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Simulation of buoyancy-driven natural ventilation of buildings—Impact of computational domain
Energy and Buildings 42 (2010) 1290–1300
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Simulation of buoyancy-driven natural ventilation of buildings—Impact of computational domain Guohui Gan ∗ Department of the Built Environment, University of Nottingham, University Park, Nottingham NG7 2RD, UK
a r t i c l e
i n f o
Article history: Received 8 January 2010 Accepted 25 February 2010 Keywords: CFD Computational domain Solar chimney Buoyancy Natural ventilation Ventilation rate Heat transfer coefficient Heat flux Heat distribution ratio
a b s t r a c t Two computational domains have been used for simulation of buoyancy-driven natural ventilation in vertical cavities for different total heat fluxes and wall heat distributions. Results were compared between cavities with horizontal and vertical inlets. The predicted ventilation rate and heat transfer coefficient have been found to depend on the domain size and inlet position as well as the cavity size and heat distribution ratio. The difference in the predicted ventilation rate or heat transfer coefficient using two domains is generally larger for wider cavities with asymmetrical heating and is also larger for ventilation cavities with a horizontal inlet than those with a vertical inlet. The difference in the heat transfer coefficient is generally less than that in the ventilation rate. In addition, a ventilation cavity with symmetrical heating has a higher ventilation rate but generally lower heat transfer coefficient than does an asymmetrically heated cavity. A computational domain larger than the physical size should be used for accurate prediction of the flow rate and heat transfer in ventilation cavities or naturally ventilated buildings with large openings, particularly with multiple inlets and outlets. This is demonstrated with two examples for natural ventilation of buildings. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Natural ventilation is an energy efficient means of delivering fresh air to occupants of a building. Cavity structures such as solar chimneys and Trombe walls rely on the storage wall to induce thermal buoyancy for passive solar heating and natural ventilation of buildings. The air flow and heat transfer in the cavity of such a structure with one wall heated are asymmetrical. Integration of photovoltaic (PV) devices into the exterior skin of the structures leads to redistribution of heat on the two cavity walls due to absorption of solar heat by PV cells. The proportion of heat distribution on the two walls depends on various factors such as the type, transparency and coverage of PV cells as well as operating time. The resulting air flow and heat transfer in the cavity become more complex ranging from laminar to turbulent local flow and symmetrical to asymmetrical global variation patterns. The accuracy of simulation of buoyancy-driven natural ventilation in the cavity or other types of enclosure is influenced by the boundary conditions at the cavity openings in addition to other factors such as turbulence modelling. In most numerical studies of buoyancy-driven natural ventilation of enclosures or buildings, the main concerns are the internal
∗ Tel.: +44 115 9514876; fax: +44 115 9513159. E-mail address: [email protected]. 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.02.022
air flow and resulting indoor environmental quality and so the internal space is defined as the computational domain for simulation [1–4]. When a computational domain of the same size as the ventilation cavity or naturally ventilated enclosure is used for flow simulation, uniform pressures are generally prescribed for the inlet and outlet openings. The assumption of a uniform pressure would result in a nearly uniform distribution of velocity at an inlet [5,6] and so could lead to significant errors when the actual flow at the inlet as well as outlet openings deviates from uniform distribution. Allocca et al. [7] used a small computational domain for the indoor space and a large extended domain including both the indoor and outdoor spaces to predict the ventilation rate for a three-storey building with single-sided natural ventilation, each room with a lower inlet opening and upper outlet opening. It was found that the predicted ventilation rate using the small domain was much lower than that using the large domain. An extended computational domain is often used for simulation of buoyancy-driven flow through an open-ended horizontal cavity [8,9]. The author [10] has recently analysed the effect of computational domain on the prediction of natural ventilation through vertical cavities of various sizes and heat distribution ratios. It has been found that using the domain of the same size as a cavity would result in over-prediction of the degree of reverse flow at the top outlet of a wide cavity and consequently under-prediction of the ventilation rate. The problem can be overcome using an extended computational domain larger than the physical size of the cavity
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Fig. 2. Variation of the predicted air flow rate with domain extension size for two 3 m tall and 0.6 m wide cavities one with horizontal inlet and another with vertical inlet.
