HEAT TRANSFER INVESTIGATION OF A WOOD WINDOW USING THE FINITE ELEMENT METHOD

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1 MIE 605 Finite Element nalysis Department of Mechanical engineering University of Massachusetts, mhesrt HET TRNSFER INVESTIGTION OF WOOD WINDOW USING THE FINITE ELEMENT METHOD 1.BSTRCT Presented by:- Sneh kumar In this work heat transfer analysis has been done for the double glazed PFM wood window by 2-D and 3-D modeling. Fluid inside the glazing cavity had been modeled as solid and effective conductivity had been used. Results have been reported for three sizes of wood window with same frame cross-section size. The results have been reported in terms of local temperature distribution, averaged heat flux, heat transfers U-factors. The overall heat transfer results have been compared with Therm5/Window5 (FEM software) results and the effect of size change has been observed. 2.NOMENCLTURE U=Thermal transmittance h i =inside film heat transfer coefficient h 0 =outside film heat transfer coefficient T i =Inside bulk temperature T o =Outside bulk temperature 3.INTRODUCTION Window is one of the fenestration products. Fenestration is an architectural term that refers to the arrangement, proportion and design of window, skylight, and door system within a building. Study of thermal performance of fenestration systems is not only important from energy conservation point of view but also occupant s comfort. ccording to the annual report of Lawrence Berkeley Laboratory, 5% energy consumption is directly related to the fenestration systems, it represents one of the largest energy holes through the building envelope. Thus focusing research attention to the phenomena of heat transfer through these building elements has great significance, which can assist engineers and architects to optimize their design, in order to minimize the energy transmittance through windows, so as to improve the energy efficiency of buildings. 4.MODELING DESCRIPTION 4.1The geometric dimensions and boundary conditions The fig.1 shows the cross-section view of this single casement double-glazed wood window. The geometry of window, boundary conditions and heat transfer through window is symmetric about the vertical plane of symmetry shown in the figure 1. This allows us to model only one half of the window about the symmetric plane for 3-D modeling. This saves lot of modeling and computational time. 0.6m Fig 1: Cross-section and plane view of the window In 2-D we are only able to model the sill and jamb part of the window while in 3-D we model all the parts. But from THERM5/WINDOW5 we get the results for all parts of the window. For detailed comparison with those results, 2-D and 3- D models were was subdivided into various zones while creating geometry for easier obtaining of results. Figure2 shows the inside plane of the window (3-D model) with its subdivided zones. It has been divided into the 13 zones, which would allow us in-depth comparison, and in finding the root of in discrepancy with THERM/WINDOW5 software. Figure 3 shows the half window and the boundary conditions. Standard NFRC 100 boundary conditions were applied (shown earlier fig3). In 2-D only the vertical cross-section of window was modeled. 1 Copyright #### by SME

2 4.2 Creation of geometry and meshing The frame cross-section geometry was provided in utocd. To the frame cross-section in utocd command region was applied to convert the closed planar loops into faces. It was exported as CIS file. This CIS file of frame cross-section was imported to GMBIT. Here the full model was created and meshed. Structural meshing was applied. The meshing was done such that it would accommodate the convection modeling also. Figure * shows the meshed view of the sill cross-section and figure * shows the 3-D meshed window. Figure 2:Different zones on the inside window surface Figure 4: Meshed view of sill cross-section Figure 3: Boundary conditions for the modeled window Figure 5: Meshed view of window. 2 Copyright #### by SME

