AN INTERFEROMETRIC STUDY OF FREE CONVECTION IN A WINDOW WITH A HEATED BETWEEN-PANES BLIND

AN INTERFEROMETRIC STUDY OF FREE CONVECTION IN A WINDOW WITH A HEATED BETWEEN-PANES BLIND F. Almeida 1, D. Naylor 1, and P.H. Oosthuizen 2 1 Department of Mechanical & Industrial Engineering, Ryerson University, Toronto, Ontario, Canada 2 Department of Mechanical and Materials Engineering, Queen s University, Kingston, Ontario, Canada ABSTRACT An experimental study has been conducted to examine free convection in a window with an enclosed aluminum Venetian blind. The unique feature of this experiment was that the blind slats were heated electrically to simulate absorbed solar radiation. Centre-glass convective heat transfer measurements and temperature field visualization were obtained using a laser Mach-Zehnder interferometer. Measurements were made for two plate (glazing) spacings, two blind slat angles, two blind heat fluxes, and two plate temperature differences. It was found that a recently proposed simplified model, called the Reduced Slat Length (RSL) model, closely predicted the experimental results when the flow appeared to be laminar and steady. Under these conditions the temperature field and lateral heat transfer was dominated by conduction. Under some conditions, evidence of highly unsteady/turbulent flow was observed. As expected, the RSL model performed poorly under these conditions. INTRODUCTION The current experimental study examines natural convective heat transfer within a tall window with a between-panes louvered blind. The general problem geometry is shown in Figure 1. A blind consisting of a set of horizontal metal slats is enclosed between two window glazings. It has become increasingly common to find slat-type blinds located between the panes of a window, or even within the double facade of a building. There is substantial interest in this type of shading for the control of building solar gains, with the goal of lowering both heating and cooling loads. However, experimental data on the thermal performance of these shading systems is currently limited. There have been three experimental studies of the heat transfer performance of a window with a betweenpanes Figure 1. Problem geometry and coordinate system. louvered blind. Garnet et al. (1995) measured the centre-glass overall heat transfer rates at several blind slat angles using a guarded heater plate apparatus. Using the same instrumentation, these measurements were extended to include a wider range of glazing spacings, and low-e glazings by Haung et al. (2006). It is perhaps significant that both of these experimental studies were done using an aluminum mini-blind with a blind slat width of 14.8 mm. As a result, the glazing spacing and enclosure Rayleigh number was relatively low. In a closely related study, Naylor and Lai (2007) measured the local and average convective heat transfer coefficients in a vertical window-like enclosure with an internal Venetian blind. These measurements were made using a laser interferometer, and provided both temperature field visualization and local convective heat transfer results. It is important to emphasize that none of the previous experimental

studies considered the effects of absorbed solar radiation on the slats. Recently, Wright et al. (2008) have proposed a simplified model to predict the centre-glass U-value and solar heat gain coefficient (SHGC) of a window with louvered between-panes shading. In this onedimensional model, they propose treating the free convection within the window using a Reduced Slat Length (RSL) model. Based on physical arguments, they propose that the blind effectively segregates the window into two side-by-side gas filled enclosures. Empirical correlations are used to calculate the convection coefficient within the each subcavity, using an effective spacing between the blind tip and the glass. For the narrow glazing spacings (W G =17.8mm, 25.4mm), the RSL model compared very favourably to the measurements of Garnet et al. (1995) and Haung et al. (2006). For the cases with the closest agreement, the two subcavity Rayleigh numbers corresponded to essentially pure conduction. Under such conditions, the RSL model predictions were within a