in an asymmetrically heated cavity. It is also seen that the effect of domain size on the flow rate in the cavity with horizontal inlet was approximately twice that in the cavity with vertical inlet. Air flow in a solar heated tall cavity would likely be turbulent and the RNG k- turbulence model [12] was used for modelling. The model equations for buoyancy-driven flow are represented by the following expression [13]:
∇ • (V៝ ϕ − ϕ ∇ ϕ) = Sϕ
Fig. 1. Schematic diagram of two types of computational domain for simulation of cavity flow.
such that flow patterns at inlet and outlet openings are established naturally from the flow within the cavity and without. This paper aims to demonstrate the importance of using such a large extended domain for accurate simulation of air flow and heat transfer in open vertical cavities with horizontal inlet for natural ventilation of buildings. 2. Methodology A commercial computational fluid dynamics (CFD) software package FLUENT [11] was used for simulation of steady-state air flow and heat transfer through two-dimensional ventilation cavities with a horizontal inlet for different proportions of heat distribution on two vertical walls ranging from heat transfer from either of the walls to heat transfer equally from both walls. Two sizes of computational domain – one larger than the physical size of a ventilation cavity (defined as Domain L) and the other the same size as the cavity (Domain S) – were used for simulation. Fig. 1 shows the schematic diagram of the two domains for a ventilation cavity with a horizontal inlet and a vertical outlet. The required extension (L) from Domain S to create Domain L depends on the cavity width and heat distribution ratio; it varies from about five times the cavity width for symmetrically heated to 10 times the width for asymmetrically heated cavities with a vertical inlet [10]. A similar domain extension would be required for cavities with a horizontal inlet. Fig. 2 shows the variation of the predicted flow rate with extension size for two 3 m tall and 0.6 m wide cavities with asymmetrical heating, where QL and QS are the flow rates from the simulations using Domains L and S, respectively. It is seen that the flow rate increased with the size of extension up to about 3 m or five times the cavity width. The increase became much less when the extension size increased further and there was little difference between the predicted flow rates in the cavities with domain extensions of 5.4 and 6 m, i.e., nine and 10 times the cavity width. Therefore, an extension of 10 times the cavity width would be sufficient to create Domain L for the simulation of flow
(1)
where ϕ is variables representing the mean velocity V, mean enthalpy, turbulent kinetic energy and its dissipation rate, ϕ is the diffusion coefficient and Sϕ is the source for ϕ. In the simulation, the heat flux was used as the wall boundary condition and equal uniform pressure was prescribed as the conditions at the inlet and outlet either as cavity openings for Domain S or the domain boundary for Domain L. The wall with the inlet is referred to as the inlet wall and the heated section of the opposing vertical wall as the opposite wall. The height of the opposite wall was the same as that of inlet wall and the inlet size (height) was equal to the cavity width. To compare with a similar cavity with a vertical inlet (which consists of two parallel walls—the inlet and opposite walls in Fig. 1), the rate of heat transfer from or distribution on the inlet (right) wall is defined as the heat flux q2 and that on the opposite (left) wall as heat flux q1 . The heat distribution ratio (qr ) is the ratio of uniform heat flux from the inlet wall to the total heat flux from both walls: q2 qr = (2) q1 + q2 Determination of the effect of computational domain was based on the predicted air flow and heat transfer rates in a ventilation cavity. The air flow rate (Q) through the cavity is the product of average velocity and opening area of the inlet, with a unit of m3 /s-m for two-dimensional flow. The heat transfer rate is expressed in terms of heat transfer coefficient or Nusselt number which is defined as Nu =
hc b qw b = k (tw − ta )k
(3)
where hc is the convective heat transfer coefficient, b is the cavity width, qw (=((q1 +q2 )/2) is the average heat flux for the inlet and opposite walls, and k is the thermal conductivity of air based on the average temperature of the inlet and opposite walls, tw , and ambient air temperature, ta . Validation of the model for buoyancy-driven natural ventilation was carried out through comparison with experimental data from literature for vertical cavities. Chen et al. [14] measured air flow rates through an asymmetrically heated 1.5 m tall and up to 0.6 m wide vertical cavity. A comparison with the measurements indicated that more accurate simulation of natural ventilation was achieved using a computational domain larger than the cavity [10]. The effect of domain size would be less where the friction loss in
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Fig. 3. Predicted air flow patterns near the horizontal inlet and vertical outlet of a 3 m tall cavity with 100% heat distribution ratio using Domain L.
