CFD modelling of 2-D heat transfer in a window construction including glazing and frame

Transcription

1 CFD modelling of 2-D heat transfer in a window construction including glazing and frame Morten V. Vendelboe, Ph.D student Technical University of Denmark Department of Civil Engineering mvv@byg.dtu.dk Svend Svendsen, Professor Technical University of Denmark Department of Civil Engineering ss@byg.dtu.dk Toke R.. Nielsen, Associate Professor Technical University of Denmark Department of Civil Engineering trn@byg.dtu.dk KEYWORDS: fenestration, window, numerical simulation, thermal transmittance, glazing temperature, CFD SUMMARY: A numerical model for the simultaneous calculation of 2-D heat transfer and indoor surface temperatures for a three layer glazing unit and a frame construction based on a commercial CFD code is presented. The calculated heat flow and the surface temperatures of the inner glazing layer are compared to results obtained using the finite element code Therm 5.2 by calculations according to EN ISO and ISO The models compared produce almost identical results with respect to the overall thermal transmittance of the glazing and frame, whereas differences in the range 3-7% are found for the thermal transmittance of the frame part only. The calculated distributions of surface temperatures for the inner pane also agree quite well when convection in the glazing cavities is accounted for in the finite element calculation. 1. Introduction Window design affects energy consumption in buildings significantly with respect to both cooling and heating demand. Sensible design solutions to improve the thermal properties of windows are therefore crucial in the effort to reduce the overall energy consumption in buildings. One of the most widely used tools (Gustavsen 2005, Song 2007) for detailed analysis of the thermal properties of the connection between glazing and window frames is the 2-D finite element code Therm5.2 (Finlayson 1998). The code can be used for calculation of the thermal transmittance of glazing and frame connections according to the EN ISO (CEN 2003) and the ISO (ISO 2003) standards. The EN ISO procedure for calculation of thermal transmittance is however not suited for determination of condensation risk due to low inside surface temperatures but a suitable alternative is not prescribed in the European standards (CEN 2001). A condensation resistance model has however been implemented in Therm for more precise calculation of indoor surface temperatures (Zhao 1996, Mitchell 2003, Kohler 2003) in compliance with North American standards (NFRC 2004). In the following the preliminary investigations regarding the possibility to apply a commercial CFD code for detailed 2-D analysis of heat transfer and simultaneous calculation of indoor surface temperatures is presented. Calculated thermal transmittances as well as indoor surface temperature distribution are compared to Therm models to observe the difference due to more comprehensive modelling of the cavities of the glazing and frame

2 2. Method 2.1 Geometry and materials The modelled window cross section consists of three 4 mm glass layers and two 12 mm air cavities. The panes have an emissivity of 0.84 on all surfaces except the outer surface of the inner pane which has a low emissivity coating with an emissivity of Since the focus is on model comparison, and not on calculating the properties of an actual window, all other emissivities are set to 0.9. For the same reason the detailed geometry and thermal properties of the spacer are represented by a box of an equivalent fixed thermal conductivity. The applied thermal properties of the materials used in the calculations are listed in TABLE. 1. The model geometry is displayed in FIG. 1. FIG. 1: Figure showing the cross section of the window. Left: The sill and the lower part of the glazing unit. Right: The entire model. TABLE. 1: Material properties used for the calculations. Material Conductivity [W/mK] Emissivities [-] Aluminium Wood EPDM Sealing Spacer Glass Glass with low emissivity coating

