate the numerical methods. Several works show the application of numerical models in order to evaluate the frame thermal performance in accordance with standard ISO 10077. Cardinale & Al [34]. have investigated several window frames with rolling shutters-boxes by a Finite Element Method (FEM) analysis and the thermal transmittance has been checked using the software FRAME SIMULATOR 2 Dartwin. In Ref. [35] the thermal performance of the glazing on the frame and the edge-of glazing behaviour in a wood-frame window, with regard to condensation risk, have been analysed using THERM and WINDOW software packages. An artificial neural network (ANN) model has been developed to predict the thermal transmittance of wooden windows; the results show an error of about 1% compared to the solutions provided by the Computational Fluid Dynamics (CFD) numerical procedure [36]. A comparison between the methods suggested by ASHRAE and ISO for the calculation of the thermal transmittance has been performed using the FRAMEplus Toolkit Version 3.0 and THERM 2 software [37]. Numerical simulations in two-dimensional and threedimensional domains have been implemented with the CFD code Fluent to investigate the wood and aluminium framed windows [38]. The geometry and the characteristics of the cavities influence the overall performance of the profile. A numerical analysis was carried by CFD code Fluent to simulate the effects due to the insert of ethyleneepropylene diene monomer (EPDM) gaskets inside the frame cavities and to evaluate the emissivity of the cavities [39]. The present study proposes a two-dimensional numerical method to investigate the thermal performance of frame profiles. The procedure is performed using the fluid-dynamic calculation ANSYS FLUENT Release 14.5 and the pre-processor GAMBIT 2.2. A detailed analysis of the thermal performance is carried out. Moreover, the proposed model verifies the criteria of validation for the ten frame sections, illustrated in annex D of the ISO 10077-2. The work is organized into three sections. The main concepts of the standard ISO are reported in the Section 1, the Section 2 show a detailed description of the geometry, boundary condition, computational grid model and settings solver. The results are reported in the final section. 2. International standard ISO 10077: numerical method for frame The UNI EN ISO 10077-2 specifies the methodology and the
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input data to calculate the thermal transmittance of the frame profiles Uf and the linear thermal transmittance jg of their junction with glazing or opaque panels. It also provides the criteria to validate the implemented numerical model. In according to the UN EN ISO 10211:2008 [40] the geometrical model must consider an adequate number of sub-sections. Solid materials, boundary conditions and cavities must fulfil particular features, as explained below. 2.1. Treatment of solid sections and boundary conditions Thermal conductivity l is calculated in accordance with the Annex A of ISO 10077-2. The reference winter temperatures of internal and external side are, respectively, 293 K and 273 K, while the thermal resistance values of the external and internal surfaces of the node are defined in accordance to the Annex B of ISO 10077. The node surfaces in junction with the wall are considered adiabatic, as well as the outer edge of the insulating panel. 2.2. Treatment of cavities The air cavities must be replaced with a solid material, therefore the heat flow in cavities is represented by an equivalent thermal conductivity leq that includes the various mechanisms of heat transfer, such as thermal conduction, convection and radiation. The geometry, the ventilation degree and the materials of the cavities influence the thermal conductivity. In case of the width of the slit is not over than 2 mm or completely closed, the air cavity shall be treated as unventilated. Otherwise, the cavity can be considered ventilated. Slightly ventilated air cavities are characterized by small cross-sections and connected to the external or internal air through a slit of 2e10 mm. When the width of the groove is over than 10 mm, the entire surface is exposed to the external or internal environment. In the case of a large cavity connected by a single slit and a developed surface exceeding the width of the slit by a factor of ten, the surface resistance with reduced radiation can be used. Unventilated and slightly ventilated air cavities have the same value of equivalent thermal conductivity leq. 2.3. Determination of the thermal performance To calculate the thermal transmittance of the frame section, an insulation panel with thermal conductivity l ¼ 0,035 W/m k replaces the existing glazing or the opaque panel of the thickness d or dg. The length of insulated panel bp must be more than 190 mm and its height is equal to 1000 mm. The surface of the panel is considered an adiabatic boundary. The thermal transmittance of the frame section Uf [W/m2 K] is defined as follows [33]:
Uf ¼
L2D Up b p f bf
(1)
where L2D f [W/m K] is the thermal conductance of the frame section; Up [W/m2 K] is the thermal transmittance of the central area of the panel; bp [m] is the visible width of the panel; bf [m] is the width of the frame section. The two-dimensional thermal conductance L2D is defined as f [40]:
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L2D f ¼
FS DT
(2)
with FS [W/m] is the total heat flow rate for length through the section; DT [K] is the temperature difference between both adjacent environments. The thermal transmittance of the panel Up is calculated as follows:
UP ¼
qP AP DT
3.1. Geometrical model: aluminium frame section with thermal break and insulation panel (D.1)
(3)
where qP [W] is the total heat flow rate through the visible width of the panel; AP [m2] is the central area of the panel; DT [K] is the temperature difference between both adjacent environments. The linear thermal transmittance of the junction with the glazing or opaque panel jg [W/m K] is defined as follows [33]:
Jg ¼ L2D J Uf bf Ug bg
- “Segregated numerical scheme” involves the resolution of the equation of the moment, continuity and transport in sequential steps; - “Steady” condition, because of fixed wall temperatures on the frame and glasses; - The standard k-epsilon turbulence model has been enabled; - Operating conditions with pressure equal to the standard atmospheric one (101.325 Pa) and gravity enabled.
(4)
with Uf [W/m2 K] is the thermal transmittance of the frame section; Ug [W/m2 K] is the thermal transmittance of the central area of the glazing; bg [m] is the visible width of the glazing.
The mesh is constituted by cells or elements, which represent the geometry of the phenomena. In this study GAMBIT 2.2 tool has been used to generate the computational grid. Fig. 1 show D.1 frame section. It is characterized by a fixed and mobile frame in aluminium (thermal break) with a maximum thickness equal to 63 mm and width bf of 110 mm. The insulation thickness is of 28 mm and width bp at least 190 mm. The thermal break is achieved through the polyamide with 25% glass fibre, which carries out the breakdown of the single aluminium profiles into two parts, external and internal side. The continuous elements of the frame perimeter have been considered: the rebate seal between sash and frame, the central gasket, the internal and external gasket of glass. The profile section is considered as a barrier between the external (B) and the internal (C) side. Fig. 2 show the computational grid for the selected area highlighted by a circle in Fig. 1. The maximum value of the equiangle and equisize skew are 0.43 and 0.54 respectively. As regards the Aspect Ratio, the 99.9% of the cells differs from the cell with the value 1 for a maximum of 20%. The “reticular” structure of frames shows several air cavities, identified with red numbers in Fig. 1, enclosed between the aluminium walls, gaskets and thermal break.