the cavity was much larger than the influences of flow resistance and velocity variation at inlet and outlet openings, as shown for a much taller cavity (6.5 m tall and 0.23 m wide [15]) with horizontal inlet. In addition to providing more accurate simulation, Domain L is more universal for predicting buoyancy-driven ventilation than Domain S. Domain L is suitable for use in predicting the buoyancydriven flow rates in any ventilation cavities or combination of ventilated spaces whereas Domain S can provide reasonable predictions of ventilation rates for limited circumstances such as in very tall and/or narrow ventilation cavities where flow is unidirectional.
The similarities and differences between the results using the two domains are further examined in the following two sections. 3. Ventilation cavities Simulation was carried out for vertical ventilation cavities of different heights ranging from 1 to 6 m and widths from 0.05 m (for cavity heights up to 3 m and from 0.1 m for taller cavities) to 0.6 m under the entire range of heat distribution ratios from 0% for heat from the opposite wall only, to 50% for heat equally distributed on both the inlet and opposite walls and to 100% for heat from the inlet
Fig. 4. Predicted air flow patterns near the horizontal inlet and vertical outlet of a 3 m tall cavity with 100% heat distribution ratio using Domain S.
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wall only. The variations of cavity width and height gave aspect ratios (height/width) between 5 and 60. In the simulation, the total heat gain by the two vertical walls of a ventilation cavity was generally fixed at 100 W/m2 but the effect of total heat flux was also investigated. The ambient air temperature was fixed at 20 ◦ C. Discussion of the simulation results is here focused on cavities with a horizontal inlet. Nevertheless, the results are also briefly compared between cavities with a horizontal inlet and those with a vertical inlet; details for the latter are presented elsewhere [10]. The predicted flow patterns of air through the horizontal inlet and vertical outlet of a 3 m tall ventilation cavity of three different widths and with a heat distribution ratio of 100% are shown in Figs. 3 and 4 using Domains L and S, respectively. The air flowed along the opposite wall after turning from horizontal at the inlet to vertical direction. A large recirculation zone was formed above the inlet and near the inlet wall. The two domains resulted in different flow patterns in the bottom corner and near the outlet of the cavity. Using the large domain, incoming air is seen from Fig. 3 to detach from the bottom wall and be deflected upwards, forming another large recirculation zone in the corner between the bottom wall and opposite wall. By comparison, using the small domain, horizontal incoming air flowed along part of the bottom wall and then turned upwards along the opposite wall with very little air movement in the corner, see Fig. 4. Reverse flow at the outlet of 0.3 m wide cavity disappeared using Domain L but would still occur using Domain S. Therefore, Domain S could over-predict the possibility of reverse flow at the outlet of a wide cavity with horizontal inlet. Similar flow patterns were observed at the outlet of a cavity with vertical inlet [10]. However, deflection of incoming air towards the opposite wall of a cavity with horizontal inlet led to less or no reverse flow at the outlet than a cavity with vertical inlet, depending on the cavity width and computational domain. Because of reduced reverse flow, the predicted flow rate in an asymmetrically heated cavity with horizontal inlet was higher than that with vertical inlet for wide cavities (width ≥ 0.3 m) as seen from Fig. 5 (where H and V denote horizontal and vertical inlets, respectively), even though the flow resistance of the horizontal inlet would be larger resulting from flow