Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition IMECE2012 November 9-15, 2012, Houston, Texas, USA IMECE2012-87735 A NUMERICAL STUDY OF THE EFFECT OF AN IRRADIATED SLATTED TOP DOWN BOTTOM UP BLIND ON THE CONVECTIVE HEAT TRANSFER RATE FROM A RECESSED WINDOW TO AN ADJACENT ROOM Patrick H. Oosthuizen and J.T. Paul Queen s University Kingston, ON, Canada oosthuiz@me.queensu.ca ABSTRACT Top Down Bottom Up blinds have become quite popular in recent times. However the effects of such blind systems on the convective heat transfer from the window to the surrounding room have not been extensively studied and the effect of solar irradiation of the blind on the window heat transfer has not received significant attention. The purpose of the present work was therefore to numerically investigate the effect of solar irradiation of Top Down Bottom Up slatted blinds on this convective heat transfer. An approximate model of the window-blind system has been adopted. The solar radiation falling on the blinds is assumed to produce a uniform rate of heat generation in the blind. The Boussinesq approximation has been used. Radiant heat transfer effects have been neglected. Conditions under which laminar, transitional and turbulent flows occur have been considered. The main emphasis is on the effect of the magnitude of the irradiation and of the size of the blind openings at the top and bottom of the window on the convective heat transfer rate from the window to the room. INTRODUCTION Improved models for the convective heat transfer rate from the inner surface of a window to the surrounding room for the case where the window is fully or partially covered by a blind are needed to assist in the development of systems that reduce the overall heat transfer rate through the window. Top Down Bottom Up blinds have become quite popular in recent times Figure 1. Flow situation considered. and have the potential to reduce energy consumption by allowing the controlled use of sunlight to illuminate the house (day lighting) and/or to use passive solar room heating while still providing shade and privacy to the occupants. However, the effects of such blind systems on the convective heat transfer from the window to the surrounding room have not been 1
Figure 2. Slat size and recess depth definitions. extensively studied. Furthermore solar irradiation of the blind system can have a major effect on the heat transfer between the blind and the window. The purpose of the present work was, therefore, to numerically investigate the effect of the size of the top and bottom blind openings with Top Down Bottom Up slatted type blinds on the convective heat transfer rate from the window and to investigate the effect of the solar irradiation of the blind on this heat transfer rate. There have been many studies of the effect of blinds on the heat transfer rate between the room-side of the window and the room but these have mainly been concerned with traditional Bottom-Up type blinds. Typical of such studies of the case where plane blinds are being used are those of Oosthuizen et al. [1, 2] and Oosthuizen [3, 4]. These studies are for the case where the flow over the window-blind system is laminar. The effect of flow transition for the case of flow over a plane blind has been considered by, for example, Oosthuizen and Naylor [5], and Oosthuizen [6, 7]. Typical of the studies of the case where Venetian blinds are used are those of Collins et al. [8, 9], Duarte et al. [10], Machin et al. [11], Shahid [12], and Roeleveld et al. [13]. Existing studies of Top Down Bottom Up blinds have concentrated on plane blinds, e.g., see Oosthuizen and Paul [14]. There have been some studies of heat transfer from irradiated blinds but almost all have considered only plane blinds, typical of these studies being that of Oosthuizen and Naylor [15]. The present study, and also many of the previous studies related to the effects of blinds on window heat transfer, considers only the convective heat transfer. In window heat transfer situations, the radiant heat transfer can be very important and can interact with the convective flow, e.g., see Phillips et al. [16]. A recessed window with a slatted type Top Down Bottom Up blind of the type shown in Fig. 1 has been considered. With the type of blind here being considered the blind opening is achieved by adjusting