2.4. Criteria to validate the numerical model In order to validate the proposed calculation method, the results of thermal conductance and transmittance must be in the range as specified in the Annex D of standard ISO. The calculation must be verified for frame sections reported in Refs. [33], figures from D.1 to D.10. It is observed that the thermal conductance L2D and the thermal transmittance Uf must be calculated for the first nine frame sections, instead, for the last frame section, the two-dimensional thermal conductance L2D and the linear thermal transmittance j must be evaluated. 3. CFD numerical analysis The CFD ANSYS FLUENT Release 14.5 has been used to investigate the thermal flux through the frames. In order to evaluate the thermal performance of aluminium-framed windows, the adopted approach requested the following steps:
3.2. Boundary conditions According to the UNI EN ISO 10077-2, the following assumptions have been considered:
1. 2. 3. 4.
Definition of geometrical model; Settings of boundaries conditions: materials, temperatures, etc.; Numerical calculation; Post processing analysis of simulations and validation of the results.
The main parameters for the CFD setup are reported in Table 1; in particular, the following settings have been used:
analysis of continuous elements (not punctual elements); vertical orientation of frame sections; the emissivity of air cavity surfaces must be of 0.9; an insulation panel with thermal conductivity l ¼ 0,035 W/m K replaces the existing glazing (the visible panel length could be less than 190 mm); the heat flow is normal at the surfaces adjacent to the internal (C) and the external side (B). The vertical surfaces to the heat flow direction are considered as adiabatic planes. The thermal resistances are illustrated in Table 2; the density of the solid sections and the thermal conductivity are reported in Table 3; the cavity 11 is considered as slightly ventilated cavity and its thermal conductivity results twice the unventilated cavity; the internal and external surface temperature are 293 K and 273 K, respectively.
The wall interface and the lateral side of the insulating panel are set by an adiabatic boundary (A in Fig. 1). A fictitious material “airsolid” has been introduced to characterize the air cavities of the Section D.1.
M. Malvoni et al. / Energy 111 (2016) 430e438
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Table 1 Details of CFD setting. Solver Numerical scheme Linearization Pressure Pressure velocity coupling Momentum, turbulence kinetic energy, turbulence dissipation rate Fluid Turbolence model Time step Number of faces (Section D.1) Typology of elements (Section D.1) Total number of elements (Section D.1)
2D double precision Segregated Implicit Standard Standard 2nd order upwind Ideal gas Standard k-є (only for gas air) Steady 24 Triangular 108.374
3.3. Sensitivity analysis of grid spacing A sensitivity analysis of the grid has been carried out to evaluate the error caused by the spatial discretization. The Grid Convergence Index (GCI) shows how the computed value is far from the asymptotic numerical value. This study uses three different grids and the GCI is calculated as follows:
GCI12 ¼
Fs jε12 j with fine and medium grids; p r12 1
(5)
GCI23 ¼
Fs jε23 j with coarse and medium grids; p r23 1
(6)
The factor of safety Fs is equal to 1.25 for the comparison of three grids with: Fig. 1. Aluminium frame section with thermal break and insulation panel (D.1).
h1 < h2 < h3
(7)
εnnþ1 ¼
fnþ1 fn fn
(8)
rnnþ1 ¼
hnþ1 hn
(9)
p¼
fnþ1 ln fnþ2 f f nþ1
n
ln r
(10)
where h is the grid spacing i.e. the minimum value of the distance of the nodes, p is the order of convergence, f is the value of the parameter chosen for the comparison. When the result of the considered grid is in the asymptotic range means that if the number of cells grows, the value of the solution f does not change:
GCI23 y1 r p GCI12
(11)
The evaluated value of the grid is:
Fig. 2. Grid convergence indexes, auditing ratio and order of convergence (grid spacing analysis).
f ¼ f1 þ
f1 f2 p 1 r12
(12)
The sensitivity analysis has been performed by the use of the average volume temperature of the cavities and the total heat flux through internal and external surfaces. The results of the sensitivity analysis are shown in Table 4 and Fig. 3. Table 2 Thermal resistance of external and internal surfaces.
Plane surface Corners (enhanced resistance)
External side
Internal side
Rse ¼ 0.04 m2 K/W Rse ¼ 0.04 m2 K/W
Rsi ¼ 0.13 m2 K/W Rsi ¼ 0.20 m2 K/W
4. Simulation results This section shows the simulation results and the comparison with the values provided by the ISO 10077 in order to validate the model.
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Table 3 Thermo-physical properties of the materials. Key
Material
Density r [kg/m3]
Thermal conductivity l [W/m K]
a b c d e f g h i k l m n o
Insulation panel Soft wood PVC EPDM Polyamide 6.6 with 25% glass Glass Still Aluminium Pile weather stripping Polyamide PU rigid Polysulfide Silica gel Gas filling
37 500 1390 1150 1450 2500 7800 2800 30 1150 1200 1400 720 1.784
0.035 0.13 0.17 0.25 0.30 1.00 50 160 0.14 0.25 0.25 0.40 0.13 0.034
Table 4 Sensitivity analysis. No
Description
f1 (K)
f2 (K)
f3 (K)
p
ASS(e 1-2)
ASS (e 2-3)
GCI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Cavity1 Cavity10 Cavity11 Cavity2 Cavity3 Cavity4 Cavity5 Cavity6 Cavity7 Cavity8 Cavity9 Panel Frame internal Polyamide1 frame Polyamide2 frame Polyamide2 shutter Polyamide1 shutter Gasket glass2 Gasket glass1 Shutter external Gasket central Gasket jamb Shutter internal Frame external Internal heat flux External heat flux
281.9614 281.0831 275.3985 284.4085 279.7850 285.6529 279.8074 286.2426 281.1049 275.6754 286.3072 281.9487 284.4006 279.7962 279.7433 281.1568 281.1885 275.5854 286.3035 275.6573 284.7211 285.6387 286.2639 275.2688 11.0960 11.0961
281.9616 281.0847 275.3978 284.4094 279.7851 285.6554 279.8080 286.2463 281.1064 275.6747 286.3109 281.9489 284.4014 279.7970 279.7435 281.1583 281.1902 275.5849 286.3069 275.6566 284.7216 285.6406 286.2675 275.2681 11.0927 11.0927
281.9662 281.0898 275.3942 284.4177 279.7872 285.6666 279.8110 286.2596 281.1114 275.6710 286.3243 281.9497 284.4098 279.7980 279.7447 281.1633 281.1958 275.5817 286.3200 275.6529 284.7283 285.6501 286.2809 275.2651 11.0799 11.0799