3 2.2 Boundary conditions For all models boundary conditions are chosen according to EN ISO Constant heat transfer coefficients of 7.69 W/m 2 K and 25 W/m 2 K are assigned to the internal and external boundaries respectively. The indoor temperature is set to 20 C and the outdoor temperature to 0 C. 2.3 Glazing For the finite element calculations thermal properties of the glazing unit are calculated in Window5.2 (Mitchell 2001) and imported to Therm. To ensure that the glazing unit, modelled using the CFD code, has the same thermal properties as the glazing unit imported for the finite element calculations, a comparison is made for the two models of the glazing unit alone. In both cases boundary conditions according to section 2.2 are applied for the internal and external boundaries while the top and bottom of the glazing is adiabatic. The height of the glazing is 0.5 m. The calculated thermal transmittance of the glazing using Window is 1.25 W/m 2 K. The calculated thermal transmittance for the CFD model is 1.27 W/m 2 K. The calculated thermal transmittances of the two models are in very good agreement with a difference of 1.6 % and are thus used in the integrated calculations for glazing and frame. The settings for the separate CFD model for the glazing are presented in section 2.5. For the finite element calculations two calculations are performed for each model. For calculations of thermal transmittance (U-value) the air in the glazing cavities is replaces by a solid material with a thermal conductivity that is calculated based on the heat transfer due to convection and radiation across the cavity. For calculation of indoor surface temperatures a convection model for the local temperature distribution inside the glazing cavities developed for Condensation Resistance rating according to NFRC 500 is applied. 2.4 Frame cavities While the thermal properties for the solid domains are identical for the finite element models and the CFD model, the cavity modelling is different. In the first two finite element models the frame cavities are modelled according to EN ISO where a simplified radiation model is prescribed. These models are referred to as CEN CR and CEN U-value. In the other two models the frame cavities are modelled according to ISO including a detailed view factor based radiation model. These models are referred to as ISO CR and ISO U- value. In all cases the cavities are defined as non ventilated to match the assumptions made in the CFD model. The settings for the CFD model for the convective and radiative heat transfer in the frame cavities is presented in section CFD settings and mesh CFD settings A list of settings for the CFD model is presented in TABLE 2. The settings are used for both the separate model for the glazing and the model including both the frame and the glazing

4 TABLE. 2: Settings for CFD model. Solver Viscous model Fluid thermal properties Stationary Laminar Density modelled according to the Boussinesq approximation. All other properties are constant. Discretization schemes Pressure Standard Radiation model Momentum 2 nd order Energy 2 nd order Discrete Transfer Radiation Model (DTRM) Though the PRESTO! discretization scheme for pressure is recommended for modelling of natural convection (Fluent Inc. 2005) convergence is only achieved when the standard scheme is applied for the model including both the frame and the glazing. A comparison for the separate glazing model does not however show any effect of enabling the PRESTO! discretization scheme for pressure Mesh The calculation of heat transfer across the window construction including glazing and frame is performed with a triangular mesh of ~120,000 cells. The solution is grid independent with respect to the total thermal transmittance of the glazing and frame to less than 1 %. Grid independence could probably be achieved with a lower number of cells, but due to the complex nature of the geometry a fine mesh is needed to reduce the number of poor quality cells. Thus critical mass imbalances due to poor mesh quality within key areas of the frame cavities occurs at both ~30,000 and ~60,000 cells. While calculation time is not comparable to that of Therm (order of seconds) the model does however converge in less than 1 hour (Intel Centrino Duo, 2 GHz, 4 GB). 3. Results and discussion 3.1 Comparison of total thermal transmittance of glazing and frame The calculated total thermal transmittance of glazing and frame is presented in TABLE. 3. Since the modelled thermal transmittance of the glazing in the CFD model is 1.6 % higher than for the glazing imported in the finite element calculations and the thermal transmittance of the glazing make up the majority of the total thermal transmittance the results for the CFD model have been corrected for appropriate comparison. As TABLE. 3 shows the calculated results are essentially identical whether or not the CFD results are corrected. TABLE. 3: Comparison of calculated total thermal transmittance of window cross section including glazing and frame Model Thermal transmittance (corrected with regard to U gl ) [W/m 2 K] Relative difference to CFD model [%] CFD CEN U-value ISO U-value

5 3.2 Comparison of thermal transmittance of the frame By subtracting the 1-D thermal transmittance from the separate glazing models calculated in section 2.3 from the total thermal transmittances presented in section 3.1 the following results are obtained for the thermal transmittance of the frame including the spacer. TABLE. 4: Comparison of calculated thermal transmittance of frame Model Thermal transmittance [W/m 2 K] Relative difference to CFD model [%] CFD CEN U-value ISO U-value Though larger discrepancies are found compared to the total thermal transmittance of glazing and frame the results shown in TABLE. 4 still agree very well. The reason why the results agree so well despite the different treatment of the heat transfer in the frame cavities is probably that the size and temperature difference across the cavities result in only very limited convection as illustrated in FIG. 2. FIG. 2: Calculated velocity distribution for the CFD model for the frame cavities and the lower part of the glazing cavities