few percent of the measured U-values. At the largest glazing spacing (W G =40.0mm), the agreement was not as close. As noted by the authors, this is likely because the primary fill gas flow becomes unstable and less well behaved as Rayleigh number increases. Collins et al. (2008) have recently applied the RSL model to a between-panes blind that is heated by absorbed solar radiation. CFD data were obtained assuming a steady laminar flow, for the same miniblind geometry as used by Huang et al. (2006). The RSL model was shown to compare well with the CFD simulations, especially at low values of the subcavity Rayleigh number. The objective of the current study is to obtain experimental measurements of free convective heat transfer rates in a tall enclosure with internal blind. Emphasis is placed on the case where the blind is electrically heated to simulated absorbed solar radiation. To the authors knowledge, there are no experimental data in the open literature for the sunlit blind case. Local and average convective heat transfer results will be obtained optically using laser interferometry. Also, full field temperature visualization will be obtained. The main utility of these results is expected to be for the validation of simplified models and CFD simulations. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental model consisted of two vertical temperature controlled aluminum plates to simulate the glazings of a window. Each aluminum plate was machined to have a width of 540mm, a height of 994mm, and a thickness of 19.05mm. An array of copper tubes was sandwiched to the back of each plate by an insulating material. Temperature control was achieved by two constant temperature baths that pumped water through the copper pipes. Each plate had 9 type T thermocouples to measure the temperature distribution within the plate. The temperature difference between the plates was measured using high-precision platinum resistance thermometers. For these experiments, the plate temperatures were controlled to give a T of 0C and 15C. Placed between the plates were 44 aluminum Venetian blinds of length 527mm and a width of 24.9mm (the width was measured with the blind flattened). Each blind had two electric heaters adhered to the underside to simulate the effect of absorbed incident solar radiation. Prior to assembly, both plates and the blind slats were painted to give an emissivity of 0.89. The power input of the blinds was controlled by adjusting the voltage from an external DC power supply. Blind heat flux levels of q =0 W/m 2 and 75 W/m 2 were used for the experiment. The blinds were held in place on each end by a nylon rod which was threaded into vertical steel posts. This arrangement allowed the blind angle to be adjusted. Blind angles of φ= 0 and 45 were considered, with φ being measured relative to the horizontal plane (as shown in Figure 1). The blind slats were held in the horizontal position with a pitch of S=22.2mm. The steel posts where held in position by precision machined acrylic spacers, located at the top and bottom ends of the posts. The aluminum plates clamped onto these end spacers, creating a cavity of height H G =980mm. Leveling screws were used to align the blinds with the interferometer laser beam. Two acrylic spacers were machined to give a cavity width of W G = 32.7mm and 56.7mm which gives cavity aspect ratios of A = 29.97 and 17.28. The plate and blind assembly was sealed off with sheets of acrylic, to form a closed cavity. Optical access for the laser is achieved with two 150mm diameter optical windows. The model was placed in the laser Mach-Zehnder Interferometer (MZI) and aligned. The light source was a 15 mw He-Ne laser. The aluminum plates were leveled with the gravity vector using a hanging plumb bob. Further alignment was achieved through the use of leveling pins placed on the aluminum plates. The incident laser beam was adjusted such that the shadows of the leveling pins on the output coincided with each other. The blind slat angle (φ) was adjusted using the shadow of the blind on the laser output. The MZI measures the temperature field inside the airfilled enclosure. A beam splitter divides the laser beam