3 Table 1 contains the grid information for 3-D models of the windows (all three sizes). fter meshing boundary and continuum entities were defined in the Gambit. It was exported as.fiprep file to be used in Fidap for obtaining the result. Now work in Gambit is over. Table 1: Grid information for 3-d models: - 0.6m x 1.50m 0.6m x 1.20m 0.6m x 0.91m Number of nodes Number of cells Number of faces modeling of spacer The original cross-section had complicated geometry, which would have been difficult for 3-D modeling. Especially the spacer had a complicated geometry. So we use the effective conductivity for that part. Figure* shows the original sill crosssection and the spacer geometry obtained from THERM5. Different color represents different material. Spacer was modeled as a single rectangular block and effective conductivity was obtained for it. Very high film coefficient value was given so that the surface temperature is close to the temperature we got in the 1 st part. Keff is calculated using the following formula. L Keff = U ho hi TBLE 2: CLCULTION FOR SPCER KEFF Tin( o C) Tout( o C) h i h o L (m) U-value K-eff So for our modeling purpose we replaced the complicated spacer geometry with a single rectangular block with the effective conductivity of W/m-K. To check the correctness of K-eff of spacer, in THERM we modeled a sill cross-section with replaced spacer and compared its result with the model with original spacer. Table 3 shows the results for both these models. The difference between these two models in close to 1%. Table 3: U-value from THERM for spacer models: - Original spacer Replaced spacer % Diff w/ original spacer Frame Edge Fig 6 : sill cross-section and spacer geometry For getting the Keff, 1 st we get the results with actual sill geometry (Fig*) in THERM under the specified boundary condition. Then we model separately the spacer part only (Fig*) and apply the temperature conditions obtained from the results of the 1 st part. verage temperature on the spacer ends were taken from the 1 st part results and applied for the boundary conditions in obtaining the K-eff for spacer; as the spacer we are modeling has a frame cavity whose effective conductivity is sensitive to the temperature. s the overall difference between the two models is not much we can go ahead with single replaced spacer model for our 2-D and 3-D modeling in Fidap. s we ll be comparing our Fidap results with the results from the THERM, it is better if we also model the spacer as a single rectangular block with replaced effective conductivity. Hence all THERM results were obtained with single replaced spacer with the defined K-eff of W/m-K. Figure 8 shows the simplified geometry of the sill crosssection with spacer as a simple rectangular block. L Figure7: spacer with boundary conditions. Fig 8: Sill cross-section and materials 3 Copyright #### by SME

4 4.4 Getting results in Fidap The.FIPREP file, obtained from Gambit was modified and material s thermo-physical properties were defined along with the boundary condition values. Table 4 gives the thermophysical properties of the materials. Standard NFRC 100 boundary conditions were applied (shown earlier fig3). Table 4: Thermo-physical properties of Materials:- Material/component Conductivity Emissivity [W/m-K] Glass Glass with e-coating Pine/wood Spacer * 0.90 Polyfoam tape Frame cavity 0.128* - Glazing cavity * - Material Property Value IR Density ρ [kg/m 3 ] Specific heat C P [J/kg-K] Conductivity k [W/m-k] Viscosity µ [kg/m-s] 1.789E-05 Volume Expansion β[1/k] *Note: For Spacer, Frame cavity and Glazing cavity (conduction model) effective conductivity was used. 5.Mathematical model We are solving a steady state, conduction problem with out of plane convection on inside and outside surfaces. Top and bottom surfaces are adiabatic (q=0). Governing equation for this problem is: - ([ ] T ) = 0 K -For bulk ([ K] T ) + h ( T T ) = 0 c c -For the convection boundary condition. q=0 - at top and bottom surfaces Table 5. Boundary Condition Boundary Conditions Environmental Temperature [ C] Overall h [W/(m 2 - K)] Outside Surface Inside Surface The overall h value, given in the table5, is the cumulative film heat transfer coefficient, which includes the heat transfer by all the modes (conduction, convection and radiation) on the outside and inside surface. There are three major types of energy flow through windows: 1. Non-solar heat losses and gains in the form of conduction, convection and radiation; 2. Solar heat gains in the form of radiation; and 3. irflow, both intentional (ventilation) and unintentional. For modeling purpose we have ignored the solar heat gain and ventilation losses. In the glazing cavity heat transfer takes place by convection, conduction and radiation. Here we have used the effective conductivity (obtained from Window5) and modeled the glazing cavity as solid. WINDOW5 calculates the heat flow from all the three-heat transfer mechanism and provides the effective conductivity. It s generally accepted that natural convection occurs on the indoor fenestration surface and within the glazing cavity, and forced convection heat transfer on outdoor fenestration surface. Table5 lists the boundary conditions on the inside and outside surfaces (see fig3 also). Conduction heat transfer occurs in all solid fenestration elements (such as glazing panes, frame, spacers, sealant, etc.). We used effective conductivity (obtained from THERM) for the frame cavity. 5. Results and comparison 5.1 Results from Fidap and THERM/WINDOW5 In this section, results from Fidap for 3-D and 2-D models have been presented. Table 6 shows the 2-D results of conduction models for all the three sizes of windows. Table 7.a, 7.b and 7.c have the 3-D results from Fidap for all the three windows for conduction models. It should be noted that 2-D models don t have any jamb part unlike 3-D model and Therm/window5 models. Hence overall U-value of 2-D G/F model doesn t make any sense. The U- value is given by the following formula q U = T i T o For our problem (T i -T o )=( )=38.9K. q is the heat flux. 4 Copyright #### by SME