turning from horizontal to vertical direction. The additional flow resistance of the horizontal inlet would however reduce the flow rate compared with the cavities with vertical inlet where the cavity size and the heat distribution on two walls were such that no reverse flow would occur at the outlet. This is seen for both the wide cavities (e.g. the 0.5 m wide cavity in Fig. 5c) with symmetrical heating and narrow cavities (0.1 m wide in Fig. 5a) with any heat distribution ratio. Consequently, using Domain L, the predicted variation in flow rate with heat distribution ratio in the cavity with horizontal inlet was less than that with vertical inlet, due to generally a higher flow resistance with more symmetrical heating but less reverse flow with asymmetrical heating. By comparison, because the flow resistance at the inlet could not be fully taken into account using Domain S, the difference in the flow rate through the 0.3 m wide cavity with vertical inlet and that with horizontal inlet was less clear-cut as shown in Fig. 5b. Apart from asymmetrical heating (qr = 0 or qr = 100%) which resulted in a higher flow rate through the cavity with horizontal inlet, the predicted flow rate was lower for heat distribution ratios below 40% but higher for higher heat distribution ratios in the cavity with horizontal inlet than that with vertical inlet. The predicted flow rate in the 0.5 m wide cavity with horizontal inlet was generally much higher than that with vertical inlet. These variations suggest that there was significant uncertainty using Domain S for predicting buoyancy-driven flow in a very wide cavity because real flow would not be uniform at such large inlet and outlet openings and that the uncertainty resulting from using Domain S would be larger for a cavity with vertical inlet than that with horizontal inlet.
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Fig. 5. Comparison between the flow rate in a 3 m tall cavity with horizontal inlet (H) and that with vertical inlet (V): (a) cavity width = 0.1 m, (b) cavity width = 0.3 m and (c) cavity width = 0.5 m.
3.1. Effect of cavity width Fig. 6 shows the variation of the air flow rate with heat distribution ratio in a 3 m tall cavity with horizontal inlet and different widths. Unlike a cavity with vertical inlet where flow is symmetrical along the equal heat flux value (qr = 50%), the variation with heat distribution ratio of the flow rate through the cavity with horizontal inlet was not symmetrical. The flow rate was slightly higher when more heat flowed from the inlet wall than when heat flowed from the opposite wall. The highest predicted flow rate using Domain L for the cavity with the horizontal inlet was obtained when the heat distribution ratio was between 60% and 65%, compared with 50% for the cavity with vertical inlet (see Fig. 5). It is also seen from Fig. 6a or b that when heat flow from the inlet wall was 2% or more, or heat flow from the opposite wall was 10% or more of the total heat flux, the flow rate increased with cavity width. For heat flow from one wall only, the flow rate in the cavity still increased with cavity width up to 0.5 m. Besides, the effect of heat distribution on the variation in flow rate increased with cavity width. A comparison between Fig. 6c and b shows that the variation patterns of the flow rate from the maximum with heat distribution ratio were similar using two different sizes of domain although the maximum flow rate was attained at different heat distribution ratios—about 70% using Domain S compared with 60–65% using Domain L.
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Fig. 6. Effects of heat distribution ratio and cavity width on the flow rate in a 3 m tall cavity with horizontal inlet: (a) air flow rate Q predicted using Domain L, (b) variation from maximum Q predicted using Domain L and (c) variation from maximum predicted using Domain S.