4.536 1.733 2.465 3.278 4.728 2.144 2.158 1.880 1.768 2.459 1.870 1.506 3.278 0.291 2.843 1.693 1.721 2.730 1.916 2.419 3.592 2.354 1.876 2.095 1.959 1.930
7.093E-07 5.479E-06 2.360E-06 3.024E-06 2.859E-07 8.857E-06 2.395E-06 1.265E-05 5.265E-06 2.467E-06 1.278E-05 8.867E-07 3.024E-06 3.038E-06 6.077E-07 5.513E-06 6.010E-06 1.778E-06 1.205E-05 2.503E-06 1.932E-06 6.547E-06 1.268E-05 2.543E-06 2.956E-04 3.028E-04
1.646E-05 1.822E-05 1.304E-05 2.932E-05 7.577E-06 3.914E-05 1.069E-05 4.653E-05 1.793E-05 1.357E-05 4.673E-05 2.518E-06 2.932E-05 3.717E-06 4.361E-06 1.782E-05 1.981E-05 1.179E-05 4.548E-05 1.339E-05 2.329E-05 3.347E-05 4.653E-05 1.086E-05 1.149E-03 1.154E-03
3.994E-06 2.946E-04 6.523E-05 4.346E-05 1.402E-06 3.238E-04 8.644E-05 5.900E-04 2.736E-04 6.852E-05 6.017E-04 6.024E-05 4.346E-05 1.699E-03 1.230E-05 3.087E-04 3.272E-04 3.946E-05 5.430E-04 7.196E-05 2.184E-05 1.990E-04 5.938E-04 9.717E-05 1.280E-02 1.347E-02
1-2
GIC
2-3
9.266E-05 9.794E-04 3.603E-04 4.214E-04 3.714E-05 1.431E-03 3.858E-04 2.171E-03 9.317E-04 3.769E-04 2.200E-03 1.711E-04 4.214E-04 2.079E-03 8.826E-05 9.978E-04 1.078E-03 2.617E-04 2.049E-03 3.849E-04 2.633E-04 1.017E-03 2.179E-03 4.150E-04 4.976E-02 5.134E-02
f
Band Er (%)
Error
281.96 281.08 275.40 284.41 279.78 285.65 279.81 286.24 281.10 275.68 286.31 281.95 284.40 279.79 279.74 281.16 281.19 275.59 286.30 275.66 284.72 285.64 286.26 275127 11110 11110
0.00000 0.00029 0.00007 0.00004 0.00000 0.00032 0.00009 0.00059 0.00027 0.00007 0.00060 0.00006 0.00004 0.00170 0.00001 0.00031 0.00033 0.00004 0.00054 0.00007 0.00002 0.00020 0.00059 0.00010 0.01280 0.01347
0.00001 0.00083 0.00018 0.00012 0.00000 0.00092 0.00024 0.00169 0.00077 0.00019 0.00172 0.00017 0.00012 0.00475 0.00003 0.00087 0.00092 0.00011 0.00155 0.00020 0.00006 0.00057 0.00170 0.00027 0.00142 0.00150
Fs ¼ 1.25, h1 ¼ 0.125 mm (Fine), h2 ¼ 0.250 mm (Medium), h3 ¼ 0.500 mm (Coarse), r1-2 ¼ 2.00, r2-3 ¼ 2.00.
Fig. 3. Computational grid detail of aluminium frame section.
Fig. 4. Temperature distribution of D.1 section in case of solid material.
M. Malvoni et al. / Energy 111 (2016) 430e438
Fig. 5. Temperature distribution of D.1 section in case of ideal gas.
Figs. 4 and 5 shows the isotherms of the frame Section D.1 for a temperature difference between internal and external side of 20 K. In the first case, the cavities are constituted by the “air solid” and in the second one by air ideal gas. The air velocity magnitude with ideal gas air in cavities is underlined in Fig. 6. In Fig. 7 the isotherms are shown for the frame Section D.1 with air solid material in the cavities. The thermal bridge between the fixed frame and the wall is overlooked. Table 5 summarizes the main values of internal surface temperature and total heat flow for the D.1 frame section in the case of solid material, ideal gas and solid material without thermal breaks. It is noted that when the ideal gas is considered into the cavities, the temperature assumes a higher value than the “air solid” case. Furthermore, the standard ISO imposes computational conditions, which are more preventive than to consider ideal gas in the cavities. In order to validate the calculation model in according to standard ISO, the simulations were performed for the ten sections. The results for the two-dimensional thermal conductance L2D f and the thermal transmittance Uf are reported in Table 6. The comparison between the obtained values and the limits imposed by the standard ISO demonstrates that the proposed numerical model is validated. A comparison of the thermal performance of the different frame materials for the frame section from D.1 to D.9 is illustrated in Fig. 8. It is observed that the thermal transmittance generally depends on the combined effects of the geometry, the total
Fig. 6. Velocity vectors coloured by velocity magnitude on frame with ideal gas air in cavities.
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Fig. 7. Temperature distribution of D.1 section in case of solid material without thermal break.
number of cavities, the internal insulating materials and their width. Considering the Sections D.3, D.7, D.8, D.9 characterized by Poly Vinyl Chloride (PVC) material, in Fig. 9 it is possible to note that there is no correlation between the thermal transmittance and the width bf . Finally, the proposed model is implemented using ideal gas into the cavities. The simulation results are reported in Table 7. The percentage difference has been computed to compare the results with the lowest values of the standard ISO. The percentage variation is positive except for the Section D.9 that does not improve the final thermal performance respect to the case of the air solid material.
5. Conclusion The building sector causes significant environmental impacts, therefore there is an urgent need to decrease the energy consumption and the greenhouse gas emissions in such a sector in accordance with the European Commission challenges. By a correct design of the envelope it is possible to reduce the energy requirement of the whole building providing, at the same time, comfort to the end-users. The windows are considered the weak point of the building, causing energy losses and several criticisms that decrease the interior comfort. This study shows an accurate calculation procedure based on the CFD approach, according to ISO 10077-2 to investigate the thermal performance of window frames. The proposed numerical model is applied to the ten frame sections, as requested by the standard ISO 10077-2, in which the air solid material replaces the ideal air gas. The results demonstrate that the implemented method verifies the criteria of validation for all sections. Additional simulation has been performed in the real operating conditions. The obtained values of the thermal conductance and transmittance are lower than values proposed in the ISO, confirming that the standard provided values are more preventive than the real one. Since the numerical method can evaluate the thermal transmittance of several frame profiles with different features in terms of glazing, cavities and thickness of the frame connection; it represents a valid support in the design of new products with higher thermal performance, keeping in mind the convective motions and the heat exchange into the cavities.
