1、O R-05-4-3 Two-Dimensional Conduction and CFD Simulations of Heat Transfer in Horizontal Window Frame Cavities Arild Gustavsen, PhD Member ASHRAE Dariush Arasteh, PE Member ASHRAE ABSTRACT Accurately analyzing heat transfer in window frames and glazings is important for developing and characterizing
2、 the performance of highly insulating window products. This paper uses computationalfluid dynamics (CFD) modeling to assess the accuracy ofthe simpled frame cavity conductionkonvec- tion models presented in IS0 15099 and used in software for rating and labeling window products. Three representative
3、complex cavity cross-section profiles with varying dimensions and aspect ratios are examined. The results presented support the IS0 15099 rule that complex cavities with small throats should be subdivided; however, our data suggest that cavities with throats smaller than 7 mm should be subdivided, i
4、n contrast to the IS0 15099 rule, which places the breakpoint at 5 mm. The agreement between CFD modelingresults and the results of the simplified models is moderate for the heat trans- fer rates through the cavities. The diflerences may be a result of the underlying IS0 15099 Nusselt number correla
5、tions being based on studies where cavity heightdlength aspect ratios were smaller than 0.5 and greater than 5 (with linear interpo- lation assumed in between). The results presented here are for horizontal frame members because convection in vertical jambs involves very diflerent aspect ratios that
6、 require three- dimensional CFD simulations. INTRODUCTION The frame is an important part of a fenestration product. In a window with a total area of 1.2 x 1.2 m2 and a frame with a width of 10 cm, the frame occupies 30% of the windows total area. If the total area of the window is increased to 2.0 x
7、 2.0 m2 and the window still has a frame with a width of 10 cm, the frame occupies 19% of the total area. When rating a fenes- Christian Kohler Dragan Curcija, PhD Member ASHRAE tration product, engineers area-weight the thermal perfor- mance of the different parts of the product to determine a sing
8、le number that describes the entire product. Thus, to be able to accurately calculate a products thermal performance, engineers need models that accurately describe the thermal performance of each part of the product or accurate measure- ments of actual thermal performance. Because measurement is ex
9、pensive, use of accurate models is preferable. A significant body of research has focused on heat-trans- fer effects in glazing cavities. The primary goal of that work has been to develop accurate correlations for natural convec- tion effects inside multiple-pane windows (Batchelor 1954; Eckert and
10、Carlson 1961; Hollands et al. 1976; Raithby et al. 1977; Berkovsky and Polevikov 1977; Korpela et al. 1982; ElSherbiny et al. 1982; Shewen et al. 1996; Wright 1996; Zhao 1998). Less research has been conducted on heat transfer in window frames that have internal cavities. This is an important issue
11、for high-performance window frames because cavities are a primary area where frame heat transfer can be minimized (the thermal conductivity of solid framing materials is another key area). In window frames with internal cavities, the heat- transfer process involves a combination of conduction, conve
12、ction, and radiation. To fully describe heat transfer through these window frames, it would be necessary to simu- late fluid flow to determine the convection effects and to use either view factors or ray-tracing techniques to determine the radiation effects inside the cavities. However, these types
13、of simulations and techniques are rarely undertaken because they require significant computational resources and modeling efforts. Instead, air cavities in window frames are treated as solid materials that have an effective conductivity (Standaert 1984; Jonsson 1985; Carpenter and McGowan 1989); tha
14、t is, A. Gustavsen is associate professor in the Department of Civil and Transport Engineering, Norwegian University of Science and Technology. C. Kohler is computer systems engineer and D. Arasteh is staff scientist and deputy group leader, Windows and Daylighting Group, Lawrence Berkeley National
15、Laboratory, Berkeley, California. D. Curcija is president of Cali, Inc., Amherst, Mass. 02005 ASHRAE. 587 convection and radiation effects are combined into a single effective conductivity. With this single value, standard conduction simulation software can find the insulation value or thermal trans
16、mittance (U-factor) of the frame using the same procedure as is used for window frames without internal cavities. The proposed standard ASHRAE 142P and standards EN IS0 10077-2 and IS0 15099 (ASHRAE 1996; CEN 2003; IS0 2003) prescribe methods of this type for finding the ther- mal transmittance of w
17、indow frames. To represent the airflow in frame cavities, various sources prescribe rules for subdividing cavities at points where their dimensions are smaller than a specified minimum. NFRC (Mitchell et al. 2003) and IS0 15099 (IS0 2003) indicate that cavities are to be divided at points where thei