5 Therm/window5 uses the following formula to calculate the U- value U = cg U cg + cg + eg U eg + eg + f f U Table 6: 2-D Fidap results for all the three sizes of windows 0.6mX1.5m Projected Heat flow Heat flux U-value Length [m] [W] [W/m 2 ] [W/m 2 -K] Frame_sill Frame_head Center of glass Edge_sill Edge_head TOTL mX1.m2 Projected Heat flow Heat flux U-value Length [m] [W] [W/m 2 ] [W/m 2 -K] Frame_sill Frame_head Center of glass Edge_sill Edge_head TOTL mX0.91m Projected Heat flow Heat flux U-value Length [m] [W] [W/m 2 ] [W/m 2 -K] Frame_sill Frame_head Center of glass Edge_sill Edge_head TOTL f Table 7.a: 3-D result for 0.6mX1.5m window: - 0.6X1.5 Projected rea heat flow [W] heat flux [W/m 2 ] U-value [W/m 2 -K] Frame_sill Frame_head Frame_jamb Center of glass Edge_sill Edge_head Edge_jamb Corner_sill Corner_jamb_sill Corner_head Corner_jamb_head Edge_sill_jamb Edge_head_jamb TOTL Table 7.b: 3-D result for 0.6mX1.2m window: X1.2 Projected rea heat flow [W] Heat flux [W/m 2 ] U-value [W/m 2 -K] Frame_sill Frame_head Frame_jamb Center of glass Edge_sill Edge_head Edge_jamb Corner_sill Corner_jamb_sill Corner_head Corner_jamb_head Edge_sill_jamb Edge_head_jamb TOTL Copyright #### by SME

6 Table 7.c: 3-D result for 0.6mX0.91m window: - 0.6X0.91 Projected rea heat flow [W] heat flux [W/m 2 ] U-value [W/m 2 -K] Frame_sill Frame_head Frame_jamb Center of glass Edge_sill Edge_head Edge_jamb Corner_sill Corner_jamb_sill Corner_head Corner_jamb_head Fig10.Temp. Contour of sill cross-section (from Fidap) Edge_sill_jamb Edge_head_jamb TOTL The quantities relevant to this study are temperature profile and heat flow. Figure 9 shows the temperature contour for the 2-D model of 0.6mX1.5m window. Figure 10 shows the close view of sill cross-section temperature contour for 0.6mX0.91m window. Figure 11 has been taken from the THERM. It shows the isotherms for the sill cross-section. Figure 12 shows the 3-D temperature contour on inside and outside surfaces. Fig 9: Temp. Contour for 2-d model of 0.6mx1.5m window Fig 11: Temperature contour (isotherms) for sill crosssection (from THERM5, Temp in 0 C) 6 Copyright #### by SME