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M. Malvoni et al. / Energy 111 (2016) 430e438 Table 5 Internal surface temperature and total heat flow for the D.1 frame section in different cases.
Solid material Ideal gas Solid material without thermal breaks
Internal surface temperature [K]
Total heat flow [W/m2]
288.21 289.18 285.14
11.08 8.98 18.09
Table 6 Thermal conductance and transmittance to validate the calculation procedure. Section
Model e L2D [W/m K]
ISO e L2D [W/m K]
D.1 D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9 D.10
0.554 0.263 0.429 0.346 0.402 0.667 0.285 0.178 0.207 0.477
0.550 0.263 0.424 0.346 0.408 0.659 0.285 0.181 0.207 0.481
a
± ± ± ± ± ± ± ± ± ±
0.007 0.001 0.006 0.001 0.007 0.008 0.002 0.003 0.001 0.004
Model e Uf [W/m2 K]
ISO e Uf [W/m2 K]
3.25 1.44 2.10 1.37 2.07 4.76 1.33 1.03 3.63 0.08
3.22 1.44 2.07 1.36 2.08 4.67 1.31 1.05 3.64 0.084
Referred to linear thermal transmittance.
Fig. 8. Thermal transmittance in ascending order for frame sections from D.1 to D.9.
Fig. 9. Thermal transmittance of the PVC sections in order of increasing width.
± ± ± ± ± ± ± ± ± ±
0.06 0.03 0.06 0.01 0.08 0.09 0.03 0.02 0.01 0.004a
M. Malvoni et al. / Energy 111 (2016) 430e438 Table 7 Thermal conductance and transmittance in case of the ideal gas. [15]
Section
Ideal gas e L2D [W/m K]
[%]
Ideal gas e Uf [W/m2 K]
[%]
D.1 D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9
0.449 0.252 0.347 0.333 0.372 0.642 0.261 0.150 0.180
1.6 3.7 6.1 2.0 3.6 0.5 1.3 0.1 0.6
2.31 1.33 1.36 1.26 1.72 4.50 0.85 0.85 3.16
2.6 6.1 10.4 3.4 5.5 0.6 5.1 0.5 0.1
[16]
[17]
[18]
Funding
[19]
This work is supported by the Project PON02_00323_2938699 EFFEDIL of Italian Ministry of Education, University and Research.
[20]
Author contributions [21]
All authors participated in preparing the research from the beginning to end, such as establishing research design, method and analysis. All authors discussed and finalized the analysis results to prepare the manuscript according to the progress of the research.
[22]
[23]
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Comparison between ASHRAE and ISO thermal transmittance calculation methods. Energy Build 2007;39(3):374e84. [38] Baldinelli G, Bianchi F. Windows thermal resistance: infrared thermography aided comparative analysis among finite volumes simulations and experimental methods. Appl Energy 31 December 2014;136. ISSN: 0306-2619: 250e8. http://dx.doi.org/10.1016/j.apenergy.2014.09.021. [39] Asdrubali Francesco, Baldinelli Giorgio, Bianchi Francesco. Influence of cavities geometric and emissivity properties on the overall thermal performance of aluminum frames for windows. Energy Build May 2013;60. ISSN: 0378-7788: 298e309. http://dx.doi.org/10.1016/j.enbuild.2013.01.028. [40] UNI EN ISO 10211. Thermal bridges in building construction - heat flows and surface temperatures - detailed calculations. 2008.
Nomenclature L2D f : thermal conductance of the frame section (W/m K) Up: thermal trasmittance of the central area of the panel (W/m2 K) Ug: thermal transmittance of the central area of the glazing (W/m2 K) Uf: thermal trasmittance of the frame section (W/m2 K) bp: visible width of the panel (m) bf: project width of the frame section (m) bg: visible width of the glazing (m) qP: total heat flow rate through the visible width of the panel (W) AP: central area of the panel (m2) DT: temperature difference between both adjacent environments (K) Rse: thermal resistance, external side (m2 K/W) Rsi: thermal resistance, internal side (m2 K/W)
cp: specific heat capacity (J/kg K) GCI: Grid Convergence Index Fs: factor of safety h: grid spacing p: order of convergence r, f: parameter for comparison in sensitivity nalysis Greek letters
l: thermal conductivity (W/m K) r: density (kg/m3) FS: total heat flow rate for length through the section (W/m) j: linear thermal trasmittance (W/m K) 3:
turbulent dissipation
Subscripts p: panel f: frame s: section g: glazing se: external surface si: internal side eq: equivalent s: space (air or gas space)
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
CFD modeling to evaluate the thermal performances of window frames in accordance with the ISO 10077 Maria Malvoni, Cristina Baglivo, Paolo Maria Congedo*, Domenico Laforgia Department of Engineering for Innovation, University of Salento, 73100 Lecce, Lecce, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 October 2015 Received in revised form 30 May 2016 Accepted 1 June 2016
The main goal of the EPBD (Energy Performance Buildings Directive) is the improvement of the energy performance of the European buildings. The internal comfort is critically dependent on the envelope that plays a key role in the thermal balance of the entire building. In particular, the windows are one of the most critical elements in terms of solar gains, heat losses and thermal bridges; therefore, the design of high efficiency frames is requested, both in cold and warm climate, but with different peculiarity. The UNI EN ISO 10077-2 provides a methodology to evaluate the frame thermal behaviour and it proposes the criteria to validate the numerical model. This paper presents a two-dimensional numerical method for the thermal behaviour evaluation of the frame sections using GAMBIT 2.2 and ANSYS FLUENT 14.5 CFD code. The results have been validated in accordance with the UNI EN ISO 10077-2. The standard ISO replaces the air gas with a fictitious material “air solid” into the cavities. Besides the simulation carried out with ideal gas entails higher internal surface temperature than the air solid case. Therefore, the standard ISO imposes preventive computational conditions. The proposed numerical method can be implemented for several frame profiles with different features in terms of geometry and materials, representing a valid support in the design of new high thermal performance frames. © 2016 Elsevier Ltd. All rights reserved.