the angle that the interconnected blind slats make to the vertical, the greater the total blind opening the closer the slats are to the horizontal and therefore the closer there inner edges are to the window. Top Down Bottom Up blinds, in general, will have different blind openings at the top and at the bottom as shown in Fig. 1. The sizes of both the top and bottom openings will affect the convective heat transfer rate from the window to the room and this has been numerically investigated in the present study. The heat transfer rate from the window will also be influenced by the recess depth of the window, r (see Fig. 2). When the top and bottom blind openings are changed the gap between the blind and the window for a given dimensionless recess depth changes producing changes in the heat transfer rate from the window. Solar irradiation of the blind system, in general, will have an effect on the window heat transfer and the purpose of the present work was to numerically investigate the effect of solar irradiation of Top Down Bottom Up slatted blinds with various top and bottom openings on this convective heat transfer. An approximate model of the window-blind system has been adopted. The window considered is recessed and is assumed to be at a uniform surface temperature and to be exposed to a room in which the air temperature far from the window is uniform. The blind slats are assumed to be thin and to offer no resistance to heat transfer. The solar radiation falling on the blinds is assumed to produce a uniform rate of heat generation in the blind. The blind system considered is shown in Fig. 1. There are twelve full slats plus half slats at the top and bottom of the blind. SOLUTION PROCEDURE The mean flow has been assumed to be steady twodimensional. The Boussinesq approach has been used in dealing with the buoyancy forces. The window has been assumed to be at a uniform temperature, T W, this window temperature being higher than the temperature, T F, of the air in the room to which the window is exposed. Absorption of the solar radiation by the blind has been assumed to produce a uniform rate of heat generation within the blind. In general with an actual slatted type blind with the solar radiation impinging at an angle on the blind the irradiation of the blind will not be uniform and the rate of heat generation within the blind will therefore not be uniform. However, because the purpose of the present study was to investigate the effects of the blind irradiation on the convective heat transfer from the window in a general manner this has not been accounted for here. The solution has been obtained by numerically solving the governing equations subject to the boundary conditions using the commercial CFD solver, FLUENT. In the situation here considered laminar, transitional and turbulent flow can occur. The k-ε turbulence model with the full effects of buoyancy forces accounted for and with standard wall functions has been used in obtaining the solutions. This turbulence model has been found in past studies to give moderately good predictions of when transition to turbulence occurs and of the flow and heat transfer in the laminar, transitional, and turbulent regions. Extensive grid - and convergence criterion independence testing was undertaken and indicated that the heat transfer results presented here are to within 1% independent of the number of grid points and of the convergence-criterion used. 2
Figure 3. Variation of mean Nusselt number with Rayleigh number for dimensionless top and bottom openings of 0.1 and dimensionless heat generation rates of 0 and 413. Figure 5. Variation of mean Nusselt number with Rayleigh number for dimensionless top and bottom openings of 0.3 and 0.1 and dimensionless heat generation rates of 0 and 413. Ra g 2 c 3 / (2) p TW TF L k where β,, and are the bulk expansion coefficient, the density, and the viscosity respectively. The heat generation rate in the blind as a result of solar irradiation has been expressed in terms of the following dimensionless heat generation rate: q Q (3) irad kt ( W TF) where q is heat generation rate. Figure 4. Variation of mean Nusselt number with Rayleigh number for dimensionless top and bottom openings of 0.3 and dimensionless heat generation rates of 0 and 413. The mean convective heat transfer rates from the window have been