into two parts both travelling an equal distance before recombining at another beam splitter. Initially both light beams are in phase with each other. One beam passes through ambient air, while the other passes through the experimental apparatus. When the model is heated, changes in the refractive index of air cause the two beams to shift out of phase. This phase shift appears as an interference pattern when the two beams are recombined. The laser output was photographed on large format film (102mm X 127mm) using a view camera. Assuming constant pressure in the model, a change in refractive index can be related to a change in temperature. This allows the interference pattern on the output to be used for temperature field measurement. The film negative was scanned at 2400 dpi and analyzed in Matlab using imaging software developed in the Heat Transfer Laboratory at Ryerson University. For a given fringe centre (ε) the temperature is given by: TREF T = εrλt (1) REF 1± ZPG where λ is the wavelength of the He-Ne laser (λ = 6.328 x 10-7 m), Z is the length the laser travels through the model (Z=0.547 m), P is the absolute pressure, G is the Gladstone-Dale constant (G = 0.226 x 10-3 m 3 /kg), R is the gas constant of air (R = 287 J/kgK, T ref is some known reference temperature (usually the wall temperature), and ε is the fringe order relative to T ref. A positive sign is chosen in the denominator if T ref is hotter than T, and a negative sign if T ref is colder than T. The temperature gradient at the plate surface is determined by linear extrapolation, using the temperatures of two closest constructive or destructive interference fringe centres. With the temperature gradient determined, the local wall convective heat flux on the hot and cold walls can be found by: q " C = k s dt dx x= 0 q " H = k s dt dx x= W G (2) where k s is the thermal conductivity of air evaluated at the surface temperature, and x is the coordinate measured normal to the plate surface (as defined in Figure 1). To obtain the average centre-glass convective heat flux, the local heat flux was numerically integrated over four blind pitches (88.9mm), using the trapezoidal rule. In summary, experiments were performed for the following range of variables: Blind angle: φ = 0, 45 Plate temperature difference: T = 0C, 15C Gap width: W G = 32.7 mm, 56.7 mm " Blind heat flux: q B = 0 W/m 2, 75 W/m 2 The RSL Model Where possible, comparisons have been made with the RSL model of Wright et al. (2008). The RSL model treats the between the pane venetian blind geometry as two adjacent empty cavities with the middle wall retaining the blind temperature. Each cavity is assigned an affective subcavity width W defined as follows: W n * W cos φ W' = G B (3) 2 where n* is a fraction that is determined empirically. For the present analysis n*=0.7 was used, as recommended by Collins et al. (2008). With the subcavity width determined, the Nusselt number for that cavity was found using the correlation of Shewen et al.(1996): 1 2 2 1 0. 0665Ra 3 ' = 1 + 1. 4 1+ ( 9000 ) Ra Nu (4) where the subcavity Rayleigh number is defined as: 3 2 gβδtw' ρ cp Ra' = (5) μk In the current study, the convective heat flux predicted by the RSL model is calculated using the actual measured blind temperature. An energy balance is not performed. All the properties are evaluated at a mean cavity temperature as defined by Collins et al. (2008): 1 TH + TC TM = + TB (6) 2 2 where T B is the blind temperature and T H and T C are the hot and cold wall temperatures, respectively. The Nusselt number correlation applies to aspect ratios of A 40. For a blind angle of φ=45 the aspect ratio for the two subcavities correspond to A = 41.2 and 83.2. DISCUSSION OF RESULTS The infinite fringe interferograms shown in Figure 2 provide visualization of the temperature field in the centre-glass region of the enclosure, for a glazing spacing of W G =32.7mm. For cases where a temperature difference is imposed, the right surface corresponds to the hotter glazing. In all cases, it can be seen that the temperature field is highly periodic, with a spatial

frequency equal to the slat pitch. In Figures 2(c) and (f), Figure 2. Infinite fringe interferograms in the centre-glass region for an enclosure width of W G =32.7mm.