Keywords: CFD Thermal break Window Frame 10077 EPBD
1. Introduction In order to address the current global warming trend due to greenhouse emissions, the European Union (EU) is involved to develop strategies to reduce the negative effects on climate change [1e3]. The renewable source integration in power systems [4e6] and the home automation are some of the adopted solutions for the energy-saving and to guarantee high-energy performance in the buildings [7e10]. It has been noted that the building sector is responsible for about 40% of the energy requirement [11]; therefore, the Energy Efficiency Directive [12] aims to improve the level of the energy performance and to reduce the energy consumption and environmental impact [13]. In order to obtain high efficiency buildings, several studies show how it is possible to reach, keeping costs down, a decreasing in terms of primary energy consumption and CO2 gas emissions. Studies [14e19] present a methodology based on the comparison of
* Corresponding author. E-mail address: [email protected] (P.M. Congedo). http://dx.doi.org/10.1016/j.energy.2016.06.002 0360-5442/© 2016 Elsevier Ltd. All rights reserved.
several energy efficiency measures to identify the cost-optimal solutions for buildings located in a warm climate. The buildings performances are also investigated in cold areas as Estonia [20], Unit States and China [21]. Multi-objective analyses have been carried out in several studies [22e26], to optimize the thermal performance of the building envelope; such an analysis allows to identify a set of optimal external wall configurations in order to reduce winter energy consumption and to increase summer thermal comfort. The multi-layer wall system reduces heating energy consumption of 27%e38% respect to single-layer wall system [27]. Once designed a highly efficient envelope, to ensure the comfort to the end-users it is necessary to evaluate other physical factors such as heat, light and sound [28]. A numerical study presented in the [29] show a comparison between the behaviour of double, triple and quadruple pane windows in order to demonstrate that the heat loss through the transparent elements can be reduced by increasing the number of panes especially in cold climate areas. Several thermal benefits can be reached by adopting of the multi pane window solutions considering that they cause around 30e50% of the losses by transmission across the building envelope [29].
M. Malvoni et al. / Energy 111 (2016) 430e438
Hence, the window design is strategic to reach the highest performance and reduce the overall energy demand for heating and cooling [30,31]. The thermal performance of the window depends on the thermal and geometrical characteristics of the framework and the interaction effects between its components. The thermal transmittance is evaluated by International Standard ISO 10077. In particular, the first part of the ISO 10077 [32] specifies a simple calculation method for a set of fenestration. The main disadvantage is that the calculation procedure does not take into account the effects of solar radiation and the heat transfer caused by air leakage and does not consider the ventilation and the condensation phenomena. In addition, it does not consider other additional elements, as gaskets, inserts, etc., that can be introduced to reach high performance solutions. Therefore, it can be used for a first estimation of the thermal transmittance. The second part of ISO 10077 [33] details a method for the calculation of the thermal transmittance of frame profiles Uf and of the linear thermal transmittance of their junction with glazing or opaque panels L2D f , providing information about the input data useful for the calculation. Also, it provides the criteria to validate the numerical methods. Several works show the application of numerical models in order to evaluate the frame thermal performance in accordance with standard ISO 10077. Cardinale & Al [34]. have investigated several window frames with rolling shutters-boxes by a Finite Element Method (FEM) analysis and the thermal transmittance has been checked using the software FRAME SIMULATOR 2 Dartwin. In Ref. [35] the thermal performance of the glazing on the frame and the edge-of glazing behaviour in a wood-frame window, with regard to condensation risk, have been analysed using THERM and WINDOW software packages. An artificial neural network (ANN) model has been developed to predict the thermal transmittance of wooden windows; the results show an error of about 1% compared to the solutions provided by the Computational Fluid Dynamics (CFD) numerical procedure [36]. A comparison between the methods suggested by ASHRAE and ISO for the calculation of the thermal transmittance has been performed using the FRAMEplus Toolkit Version 3.0 and THERM 2 software [37]. Numerical simulations in two-dimensional and threedimensional domains have been implemented with the CFD code Fluent to investigate the wood and aluminium framed windows [38]. The geometry and the characteristics of the cavities influence the overall performance of the profile. A numerical analysis was carried by CFD code Fluent to simulate the effects due to the insert of ethyleneepropylene diene monomer (EPDM) gaskets inside the frame cavities and to evaluate the emissivity of the cavities [39]. The present study proposes a two-dimensional numerical method to investigate the thermal performance of frame profiles. The procedure is performed using the fluid-dynamic calculation ANSYS FLUENT Release 14.5 and the pre-processor GAMBIT 2.2. A detailed analysis of the thermal performance is carried out. Moreover, the proposed model verifies the criteria of validation for the ten frame sections, illustrated in annex D of the ISO 10077-2. The work is organized into three sections. The main concepts of the standard ISO are reported in the Section 1, the Section 2 show a detailed description of the geometry, boundary condition, computational grid model and settings solver. The results are reported in the final section. 2. International standard ISO 10077: numerical method for frame The UNI EN ISO 10077-2 specifies the methodology and the
431
input data to calculate the thermal transmittance of the frame profiles Uf and the linear thermal transmittance jg of their junction with glazing or opaque panels. It also provides the criteria to validate the implemented numerical model. In according to the UN EN ISO 10211:2008 [40] the geometrical model must consider an adequate number of sub-sections. Solid materials, boundary conditions and cavities must fulfil particular features, as explained below. 2.1. Treatment of solid sections and boundary conditions Thermal conductivity l is calculated in accordance with the Annex A of ISO 10077-2. The reference winter temperatures of internal and external side are, respectively, 293 K and 273 K, while the thermal resistance values of the external and internal surfaces of the node are defined in accordance to the Annex B of ISO 10077. The node surfaces in junction with the wall are considered adiabatic, as well as the outer edge of the insulating panel. 2.2. Treatment of cavities The air cavities must be replaced with a solid material, therefore the heat flow in cavities is represented by an equivalent thermal conductivity leq that includes the various mechanisms of heat transfer, such as thermal conduction, convection and radiation. The geometry, the ventilation degree and the materials of the cavities influence the thermal conductivity. In case of the width of the slit is not over than 2 mm or completely closed, the air cavity shall be treated as unventilated. Otherwise, the cavity can be considered ventilated. Slightly ventilated air cavities are characterized by small cross-sections and connected to the external or internal air through a slit of 2e10 mm. When the width of the groove is over than 10 mm, the entire surface is exposed to the external or internal environment. In the case of a large cavity connected by a single slit and a developed surface exceeding the width of the slit by a factor of ten, the surface resistance with reduced radiation can be used. Unventilated and slightly ventilated air cavities have the same value of equivalent thermal conductivity leq. 2.3. Determination of the thermal performance To calculate the thermal transmittance of the frame section, an insulation panel with thermal conductivity l ¼ 0,035 W/m k replaces the existing glazing or the opaque panel of the thickness d or dg. The length of insulated panel bp must be more than 190 mm and its height is equal to 1000 mm. The surface of the panel is considered an adiabatic boundary. The thermal transmittance of the frame section Uf [W/m2 K] is defined as follows [33]:
Uf ¼
L2D Up b p f bf
(1)
where L2D f [W/m K] is the thermal conductance of the frame section; Up [W/m2 K] is the thermal transmittance of the central area of the panel; bp [m] is the visible width of the panel; bf [m] is the width of the frame section. The two-dimensional thermal conductance L2D is defined as f [40]:
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L2D f ¼
FS DT
(2)
with FS [W/m] is the total heat flow rate for length through the section; DT [K] is the temperature difference between both adjacent environments. The thermal transmittance of the panel Up is calculated as follows:
UP ¼
qP AP DT
3.1. Geometrical model: aluminium frame section with thermal break and insulation panel (D.1)
(3)
where qP [W] is the total heat flow rate through the visible width of the panel; AP [m2] is the central area of the panel; DT [K] is the temperature difference between both adjacent environments. The linear thermal transmittance of the junction with the glazing or opaque panel jg [W/m K] is defined as follows [33]:
Jg ¼ L2D J Uf bf Ug bg
- “Segregated numerical scheme” involves the resolution of the equation of the moment, continuity and transport in sequential steps; - “Steady” condition, because of fixed wall temperatures on the frame and glasses; - The standard k-epsilon turbulence model has been enabled; - Operating conditions with pressure equal to the standard atmospheric one (101.325 Pa) and gravity enabled.