expressed in terms of the mean Nusselt number defined by: Nu q L / k( T T ) where q is the mean heat transfer rate from the window, k is the thermal conductivity, T W is the window surface temperature, T F is the room air temperature, and L is the height of the window. The Rayleigh number used is in presenting the results is also based on L and on the overall temperature difference between the window temperature and the room air temperature, i.e., is defined by: W F (1) RESULTS The solution parameters are: 1. the Rayleigh number, Ra, 2. the Prandtl number, Pr, 3. the dimensionless depth to which the window is recessed, R = r / L, r being the window recess depth, 4. the dimensionless top and bottom blind openings, W top = w top / L and W bot = w bot / L, where L is the overall height of the window and w top and w bot are the top and blind openings as shown in Fig. 1, 5. the number of slats, n, the slat size, s, being taken as L / n where n is the number of slats. The top and bottom slats have, as indicated in Fig. 1, size s/2, s being the size of the full slats, n is the number of equivalent full slats. 6. the dimensionless heat generation rate in the blind, Q irad Because attention has been restricted to air flow, the Prandtl number has been assumed constant and equal to 0.74. Results will also only be given here for R = 0.05. Results for 3
Figure 6. Variation of mean Nusselt number with Rayleigh number for dimensionless top and bottom openings of 0.1 and 0.3 and dimensionless heat generation rates of 0 and 413. Figure 7. Variation of mean Nusselt number with numbers for dimensionless top and bottom openings of 0.1. other values of R show the same basic characteristics as those presented here for R = 0.05. Results will also only be given here for n = 10. Typical variations of Nusselt number with Rayleigh number for dimensionless top and bottom openings of 0.1 and 0.1, 0.3 and 0.3, 0.3 and 0.1, and 0.1 and 0.3 are shown in Figs. 3, 4, 5, and 6. Results for the case where there is no heat generation and for the case where the dimensionless heat generation rate in the blind is 413 are shown in these figures. When there is no internal heat generation (i.e., no irradiation of the blind) the heat transfer under all conditions considered is from the window to the room, i.e., is positive. However, when Figure 8. Variation of mean Nusselt number with numbers for dimensionless top and bottom openings of 0.3. there is internal heat generation in the blind it will be at a higher temperature than the window and at the lower Rayleigh numbers considered there is heat transfer from the blind to the window, i.e., the window heat transfer is negative. However, at the higher Rayleigh numbers, particularly when turbulent flow exists, there are, under the conditions being considered, upward boundary layer type flows over both the window and the blind and because these boundary layers are thin due to the high Rayleigh numbers there is essentially no interaction between them, i.e., no interaction between the flows over the window and over the blind. As a result there is a layer of near room temperature air between the two boundary layers and the heat transfer from the window is to this air layer and is as a result positive. Also under these conditions because the heat transfer from the window is essentially to room temperature air which is the same situation that exists when there is no internal heat generation in the blind the Nusselt number variations for the with-heat generation and the without-heat generation cases are essentially the same. A comparison of the results given in Figs. 2 to 4 also shows that the variations of Nusselt number with Rayleigh number for the three blind opening situations considered are significantly different, a minimum occurring in the variations for dimensionless top and bottom openings of 0.3 and 0.3 and of 0.3 and 0.1. This is mainly due to the fact that for Rayleigh numbers near that at which the minimum in the Nusselt number variation occurs, the heat transfer from the blind to the window is largely determine by the air flow through the channel formed between the window and the blind inner surface. However, at lower Rayleigh numbers there is little flow through this channel and the heat transfer between the blind and the window is essentially by conduction between the blind and the window and thus is of a low magnitude than that which exists when there is significant flow through the channel. 4