Figure 3. Infinite fringe interferograms in the centre-glass region for an enclosure width of W G =56.7mm. both glazings are held at the same temperature and the blind heat flux is 75 W/m 2. As expected, for φ=0 o, the temperature field is symmetrical about the vertical centre line of the enclosure. For φ=45 o, shown in Figure 1(f), the inclined slats slightly disturb this symmetry. In both cases, the isotherm patterns show evidence of recirculating flows between the blind slats. Figures 2(b) and (e) show the effect of the blind heat flux on the temperature field. In these images there is a temperature difference between the glazings, T H - T C =15 o C. For these conditions, the blind heat flux warms the blind to a temperature that is close to the hot wall temperature. So, the convective heat transfer rate to the hot wall decreases almost to zero, and the convective heat loss from the blind occurs mainly via the cold wall. Figure 3 shows infinite fringe interferograms in the centre-glass region for a glazing spacing of Wc=56.7mm and a slat angle of φ=0 o. A striking feature of these images is the differences between the temperature field for Fig. 3(a) and Fig. 3(c). In Fig. 3(a), there is a 15 o C temperature difference between the glazings, and no blind heat flux. There is evidence of a strong buoyancy-induced flow. Thermal boundary layers have formed on both glazings, and the core region of the enclosure is nearly isothermal. In Fig. 3 (c) there is no temperature difference between the glazings, and the blind heat flux is 75 W/m 2. In Fig. 3 (c) it is evident that there is much less flow. The isotherms between the glazings and the blind tips are more uniformly spaced, suggesting that conduction plays a stronger role under these conditions. This suggests that heating from the centre of the enclosure produces a weaker and more stable flow than heating from one side of the enclosure. It will be shown later that this has a sigificant effect on the convective transfer rates. The average centre-glass convective heat flux measurements are shown in Tables 1 and 2. Table 1 reports the results for the cold (left) wall. Table 2 contains the data for the hot (right) wall. In both tables comparisons are made between the measured heat flux and the heat flux predicted using the RSL model. It can be seen that the RSL model gives very close agreement in some cases, and poor agreement in others. Some of the reasons for this mixed performance will be discussed next. Referring to Table 1 and Table 2, it can be seen that the RSL model performs the poorest at the widest wall spacing (W G =56.7mm) when there is a temperature difference of 15 o C across the enclosure.

These are experiments b, c, e and f in Table 1 and Table 2. For these cases, the RSL model consistently underpredicts the convective heat flux, by as much as 40% on the hot wall and by as much as 86% on the cold wall. The main reason for the poor performance Exp. Blind Flux q B Slat Angle φ (deg.) Glazing Spacing W G (mm) Table 1 Cold wall centre-glass heat transfer results. T H -T C ( o C) Blind Temp. ( o C) Exp. Heat Flux, q C RSL Model Heat Flux % Diff. Subcavity Ra Subcavity Nu a 75.0 0 56.7 0.04 30.3-12.0-12.2 1% 6.0E3 1.09 b 0.0 0 56.7 15.07 23.0-17.6-11.1 37% 6.2E3 1.10 c 74.9 0 56.7 15.00 31.2-32.5-27.6 15% 1.2E4 1.34 d 75.0 45 56.7 0.00 28.3-10.5-10.2 3% 8.0E3 1.17 e 0.0 45 56.7 15.01 22.7-17.5-10.4 40% 8.8E2 1.21 f 75.0 45 56.7 14.99 29.5-38.1-24.4 36% 1.5E4 1.50 g 75.0 0 32.7 0.00 28.0 - -19.7-2.5E2 1.00 h 0.0 0 32.7 15.04 22.7-30.6-25.4 17% 3.6E2 1.00 i 75.0 0 32.7 15.00 28.5-52.3-44.2 15% 5.9E2 1.00 j 75.0 45 32.7-0.03 26.2-16.0-13.9 13% 5.8E2 1.00 k 0.0 45 32.7 15.01 22.2-26.6-17.7 34% 8.0E2 1.00 l 75.0 45 32.7 14.99 28.3-47.3-32.2 32% 1.4E3 1.00 Table 2 Hot wall centre glass heat transfer results Exp. Blind Flux q B Slat Angle φ (deg.) Glazing Spacing W G (mm) T H -T C ( o C) Blind Temp. ( o C) Exp. Heat Flux, q C RSL Model Heat Flux % Diff. Subcavity Ra Subcavity Nu a 75.0 0 56.7 0.04 30.3-12.4-12.1 3% 6.0E3 1.09 b 0.0 0 56.7 15.07 23.0 19.1 10.4 46% 5.2E3 1.06 c 74.9 0 56.7 15.00 31.2 - -0.85-4.2E2 1.00 d 75.0 45 56.7 0.00 28.3-10.8-10.2 6% 8.0E3 1.17 e 0.0 45 56.7 15.01 22.7 23.6 10.3 57% 7.9E3 1.17 f 75.0 45 56.7 14.99 29.5 8.5 1.23 86% 1.0E3 1.00 g 75.0 0 32.7 0.00 28.0-19.3-19.7 2% 2.5E2 1.00 h 0.0 0 32.7 15.04 22.7 29.9 25.5 15% 3.1E2 1.00 i 75.0 0 32.7 15.00 28.5-6.56-7.6E1 1.00 j 75.0 45 32.7-0.03 26.2-14.7-13.9 5% 5.8E2 1.00 k 0.0 45 32.7 15.01 22.2 28.2 20.4 28% 8.0E2 1.00 l 75.0 45 32.7 14.99 28.3-5.84-2.2E2 1.00