6 3.3 Calculated indoor surface temperature distribution of the glazing The calculated surface distribution for the inside of the innermost glazing for the 5 models is shown in FIG. 3. The x-axis shows the vertical distance from the top of the glazing (x=500 mm denotes the lower edge of the daylight opening). Since the results from the CEN and ISO U-value models as well as the CEN and ISO CR models are practically identical, only one plot is included for each model category. 0 Distance from top of glazing [mm] CFD CEN/ISO U-value CEN/ISO CR Surface temperature [deg-c] FIG. 3 : Calculated surface distribution on the inside of the innermost glazing for the 5 models as a function of the vertical distance from the top of the glazing. As FIG. 3 shows, the results for the CFD model and the CR models are very similar regarding the overall tendency as well as local values with a predicted minimum temperature of 13.3 C and 12.9 C respectively. The U-value models on the other hand display similar surface temperatures on average but poor agreement concerning both overall tendency and local values in certain points. Due to the omission of the convective effects in the glazing cavities the predicted minimum temperature at the lower daylight opening is higher than predicted by the CFD and CR models with 13.8 C. 4. Conclusions and further work The conclusions are as follows: There is excellent agreement between the calculated values for the total thermal transmission whether calculated using the CFD model, the CEN U-value model or the ISO U-value model. There is good agreement between the three model types for the thermal transmittance of the frame with differences of less than 7 % in all cases

7 There is good agreement between the calculated indoor surface temperatures of the glazing for the CFD model and the CR models whereas the U-value models perform poorly with respect to both overall tendency and local values. Given the overall agreement with the results based on the simplified finite element modeling of the glazing and frame cavities the application of the more comprehensive and time consuming CFD modelling is not justifiable for the given case. This is however believed to be attributed to the limited convection occurring in the glazing and frame cavities. Further work will therefore include similar comparisons for window constructions where convection is more significant for the overall heat flow as for window solutions with larger glazing distances and cases where non laminar flow conditions may occur. In addition the comprehensive modelling capabilities of the CFD software facilitate further investigation of the impact of detailed modelling with respect to variable radiative and convective indoor boundary conditions for more precise indoor surface prediction in particular. 5. References European Committee for Standardization (2003). EN ISO : Windows, doors and shutters Calculation of thermal transmittance Part 2: Numerical method for frames. European Committee for Standardization (2001). EN ISO 13788: Hygrothermal performance of building components and building elements - Internal surface temperature to avoid critical surface humidity and interstitial condensation - Calculation methods. Finlayson, E., Mitchell R., Arasteh D., Huizenga C. and Curcija D. (1998). THERM 2.0: Program description. A PC program for analyzing the two-dimensional heat transfer through building products. University of California, Berkeley, CA, USA. Fluent Inc. (2005). Fluent 6.2 Users Guide. Gustavsen A., Uvsløkk S. and Jelle P. (2005). Numerical and experimental studies of the effects of various glazing spacer on the windows and the glazing temperature, Proceedings of the 6 th Symposium on Building Physics in the Nordic Countries, Reykjavik, Iceland, June International Organization for Standardization (2003). ISO 15099:2003(E) - Thermal performance of windows, doors and shading devices Detailed alculations. Kohler C., Arasteh D. and Mitchell R. (2003). THERM simulations of window indoor surface temperatures for predicting condensation, ASHRAE 2003 Winter meetings CD, Technical and SymposiumPapers,Vol.109, Issue 1, p Mitchell R., Kohler C., Arasteh D., Carmody J., Huizenga C. and Curcija D. (2003). Therm5/Window5 NFRC Simulation manual, Lawrence Berkeley National Laboratory, Berkeley, CA, USA. Mitchell R., Kohler C., Arasteh D., Huizenga C., Yu T., and Curcija D. (2001). WINDOW 5.0 User Manual. Lawrence Berkeley National Laboratory, Berkeley, CA, USA. National Fenestration Rating Counsel (2004). NFRC 500: Procedure for determining fenestration product condensation resistance values

8 Song S., Ho J.,Yeo M., Kim Y. and Song K. (2007). Evaluation of inside surface condensation in double glazing window system with insulating spacer: A case study of residential complex, Building and Environment, Vol. 42, p Zhao Y., Curcija D. and Goss P. (1996). Condensation Resistance Validation Project Detailed Computer Simulations Using Finite-Element Methods. ASHRAE Transactions, Vol.102 Issue 2, p