Figure 9. Variation of mean Nusselt number with numbers for dimensionless top and bottom openings of 0.3 and 0.1. Figure 10. Variation of mean Nusselt number with numbers for dimensionless top and bottom openings of 0.1 and 0.3. The effect of the magnitude of the dimensionless heat generation rate in the blind on the heat transfer from the window is illustrated by the results given in Figs. 7, 8, 9, and 10. These figures show the variations of Nusselt number with the dimensionless heat generation rate for dimensionless top and bottom openings of 0.1 and 0.1, 0.3 and 0.3, 0.3 and 0.1, and 0.1 and 0.3 for a high and a low Rayleigh number value. It will be seen that, for the reasons discussed above, the Nusselt numbers at the larger Rayleigh number considered are very weakly dependent on the value of the dimensionless heat generation rate in the blind. However at the smaller Rayleigh numbers considered the Nusselt number increases considerably in magnitude (its value being negative) as the magnitude of the dimensionless heat generation rate in the blind increases. Attention will next be turned to the local heat transfer rate variation up the window. The heat transfer rate has been expressed in terms of the local Nusselt number based on the window height, L, i.e., in terms of: Nu loc q wl L ( T T ) k where q wl is the local heat transfer rate per unit area. Typical variations of the local Nusselt number with dimensionless distance up the window, Y, for dimensionless top and bottom blind openings of 0.1 for the case of Ra = 10 10 are shown in Figs. 11 and 12 while results for the case of Ra = 10 5 are shown in Figs. 13 and 14. Here Y = y/l, y being the distance measured up the window and L being, as before, the total height of the window. In the case of the non-irradiated blind the local heat transfer is from the window to the room and is taken, as with the mean heat transfer rate, to be positive while w f (3) Figure 11. Variation of local Nusselt number based on Rayleigh number of 10 10, and a dimensionless heat generation rate of 413. in the case of the irradiated blind the local heat transfer is from the room to the window and is taken to be negative. The points of high local heat transfer in the local Nusselt number distributions shown in Figs. 11 to 14 coincide with the points where the window-side folds in the blind occur, i.e. to the points where the blind is closest to the window and where therefore the flow is accelerated in passing under the blind. 5
Figure 12. Variation of local Nusselt number based on Rayleigh number of 10 10, and a dimensionless heat generation rate of 0. Figure 14. Variation of local Nusselt number based on Rayleigh number of 10 5, and a dimensionless heat generation rate of 0. Figure 13. Variation of local Nusselt number based on Rayleigh number of 10 5, and a dimensionless heat generation rate of 413. CONCLUSIONS The results of the present study indicate that: 1. When there is no internal heat generation (i.e., no irradiation of the blind) the heat transfer under all conditions considered is from the window to the room, i.e., is positive. However when there is internal heat generation in the blind at the lower Rayleigh numbers considered there is heat transfer from the blind to the window, i.e., the window heat transfer is negative. 2. At the higher Rayleigh numbers, the Nusselt number variations for the with-heat generation and the without-heat generation cases are essentially the same and the Nusselt number variation at the larger Rayleigh number considered is only very weakly dependent on the value of the dimensionless heat generation rate in the blind. 3. At the lower Rayleigh numbers considered the Nusselt number increases considerably in magnitude (its value being negative) as the magnitude of the dimensionless heat generation rate in the blind increases. 4. When the blind is open at the top and bottom there are relatively large variations in the local heat transfer rate with distance up the window, the highest heat transfer rates occurring at the points near where the blind is closest to the window. NOMENCLATURE c p specific heat g gravitational acceleration H t dimensionless opening at top of blind h t opening at top of blind H b dimensionless opening at bottom of blind h b opening at bottom of blind L height of window Nu mean window Nusselt number Nu loc local Nusselt number based on L n number of slats Q rad dimensionless heat generation rate in blind q mean heat transfer rate from window q wl local heat transfer rate at any point on window 6