of the RSL model is almost certainly the presence of a highly unsteady (and possibly fully turbulent) flow. For these wide wall spacings, the enclosure Rayleigh number was high (Ra=2.7x10 5 ) and significant temporal fluctuations were clearly evident in the realtime interference patterns. The interferogram in Figure 2(a) clearly shows the formation of thermal boundary layers on the enclosure walls, which are likely turbulent. This appears to be far from the conditions that are required by the RSL model. As stated by Wright et al. (2008), the overiding point to be made is that the RSL model works well when the primary gas flow is well-behaved, i.e., laminar and largely parallel to the vertical cavity walls free of instabilities. So, it is not surprising that the RSL predictions are poor under these conditons. Even at the narrower glazing spacing (W G =32.7mm), when a temperature difference of 15 o C is maintaintained across the enclosure, there are significant departures between the measurements and the RSL model. The corresponding experiments are labelled h, i, k and l in Tables 1 and 2. Again, this is likely due to flow instabilities. Even though this spacing is a more realistic geometry for an actual window, the Rayleigh is still quite high (Ra=5.3x10 4 ). So, there is likely still some instability in the flow for these conditions. As a result, the RSL model consistently underpredicts the convective heat flux -- but by not as much as for the wider spacing (typically by 15-30%). It should be mentioned that at the narrow spacing, the presence of flow instabilities was less obvious in the real-time interference patterns. So, this conjecture remains to be confirmed by flow visualization experiments, which are in the planning stages. Perhaps the most interesting and surprising results where found for the cases where the blind was heated, and both walls of the enclosure were held at the same temperature. The corresponding experiments are labelled a, d, g and j in Tables 1 and 2. These experimental cases are all very closely predicted by the RSL model. Even at the widest glazing spacing, the RSL model predicts the heat flux to better than 6% on both walls! As previously noted from an inspection of the interferograms, when the heating is applied only in the middle of the enclosure, the isotherms between the enclosure walls and the blind tips are uniformly spaced. This suggests that the flow is laminar and parallel to the wall, yielding heat transfer across the primary flow that is conduction dominated. These are precisely the conditions where the RSL model is expected to perform well. Another useful observation can be made by examining the last two columns in Table 1 and Table 2. These columns provide the subcavity Rayleigh number (Ra ) and subcavity Nusselt number (Nu ), corresponding to the RSL model. It has been suggested by Wright et al. (2008) that these subcavity parameters might be used as an indicator of whether the RSL model can be applied. Using experimental data from a mini-blind, Wright et al. (2008) get accurate predictions with the RSL model for subcavity Rayleigh numbers up to about Ra =1500. However, in the current experiments we find that this parameter is, by itself, not a useful indicator. When the glazings were held at a temperature difference of 15 o C, we found that the RSL model gave consistently poor predictions at subcavity Raleigh numbers much lower than 1500. However, when the blind was heated and the glazings were held a equal constant temperature, we got excellent predictions from the RSL model even at Ra =8000! So, it appears that more detailed criteria are needed to predict the onset of flow instabilities (and hence, the range of applicablity for the RSL model). Further research is currently being done to delineate the flow structures and to investigate the critieria for the onset of flow instabilities. As previously mentioned, evidence of turbulence was observed for the widest plate spacing. Under some conditions, large fluctuations were seen, with recirculating patterns moving up and down the cavity walls. It should be mentioned that these fluctuations may have affected the accuracy of the measurements. For example, it can be seen that for experiment e