18、r dimensions are less than 5 mm, and EN IS0 10077-2 (CEN 2003) specifies that cavities with one dimension not exceeding 2 mm or subar- eas of cavities with interconnection whose size does not exceed 2 mm should be divided into separate subcavities (here, the terms subarea and subcavity are used for
19、parts of a larger cavity that can naturally be separated from the larger cavity based on its geometric configuration). No research basis is given for the values used in these rules. The standards also differ in their rules for converting nonrectangular (or irregular) cavities into equivalent rectang
20、ular cavities whose convection and radiation correlations are assumed to be the same as the correlations for the original irregular cavity. IS0 15099 and EN IS0 10077-2 specify that irregular cavities should be transformed into rectangular cavities so that the areas and aspect ratios of the original
21、 irregular cavity and the new rect- angular cavity are equal. The proposed ASHRAE Standard 142P specifies that irregular cavities should be transformed into rectangular cavities using a bounding rectangle. The aspect ratios and the total heights and widths of the original irregular cavity and the ne
22、w rectangular cavity should be equal. (The total heights and widths will most likely not be equal under IS0 15099/EN IS0 10077-2 and ASHRAE 142P.) It is noted that the conversion of irregular cavities to rectan- gular cavities only is performed for finding the effective conductivity of the irregular
23、 cavity. The true geometry is retained for the numerical simulation. In this paper, focus is put on convective heat transfer in frame cavities; problems related to dividing cavities and trans- forming irregular cavities into rectangular cavities are addressed. (Radiant heat-transfer effects are not
24、studied.) The results presented are for horizontal frame members because convection in vertical jambs involves very different aspect ratios that require three-dimensional computational fluid dynamics (CFD) simulations. CFD and conduction simula- tions were conducted for this study. In the conduction
25、 simu- lations, an effective conductivity (calculated according to procedures described in IS0 15099, see below) was used to account for convection in frame cavities. GEOMETRIES STUDIED The air cavities studied are shown in Figure 1. The partic- ular cavities were chosen to represent air cavities th
26、at can be found in real window frames. The cavities are identified as H- cavity, L-cavity, and C-cavity (left to right in Figure 1). H- cavity is square with two solid fins protruding into it. Dimen- sions and temperature differences simulated for the cavities are shown in Tables 1 to 3. Because the
27、 cavities are simulated in two dimensions, the results are valid for horizontal frame members. CFD results that are valid for jamb sections require simulations in three dimensions. NUMERICAL PROCEDURE The simulations were performed with a CFD code (Fluent 1998) and a building component thermal simul
28、ation program for implementing IS0 15099 (Finlayson et al. 1998). Double precision was used for both codes. CFD Simulations The CFD code uses a control-volume method to solve the coupled heat and fluid flow equations. Only conduction and natural convection are simulated; radiation effects are not ad
29、dressed. The maximum Rayleigh number found for the cavities studied is about 1 x 1 05. This Rayleigh number is found for the H-cavity when there is a temperature difference of 25 K separating the two isothermal walls. Ostrach (1988) reports 1 Lhl Figure I Schematics of cavities studied. From left to
30、 right-H-cavity, L-cavity, and the C-cavity. 588 ASHRAE Transactions: Symposia H12 HI3 HI4 H15 H16 30 30 10 2 15 5 30 30 7 2 15 5 30 30 5 2 15 5 30 30 3 2 15 5 30 30 O 2 15 5 ID L1 L2 L3 L4 L, mml Lh mm1 Lhl mml L, mml TH “cl Tc “CI 30 30 10 15 15 -10 30 30 10 10 15 -10 30 30 IO 7 15 -10 30 30 10 5
31、15 -10 L5 c2 I 20 I 30 I IO I 15 I 5 30 30 10 3 15 -10 L7 L8 L9 L10 30 30 10 IO 15 5 30 30 10 7 15 5 30 30 10 5 15 5 30 30 IO 3 15 5 ASHRAE Transactions: Symposia - c3 10 30 10 15 -10 589 c4 IO 30 IO 15 5 steady laminar flow for square cavities of this size. Although most of the cavities presented a
32、re not squares, incompressible and steady laminar flow are assumed. Further, viscous dissi- pation is not addressed, and all thermophysical properties are assumed to be constant except for the buoyancy term of the y- momentum equation where the Boussinesq approximation is used. The Semi-Implicit Met
33、hod for Pressure-linked Equa- tions Consistent (SIMPLEC) was used to model the interac- tion between pressure and velocity. The energy and momentum variables at cell faces were found by using the Quadratic Upstream Interpolation for Convective Kinetics (QUICK) scheme. In addition, the CFD code uses