q Ra r s T F T W Y y β μ ρ heat generation rate in blind Rayleigh number window recess depth size of blind slats room air temperature far from window window temperature dimensionless vertical distance up window vertical distance up window coefficient of bulk expansion coefficient of viscosity density acknowledgements ACKNOWLEDGEMENTS This work was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Smart Net-Zero Buildings Strategic Research Network. REFERENCES [1] Oosthuizen, P.H., Basarir, M. and Naylor, D., 2008, A Numerical Study of Three-Dimensional Convective Heat Transfer from a Window Covered by a Simple Partially Open Plane Blind, Proc. ASME IMECE 2008, Boston, MA, Nov. 02-06, Paper IMECE2008-66610. [2] Oosthuizen, P.H., Sun, L., Harrison, S.J., Naylor, D. and Collins, M.R., 2005, The Effect of Coverings on Heat Transfer From A Window to a Room, Heat Transfer Engg., 26(5), pp. 47-65. [3] Oosthuizen, P.H., 2007, Three-Dimensional Flow Effects on Convective Heat Transfer From a Cold or a Hot Window Covered By a Simple Plane Blind to a Room, Chemical Engg. Trans., 12, pp. 31-36. [4] Oosthuizen, P.H., 2008, Three-Dimensional Effects on Convective Heat Transfer From a Window/Plane Blind System, Heat Transfer Engineering, 29(6), pp. 565-571. [5] Oosthuizen, P.H. and Naylor, D., 2010, A Numerical Study of the Effect of Blind Opening on Laminar-to- Turbulent Transition in the Flow over a Simple Recessed Window-Plane Blind System, Proc. ASME IMECE 2010, Vancouver, B.C., Nov. 12-18, Paper IMECE2010-38175. [6] Oosthuizen, P.H., 2009, A Numerical Study of the Development of Turbulent Flow over a Recessed Window- Plane Blind System, Chemical Engg Trans., 18, pp. 69-74. [7] Oosthuizen, P.H., 2010, Effect of a Horizontal Frame Member on Transitional Heat Transfer from a Recessed Window to a Room, Chemical Engg Transactions, 21(1), Part 1, pp 91-96. [8] Collins, M.R., Harrison, S.J., Naylor, D, and P.H. Oosthuizen, P.H., 2002, Heat Transfer from an Isothermal Vertical Plate with Adjacent Heated Horizontal Louvers: Numerical Analysis, J. Heat Transfer, 124(6), pp. 1072-1077. [9] Collins, M.R., Harrison, S.J., Naylor, D. and Oosthuizen, P.H., 2002, Heat Transfer from an Isothermal Vertical Plate with Adjacent Heated Horizontal Louvers: Validation, J. Heat Transfer, 124(6), pp. 1078-1087. [10] Duarte, N., Naylor, D., Oosthuizen, P.H. and Harrison, S.J., 2001, An Interferometric Study of Free Convection at a Window Glazing with a Heated Venetian Blind, J. HVAC&R Research, 7(2), pp. 169-184, 2001. [11] Machin, A.D., Naylor, D., Oosthuizen, P.H. and Harrison, S.J., 1998, Experimental Study of Free Convection at an Indoor Glazing Surface with a Venetian Blind, J. HVAC&R Research, 4(2), pp. 153-166. [12] Shahid, H., Naylor, D. Oosthuizen, P.H. and Harrison, S.J., 2003, A Numerical Study of the Effect of Horizontal Louvered Blinds on Window Thermal Performance, Proc. 2nd Int. Conf. on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT), Paper SH2. [13] Roeleveld, D., Naylor, D. and Oosthuizen, P.H., 2010, A Simplified Model of Heat Transfer at an Indoor Window Glazing Surface with a Venetian Blind, J. Building Performance Simulation, 3(2), pp. 121-128. [14] Oosthuizen, P.H. and Paul, J.T., 2011, Numerical Study of the Convective Heat Transfer Rate from a Window Covered by a Top Down Bottom Up Plane Blind System to an Adjacent Room. 14th Int. Conf. on Process Integration, Modelling and Optimisation for Energy Saving and Pollution Reduction (PRES 2011), Florence, Italy, May 8-11. [15] Oosthuizen, P.H. and Naylor, D., 2006, Three- Dimensional Effects on Convective Heat Transfer from a Window Covered by an Irradiated Plane Blind, 1st Canadian Solar Bldgs. Research Network (SBRN) Conf. with the 31st Annual Conf. of the Solar Energy Society of Canada (SESCI), Montreal, Canada, Aug. 20-24. [16] J. Phillips, J., Naylor, D., Oosthuizen, P.H. and Harrison, S.J., 2001, Numerical Study of Convective and Radiative Heat Transfer from a Window Glazing with a Venetian Blind, Int. J. HVAC&R Research, 7(4), pp. 383-402. 7