that the measured hot and cold wall convective heat fluxes differ by about 26%. For the conditions of this experiment, one would expect the time-averaged convective heat transfer rates at each wall to be almost the same. It is suspected that this anomoly was caused by the instantaneous nature of the current technique. Each interferogram is actually a snap shot of the temperature field. To address this problem, a new time-averaging technique is currently being developed, using a high-speed digital camera. CONCLUSION An experimental study was performed to measure the convective heat transfer in a window with a heated between-panes venetian blind. Temperature field visualization and convective heat transfer measurements were obtained using a laser interferometry. The results have been compared to simplified model from the literature, the Reduced

Slat Length (RSL) model. The main findings are summarized as follows: (i) The infinite fringe interferograms show that the temperature field in the centre-glass region of the enclosure is highly periodic. (ii) The blinds themselves are highly conductive and, for most cases, the majority of the temperature change (i.e., thermal resistance) is in the wall-to-blind tip region. (iii) At the widest glazing spacing, evidence of highly unsteady/turbulent flow was observed when a temperature difference of 15 o C was imposed across the enclosure. As might be expected, under these conditions, the RSL model gave poor predictions of the convective heat flux for all slat angles. (iv) In constrast to the above conclusion, when the blind was heated with the glazings at the same temperature, the primary flow appeared to be laminar, steady and parallel to the glazings, even at the widest glazing spacing. Under these conditions, the lateral convective heat transfer was dominated by conduction and the RSL model performed very well. Overall, the RSL model was found to perform well, within the stated limitations of this model. However, the current results show that the main difficulty in applying the RSL model lies in determining, with confidence, whether the flow field is sufficiently stable. For the larger blind slats used in the present experiment, the model s subcavity Rayleigh number was found to be a poor indicator of flow stability. Clearly, there is a need for more research to assess the stability of the free convective flow in this window/blind geometry. These experiments are currently in the planning stages. NOMENCLATURE ACKNOWLEDGMENT The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada. The authors also wish to thank Dr. Mike Collins for making the emissivity measurements needed for these experiments. REFERENCES Collins, M., Tasnim, S., Wright, J., 2008, Determination of the Convective Heat Transfer for Fenestration with Between-the-Glass Louvered Shades, International Journal of Heat and Mass Transfer, vol. 51, pp. 2742-2751. Garnet, G., Fraser, R.A., Sullivan, H.F., Wright, J.L., 1995, Effect of Internal Venetian Blinds on Window Centre-Glass U-Values, Proc. Window Innovations 95 Conference, Toronto, Ontario, pp. 273-279. Huang, Y.T., Wright, J.L., Collins, M.R., 2006, Thermal Resistance of a Window with an Enclosed Venetian Blind, ASHRAE Transactions, vol 112, no. 2. Naylor, D., Lai, B.Y., 2007, Experimental Sudy of Natural Convection in a Window with a Between-pnaes Venetisn Blind, Experimental Heat Transfer, vol. 20, pp. 1-17. Shewen, E., Hollands, K.G.T., Raithby, G.D., 1996, Heat Transfer by Natural Convection Across a Vertical Air Cavity of Large Aspect Ratio, Journal of Heat Transfer, vol. 118, pp. 993-995 Wright, J.L., Collins, M.R., Haung, N.Y.T, 2008, Thermal Resistance of a Window with an Enclosed Venetian Blind: Simplified Model, ASHRAE Transactions, vol. 114, no. 1. A enclosure aspect ratio c p specific heat G Gladstone-Dale constant g gravity H enclosure height k thermal conductivity n* subcavity fraction width Nu Nusselt number P absolute pressure q average heat flux R gas constant of air Ra Rayleigh number S slat pitch T temperature W width x, y cartesian coordinates Z length of model in light beam direction Greek Symbols β volumetric expansion coefficient change/difference ε fringe shift order λ vacuum wavelength of laser µ dynamic viscosity ρ density φ blind angle Subscipts B blind slat C cold wall H hot wall G full enclosure REF reference M mean Superscripts modified subcavity