(4)
with Uf [W/m2 K] is the thermal transmittance of the frame section; Ug [W/m2 K] is the thermal transmittance of the central area of the glazing; bg [m] is the visible width of the glazing.
The mesh is constituted by cells or elements, which represent the geometry of the phenomena. In this study GAMBIT 2.2 tool has been used to generate the computational grid. Fig. 1 show D.1 frame section. It is characterized by a fixed and mobile frame in aluminium (thermal break) with a maximum thickness equal to 63 mm and width bf of 110 mm. The insulation thickness is of 28 mm and width bp at least 190 mm. The thermal break is achieved through the polyamide with 25% glass fibre, which carries out the breakdown of the single aluminium profiles into two parts, external and internal side. The continuous elements of the frame perimeter have been considered: the rebate seal between sash and frame, the central gasket, the internal and external gasket of glass. The profile section is considered as a barrier between the external (B) and the internal (C) side. Fig. 2 show the computational grid for the selected area highlighted by a circle in Fig. 1. The maximum value of the equiangle and equisize skew are 0.43 and 0.54 respectively. As regards the Aspect Ratio, the 99.9% of the cells differs from the cell with the value 1 for a maximum of 20%. The “reticular” structure of frames shows several air cavities, identified with red numbers in Fig. 1, enclosed between the aluminium walls, gaskets and thermal break.
2.4. Criteria to validate the numerical model In order to validate the proposed calculation method, the results of thermal conductance and transmittance must be in the range as specified in the Annex D of standard ISO. The calculation must be verified for frame sections reported in Refs. [33], figures from D.1 to D.10. It is observed that the thermal conductance L2D and the thermal transmittance Uf must be calculated for the first nine frame sections, instead, for the last frame section, the two-dimensional thermal conductance L2D and the linear thermal transmittance j must be evaluated. 3. CFD numerical analysis The CFD ANSYS FLUENT Release 14.5 has been used to investigate the thermal flux through the frames. In order to evaluate the thermal performance of aluminium-framed windows, the adopted approach requested the following steps:
3.2. Boundary conditions According to the UNI EN ISO 10077-2, the following assumptions have been considered:
1. 2. 3. 4.
Definition of geometrical model; Settings of boundaries conditions: materials, temperatures, etc.; Numerical calculation; Post processing analysis of simulations and validation of the results.
The main parameters for the CFD setup are reported in Table 1; in particular, the following settings have been used:
analysis of continuous elements (not punctual elements); vertical orientation of frame sections; the emissivity of air cavity surfaces must be of 0.9; an insulation panel with thermal conductivity l ¼ 0,035 W/m K replaces the existing glazing (the visible panel length could be less than 190 mm); the heat flow is normal at the surfaces adjacent to the internal (C) and the external side (B). The vertical surfaces to the heat flow direction are considered as adiabatic planes. The thermal resistances are illustrated in Table 2; the density of the solid sections and the thermal conductivity are reported in Table 3; the cavity 11 is considered as slightly ventilated cavity and its thermal conductivity results twice the unventilated cavity; the internal and external surface temperature are 293 K and 273 K, respectively.
The wall interface and the lateral side of the insulating panel are set by an adiabatic boundary (A in Fig. 1). A fictitious material “airsolid” has been introduced to characterize the air cavities of the Section D.1.
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Table 1 Details of CFD setting. Solver Numerical scheme Linearization Pressure Pressure velocity coupling Momentum, turbulence kinetic energy, turbulence dissipation rate Fluid Turbolence model Time step Number of faces (Section D.1) Typology of elements (Section D.1) Total number of elements (Section D.1)
2D double precision Segregated Implicit Standard Standard 2nd order upwind Ideal gas Standard k-є (only for gas air) Steady 24 Triangular 108.374
3.3. Sensitivity analysis of grid spacing A sensitivity analysis of the grid has been carried out to evaluate the error caused by the spatial discretization. The Grid Convergence Index (GCI) shows how the computed value is far from the asymptotic numerical value. This study uses three different grids and the GCI is calculated as follows:
GCI12 ¼
Fs jε12 j with fine and medium grids; p r12 1
(5)
GCI23 ¼
Fs jε23 j with coarse and medium grids; p r23 1
(6)
The factor of safety Fs is equal to 1.25 for the comparison of three grids with: Fig. 1. Aluminium frame section with thermal break and insulation panel (D.1).
h1 < h2 < h3
(7)
εnnþ1 ¼
fnþ1 fn fn
(8)
rnnþ1 ¼
hnþ1 hn
(9)
p¼
fnþ1 ln fnþ2 f f nþ1
n
ln r
(10)
where h is the grid spacing i.e. the minimum value of the distance of the nodes, p is the order of convergence, f is the value of the parameter chosen for the comparison. When the result of the considered grid is in the asymptotic range means that if the number of cells grows, the value of the solution f does not change:
GCI23 y1 r p GCI12
(11)
The evaluated value of the grid is:
Fig. 2. Grid convergence indexes, auditing ratio and order of convergence (grid spacing analysis).
f ¼ f1 þ
f1 f2 p 1 r12
(12)
The sensitivity analysis has been performed by the use of the average volume temperature of the cavities and the total heat flux through internal and external surfaces. The results of the sensitivity analysis are shown in Table 4 and Fig. 3. Table 2 Thermal resistance of external and internal surfaces.