34、central differences to approximate diffusion terms and relies on the PREssure Staggering Option scheme (PRESTO) to find the pressure values at the cell faces. PRESTO is similar to the stag- gered grid approach described by Patankar (1980). Conver- gence is determined by checking the scaled residuals
35、 and ensuring that they are less than for all variables, except for the energy equation, in which the residuals have to be less than 1 A quadrilateral grid was used for all cavities. Some grid sensitivity tests were performed for the H- and C-cavities. The L-cavity was assumed to behave similarly to
36、 the H-cavity with respect to grid density; therefore, the same grid density was used for the L-cavity as for the H-cavity. For the H-cavity, the grid size was varied between 0.5 mm and 0.06 mm, where the first size results in 3,600 nodes and the latier size results in 249,999 nodes. For the C-cavit
37、y, grid sizes of 0.5 mm, O. 1 mm, and 0.05 mm were tested, resulting in 2,369, 28,919, and 227,195 nodes, respectively. An interval size of 0.1 mm was found to be sufficient for all cavities. Reducing the grid sizes to 0.06 mm for the H-cavity and 0.05 mm for the C-cavity resulted in changes of heat
38、 fluxes of less than 0.5%. Conduction Simulations The conduction simulations were performed using a special version of the building component thermal simulation program in which the radiation calculation in frame cavities was disabled, which allowed a comparison of the convection effects with the CF
39、D calculations. A finite-element approach was used to solve the conductive heat transfer equation. The quadrilateral mesh is automatically generated. Refinement was performed in accordance with section 6.3.2b. of IS0 15099 (IS0 2003). The energy error norm was less than 10% in all cases, which resul
40、ts in an error of less than 1 % in the ther- mal transmittance of the cavities. The temperatures on the boundaries of the cavities were fixed using a very Large combined convective and radiative film coefficient (h = 99,900 W m-2 K-I). The resulting cavity wall temperatures were within 0.01 “C of th
41、e desired temperatures. For more informa- tion on the thermal simulation program algorithms, refer to ing to IS0 15099 are listed below. Note that only correlations for horizontal frame members are used in this study. The effec- tive conductivity is determined from ,fi= (h,+hr)xL, (1) where he# is t
42、he effective conductivity, h, is the convective heat transfer coefficient, hr is the radiative heat transfer coef- ficient (set equal to zero in this study), and L is the thickness or width of the air cavity in the direction of heat flow. The convective heat transfer coefficient, h, is calculated fr
43、om the Nusselt number (Nu) from air h, = NU-, L where hair is the conductivity of air. For horizontal heat flow, the Nusselt number will depend on the height-to-length aspect ratio (LJLh), where L, and LA are the cavity dimensions in the vertical and horizontal direc- tions, respectively. In a cavit
44、y with a height-to-length aspect ratio less than 0.5, the Nusselt number is found from (Rosen- how et al. i985), L 8 -0.386 L 2/5 -0.386 -2.59 ( 5, and so correlations in Equations 6 to 8 shall be used. The temperatures of the cavity walls, TH and T, are not known in advance, so it is necessary to e
45、stimate them. From previous experience it is recommended to apply TH= 10C and T,= 0C. However, after the simulation is done, it is necessary to update these temperatures from the results of the previous run. This procedure shall be repeated until values of TH and Tc from two consecutive runs are wit
46、hin 1 “C. Also, it is important to inspect the direction of heat flow after the initial run because if the direction of the bulk of heat flow is different than initially specified, it will need to be corrected for the next run. According to IS0 15099 (IS0 2003), unventilated and irregular (not recta
47、ngular) frame cavities are converted into equivalent rectangular cavities. The transformation is conducted so that the areas and aspect ratios of the original irregular cavity and the new rectangular cavity are equal. Further, if the shortest distance between two opposite surfaces is smaller than 5
48、mm, then the frame cavity is split at this throat region. The following rules are used to determine which surfaces belong to vertical and horizontal surfaces of the equivalent rectangular cavity (O“ is east right, 90“ is north up, 180“ is west left, and 270“ is south bottom): any surface whose norma
49、l is between 3 15“ and 45“ is a left vertical surface; any surface whose normal is between 45“ and 135“ is a bottom horizontal surface; any surface whose normal is between 135“ and 225“ is a right vertical surface; any surface whose normal is between 225“ and 3 15“ is a top horizontal surface. Temperatures of equivalent vertical and horizontal surfaces are calculated as the mean of the surface temperatures accord- ing to the classification above. The direction of heat flow is determined from the temperature difference between vertical and horizontal surfaces of the