7 Temperature plot Temperature[K] D Inside surface 2-D outside surface 3-D inside surface 3-D outside surface WINDOW5 Inside surface WINDOW5 Outside surface temp height from the bottom of the window [m] Figure 13: Temperature plot along the height of the window (0.6mx0.91m) on inside and outside surface Table 8.a: Comparison table for 0.6mX1.5m window Figure 12 Temperature contour for (0.6x0.91) 3-D model 5.2 Comparison of results In this section results from Fidap and been compared with the THERM/WINDOW5 results. It includes the U-value comparison and temperature plot comparison. Figure 13 shows the temperature plot on inside and outside surface (for 3-D models, symmetric planes surface temperature were taken). Window5 provides the surface temperature on each surface of glazing unit. Temperature represented in fig 13 is of the inside and outside surfaces. In Window5 heat transfer is assumed to be one-dimensional in the center of glass region. Table 8 represents the U-value comparison of Fidap 2-D and 3- D models with the Therm/window5 results. s mentioned earlier, in 2-D modeling we don t have all the components of window, hence overall U-value for 2-D models cannot be found. Though Therm/window5 are 2-D software but we get separate results for jamb parts, which give the results for all components of the window. 0.6 x 1.5 T5/W5 2D 3D U-value U-value % Diff U-value % Diff Frame_sill Frame_head Frame_jamb Center of glass Edge_sill Edge_head Edge_jamb Corner_sill Corner_jamb_sill Corner_head Corner_jamb_head Edge_sill_jamb Edge_head_jamb TOTL Copyright #### by SME

8 Table 8.b: Comparison table for 0.6mX1.2m window 0.6x1.2 T5/W5 2D 3D U-value U-value % Diff U-value % Diff Frame_sill Frame_head Frame_jamb Center of glass Edge_sill Edge_head Edge_jamb Corner_sill Corner_jamb_sill Corner_head Corner_jamb_head Edge_sill_jamb Edge_head_jamb TOTL Table 8.c: Comparison table for 0.6mX0.91m window 0.6x0.91 T5/W5 2D 3D U-value U-value % Diff U-value % Diff Frame_sill Frame_head Frame_jamb Center of glass Edge_sill Edge_head Edge_jamb Corner_sill Corner_jamb_sill Corner_head Corner_jamb_head Edge_sill_jamb Edge_head_jamb TOTL OBSERVTIONS ND DISCUSSION Overall results from Fidap match well with the Therm/window5 results. It has been observed that results of all the three sizes of window follow the same pattern for both 2-D & 3-D Fidap model as well as Therm/window5 model. From the temperature plot of figure 13 we can see that the 2-D and 3- D model predict very close temperature profile compared to the Therm/window5. There is no visible difference in the temperature results on the inside and outside surfaces given by 2-D and 3-D models. Though the over all U-value from 3-D model matches very well with the Therm/window5 results (difference less than 1%) but if we see zone wise the difference is as high as 4% which is not negligible. There are 3-d effects, mainly in the corner regions. With increase in height of window slight decrease in U-value is observed. Even with the increase in the size the U-value for the frame and sill part remain almost same. Main difference is in the center of glass region only. We see that Therm/window5 predicts higher U-value for windows 0.6mx1.5m and 0.6mx1.2m (height more than1m) while for 0.6mx0.91m it gives lower value. It should be noted that all the Therm/window5 correlations are based on the standard size of 1m high windows. So it makes sense. 7.Future work In this work, a solid replaced air inside the glazing cavity with effective conductivity. To capture the true physical phenomena in side the glazing cavity we need to do the convection model with radiation inside the glazing cavity to capture the true nature of heat flow. With convection inside the glazing cavity, heat flow is very much a 2-dimensional in case of laminar, unicellular flow; it could be 3-dimensional in case of multi-cellular/turbulent flows. So work had to be done on the convection model with radiation inside the glazing cavity. 8 Copyright #### by SME

9 8.CKNOWLEDGMENTS I would like to thank my advisor Dr. Charlie Curcija, course teacher Dr. Ian Gross and my laboratory colleagues Dr. Mahabir bhandari, Dr leksander Fomichov and Bashkar for their invaluable help. 9.REFERENCES 1.NFRC NFRC100: Procedures for determining Fenestration Product U-factors. National Fenestration Rating Council. 4.Fidap documentation, FIDP theory manual and users manual. 5.THERM5/WINDOW LBNL. FEM based program for analyzing two-dimensional heat transfer through building products. Lawrence Berkeley National Laboratory, Berkeley C. 6. Curcija, D Three-dimensional finite element model of overall nighttime heat transfer through fenestration systems. Ph.D. Dissertation, University of Massachusetts, mherst 2.ISO15099, International standard for fenestration rating. 3.GMBIT Fluent Inc. Fluid Dynamics nalysis Package Revision 8.52, Evanston, IL. 9 Copyright #### by SME