Plane surface Corners (enhanced resistance)
External side
Internal side
Rse ¼ 0.04 m2 K/W Rse ¼ 0.04 m2 K/W
Rsi ¼ 0.13 m2 K/W Rsi ¼ 0.20 m2 K/W
4. Simulation results This section shows the simulation results and the comparison with the values provided by the ISO 10077 in order to validate the model.
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Table 3 Thermo-physical properties of the materials. Key
Material
Density r [kg/m3]
Thermal conductivity l [W/m K]
a b c d e f g h i k l m n o
Insulation panel Soft wood PVC EPDM Polyamide 6.6 with 25% glass Glass Still Aluminium Pile weather stripping Polyamide PU rigid Polysulfide Silica gel Gas filling
37 500 1390 1150 1450 2500 7800 2800 30 1150 1200 1400 720 1.784
0.035 0.13 0.17 0.25 0.30 1.00 50 160 0.14 0.25 0.25 0.40 0.13 0.034
Table 4 Sensitivity analysis. No
Description
f1 (K)
f2 (K)
f3 (K)
p
ASS(e 1-2)
ASS (e 2-3)
GCI
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Cavity1 Cavity10 Cavity11 Cavity2 Cavity3 Cavity4 Cavity5 Cavity6 Cavity7 Cavity8 Cavity9 Panel Frame internal Polyamide1 frame Polyamide2 frame Polyamide2 shutter Polyamide1 shutter Gasket glass2 Gasket glass1 Shutter external Gasket central Gasket jamb Shutter internal Frame external Internal heat flux External heat flux
281.9614 281.0831 275.3985 284.4085 279.7850 285.6529 279.8074 286.2426 281.1049 275.6754 286.3072 281.9487 284.4006 279.7962 279.7433 281.1568 281.1885 275.5854 286.3035 275.6573 284.7211 285.6387 286.2639 275.2688 11.0960 11.0961
281.9616 281.0847 275.3978 284.4094 279.7851 285.6554 279.8080 286.2463 281.1064 275.6747 286.3109 281.9489 284.4014 279.7970 279.7435 281.1583 281.1902 275.5849 286.3069 275.6566 284.7216 285.6406 286.2675 275.2681 11.0927 11.0927
281.9662 281.0898 275.3942 284.4177 279.7872 285.6666 279.8110 286.2596 281.1114 275.6710 286.3243 281.9497 284.4098 279.7980 279.7447 281.1633 281.1958 275.5817 286.3200 275.6529 284.7283 285.6501 286.2809 275.2651 11.0799 11.0799
4.536 1.733 2.465 3.278 4.728 2.144 2.158 1.880 1.768 2.459 1.870 1.506 3.278 0.291 2.843 1.693 1.721 2.730 1.916 2.419 3.592 2.354 1.876 2.095 1.959 1.930
7.093E-07 5.479E-06 2.360E-06 3.024E-06 2.859E-07 8.857E-06 2.395E-06 1.265E-05 5.265E-06 2.467E-06 1.278E-05 8.867E-07 3.024E-06 3.038E-06 6.077E-07 5.513E-06 6.010E-06 1.778E-06 1.205E-05 2.503E-06 1.932E-06 6.547E-06 1.268E-05 2.543E-06 2.956E-04 3.028E-04
1.646E-05 1.822E-05 1.304E-05 2.932E-05 7.577E-06 3.914E-05 1.069E-05 4.653E-05 1.793E-05 1.357E-05 4.673E-05 2.518E-06 2.932E-05 3.717E-06 4.361E-06 1.782E-05 1.981E-05 1.179E-05 4.548E-05 1.339E-05 2.329E-05 3.347E-05 4.653E-05 1.086E-05 1.149E-03 1.154E-03
3.994E-06 2.946E-04 6.523E-05 4.346E-05 1.402E-06 3.238E-04 8.644E-05 5.900E-04 2.736E-04 6.852E-05 6.017E-04 6.024E-05 4.346E-05 1.699E-03 1.230E-05 3.087E-04 3.272E-04 3.946E-05 5.430E-04 7.196E-05 2.184E-05 1.990E-04 5.938E-04 9.717E-05 1.280E-02 1.347E-02
1-2
GIC
2-3
9.266E-05 9.794E-04 3.603E-04 4.214E-04 3.714E-05 1.431E-03 3.858E-04 2.171E-03 9.317E-04 3.769E-04 2.200E-03 1.711E-04 4.214E-04 2.079E-03 8.826E-05 9.978E-04 1.078E-03 2.617E-04 2.049E-03 3.849E-04 2.633E-04 1.017E-03 2.179E-03 4.150E-04 4.976E-02 5.134E-02
f
Band Er (%)
Error
281.96 281.08 275.40 284.41 279.78 285.65 279.81 286.24 281.10 275.68 286.31 281.95 284.40 279.79 279.74 281.16 281.19 275.59 286.30 275.66 284.72 285.64 286.26 275127 11110 11110
0.00000 0.00029 0.00007 0.00004 0.00000 0.00032 0.00009 0.00059 0.00027 0.00007 0.00060 0.00006 0.00004 0.00170 0.00001 0.00031 0.00033 0.00004 0.00054 0.00007 0.00002 0.00020 0.00059 0.00010 0.01280 0.01347
0.00001 0.00083 0.00018 0.00012 0.00000 0.00092 0.00024 0.00169 0.00077 0.00019 0.00172 0.00017 0.00012 0.00475 0.00003 0.00087 0.00092 0.00011 0.00155 0.00020 0.00006 0.00057 0.00170 0.00027 0.00142 0.00150
Fs ¼ 1.25, h1 ¼ 0.125 mm (Fine), h2 ¼ 0.250 mm (Medium), h3 ¼ 0.500 mm (Coarse), r1-2 ¼ 2.00, r2-3 ¼ 2.00.
Fig. 3. Computational grid detail of aluminium frame section.
Fig. 4. Temperature distribution of D.1 section in case of solid material.
M. Malvoni et al. / Energy 111 (2016) 430e438
Fig. 5. Temperature distribution of D.1 section in case of ideal gas.
Figs. 4 and 5 shows the isotherms of the frame Section D.1 for a temperature difference between internal and external side of 20 K. In the first case, the cavities are constituted by the “air solid” and in the second one by air ideal gas. The air velocity magnitude with ideal gas air in cavities is underlined in Fig. 6. In Fig. 7 the isotherms are shown for the frame Section D.1 with air solid material in the cavities. The thermal bridge between the fixed frame and the wall is overlooked. Table 5 summarizes the main values of internal surface temperature and total heat flow for the D.1 frame section in the case of solid material, ideal gas and solid material without thermal breaks. It is noted that when the ideal gas is considered into the cavities, the temperature assumes a higher value than the “air solid” case. Furthermore, the standard ISO imposes computational conditions, which are more preventive than to consider ideal gas in the cavities. In order to validate the calculation model in according to standard ISO, the simulations were performed for the ten sections. The results for the two-dimensional thermal conductance L2D f and the thermal transmittance Uf are reported in Table 6. The comparison between the obtained values and the limits imposed by the standard ISO demonstrates that the proposed numerical model is validated. A comparison of the thermal performance of the different frame materials for the frame section from D.1 to D.9 is illustrated in Fig. 8. It is observed that the thermal transmittance generally depends on the combined effects of the geometry, the total
Fig. 6. Velocity vectors coloured by velocity magnitude on frame with ideal gas air in cavities.
435
Fig. 7. Temperature distribution of D.1 section in case of solid material without thermal break.
number of cavities, the internal insulating materials and their width. Considering the Sections D.3, D.7, D.8, D.9 characterized by Poly Vinyl Chloride (PVC) material, in Fig. 9 it is possible to note that there is no correlation between the thermal transmittance and the width bf . Finally, the proposed model is implemented using ideal gas into the cavities. The simulation results are reported in Table 7. The percentage difference has been computed to compare the results with the lowest values of the standard ISO. The percentage variation is positive except for the Section D.9 that does not improve the final thermal performance respect to the case of the air solid material.
5. Conclusion The building sector causes significant environmental impacts, therefore there is an urgent need to decrease the energy consumption and the greenhouse gas emissions in such a sector in accordance with the European Commission challenges. By a correct design of the envelope it is possible to reduce the energy requirement of the whole building providing, at the same time, comfort to the end-users. The windows are considered the weak point of the building, causing energy losses and several criticisms that decrease the interior comfort. This study shows an accurate calculation procedure based on the CFD approach, according to ISO 10077-2 to investigate the thermal performance of window frames. The proposed numerical model is applied to the ten frame sections, as requested by the standard ISO 10077-2, in which the air solid material replaces the ideal air gas. The results demonstrate that the implemented method verifies the criteria of validation for all sections. Additional simulation has been performed in the real operating conditions. The obtained values of the thermal conductance and transmittance are lower than values proposed in the ISO, confirming that the standard provided values are more preventive than the real one. Since the numerical method can evaluate the thermal transmittance of several frame profiles with different features in terms of glazing, cavities and thickness of the frame connection; it represents a valid support in the design of new products with higher thermal performance, keeping in mind the convective motions and the heat exchange into the cavities.
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M. Malvoni et al. / Energy 111 (2016) 430e438 Table 5 Internal surface temperature and total heat flow for the D.1 frame section in different cases.
Solid material Ideal gas Solid material without thermal breaks
Internal surface temperature [K]
Total heat flow [W/m2]
288.21 289.18 285.14
11.08 8.98 18.09
Table 6 Thermal conductance and transmittance to validate the calculation procedure. Section
Model e L2D [W/m K]
ISO e L2D [W/m K]
D.1 D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9 D.10
0.554 0.263 0.429 0.346 0.402 0.667 0.285 0.178 0.207 0.477
0.550 0.263 0.424 0.346 0.408 0.659 0.285 0.181 0.207 0.481
a
± ± ± ± ± ± ± ± ± ±
0.007 0.001 0.006 0.001 0.007 0.008 0.002 0.003 0.001 0.004
Model e Uf [W/m2 K]
ISO e Uf [W/m2 K]
3.25 1.44 2.10 1.37 2.07 4.76 1.33 1.03 3.63 0.08
3.22 1.44 2.07 1.36 2.08 4.67 1.31 1.05 3.64 0.084
Referred to linear thermal transmittance.
Fig. 8. Thermal transmittance in ascending order for frame sections from D.1 to D.9.
Fig. 9. Thermal transmittance of the PVC sections in order of increasing width.
± ± ± ± ± ± ± ± ± ±
0.06 0.03 0.06 0.01 0.08 0.09 0.03 0.02 0.01 0.004a
M. Malvoni et al. / Energy 111 (2016) 430e438 Table 7 Thermal conductance and transmittance in case of the ideal gas. [15]
Section
Ideal gas e L2D [W/m K]
[%]
Ideal gas e Uf [W/m2 K]
[%]
D.1 D.2 D.3 D.4 D.5 D.6 D.7 D.8 D.9
0.449 0.252 0.347 0.333 0.372 0.642 0.261 0.150 0.180
1.6 3.7 6.1 2.0 3.6 0.5 1.3 0.1 0.6
2.31 1.33 1.36 1.26 1.72 4.50 0.85 0.85 3.16
2.6 6.1 10.4 3.4 5.5 0.6 5.1 0.5 0.1
[16]
[17]
[18]
Funding
[19]
This work is supported by the Project PON02_00323_2938699 EFFEDIL of Italian Ministry of Education, University and Research.
[20]
Author contributions [21]
All authors participated in preparing the research from the beginning to end, such as establishing research design, method and analysis. All authors discussed and finalized the analysis results to prepare the manuscript according to the progress of the research.
[22]
[23]
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Nomenclature L2D f : thermal conductance of the frame section (W/m K) Up: thermal trasmittance of the central area of the panel (W/m2 K) Ug: thermal transmittance of the central area of the glazing (W/m2 K) Uf: thermal trasmittance of the frame section (W/m2 K) bp: visible width of the panel (m) bf: project width of the frame section (m) bg: visible width of the glazing (m) qP: total heat flow rate through the visible width of the panel (W) AP: central area of the panel (m2) DT: temperature difference between both adjacent environments (K) Rse: thermal resistance, external side (m2 K/W) Rsi: thermal resistance, internal side (m2 K/W)
cp: specific heat capacity (J/kg K) GCI: Grid Convergence Index Fs: factor of safety h: grid spacing p: order of convergence r, f: parameter for comparison in sensitivity nalysis Greek letters
l: thermal conductivity (W/m K) r: density (kg/m3) FS: total heat flow rate for length through the section (W/m) j: linear thermal trasmittance (W/m K) 3:
turbulent dissipation
Subscripts p: panel f: frame s: section g: glazing se: external surface si: internal side eq: equivalent s: space (air or gas space)