The variation with heat distribution ratio of the heat transfer coefficient for the 3 m tall cavity with horizontal inlet is shown in Fig. 7 for different cavity widths. The heat transfer coefficient was generally higher when heat flowed from one wall only and the highest heat transfer coefficient was obtained when heat flowed only from the opposite wall. The variations with heat distribution ratio of the heat transfer coefficient for the 3 m tall cavity with horizontal inlet and vertical inlet are compared in Fig. 8 for three selected cavity widths. The predicted heat transfer coefficient was lower for narrow cavities but higher for wide cavities with horizontal inlet than vertical inlet particularly using Domain L. Unlike for the cavity with vertical inlet where the lowest heat transfer coefficient was obtained when heat was equally distributed on both walls, the lowest heat transfer coefficient in a cavity with horizontal inlet generally occurred at a point when more heat flowed from the inlet wall than from the opposite wall. The effect of heat distribution on the variation in heat transfer coefficient and the lowest heat transfer coefficient depended on the cavity width (Fig. 7b). The largest variation in heat transfer coefficient with heat distribution ratio from the predictions using Domain L was 19% for flow in a cavity with an aspect ratio of 10 at a heat distribution ratio of about 98% compared with 12% variation at 60% heat distribution ratio for the 0.6 m wide cavity with an aspect ratio of 5 or negligible variation for a very narrow cavity (width = 0.06 m and aspect ratio = 50).
Fig. 7. Effects of heat distribution ratio and cavity width on the heat transfer coefficient in a 3 m tall cavity with horizontal inlet: (a) heat transfer coefficient Nu predicted using Domain L, (b) variation from maximum Nu predicted using Domain L and (c) variation from maximum predicted using Domain S.
In contrast with similar variation patterns of the flow rate from the maximum with heat distribution ratio, large differences were found in the variation patterns of heat transfer coefficient particularly for wide cavities with horizontal inlet using two different domains. The heat transfer coefficient reached minimum in cavities wider than 0.065 m when the heat distribution ratio was about 50% or slightly over using Domain S (Fig. 7c) rather than close to 100% for wide cavities using Domain L, shown in Fig. 7b. The heat transfer coefficient became independent of the heat distribution ratio for 3 m tall cavities of 0.065 and 0.06 m wide, respectively, using Domain S and Domain L, or the variation trend inverted when the cavity widths decreased further, i.e., the heat transfer coefficient increased with heat distribution from asymmetrical to symmetrical heating. Fig. 9a shows that the predicted flow rate in cavities with horizontal inlet was higher using Domain S than that using Domain L for cavity widths less than 0.3 m and also for cavity widths between 0.3 and 0.5 m and with heat distribution ratios between 20% and 95%. The reason for the higher predicted flow rate using the smaller domain was disregarding the flow resistance through the horizontal inlet where flow had to turn at a right angle from the ambient to the cavity. For very low or high heat distribution ratios or for the widest cavity (0.6 m wide and 3 m tall), the predicted flow rate
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Fig. 9. Effect of domain size on the variations in air flow rate and heat transfer coefficient with heat distribution ratio in a 3 m tall cavity with horizontal inlet: (a) air flow rate and (b) heat transfer coefficient.
with cavity height was small (less than 4%) using Domain L but the variations from the maximum increased considerably using Domain S with a maximum difference of about 20% between the variations from about 20% to 40% when the cavity height increased from 1 to 6 m. By contrast, the variations of the predicted flow rate through cavities with vertical inlet were larger using Domain L than using Domain S as shown in Fig. 11 for comparison between two cavities with minimum and maximum variations. The maximum differences that occurred between 0.1 and 0.6 m wide cavities with Fig. 8. Comparison of the heat transfer coefficient in a 3 m tall cavity with horizontal inlet (H) with that with vertical inlet (V): (a) cavity width = 0.1 m, (b) cavity width = 0.3 m and (c) cavity width = 0.5 m.
using the larger domain was higher due to reduced reverse flow at the outlet which outweighed the effect of additional inlet flow resistance. The maximum difference in flow rate using the two domains was generally within 10% (and less than 2% for a symmetrically heated 0.5 m wide cavity) but much higher for asymmetrically heated cavities wider than 0.3 m and with heat distribution ratios less than 5% or greater than 98%, with the largest differences of about 40% and 43%, respectively, for 0.5 and 0.6 m wide cavities with only the opposite wall heated. Similar to the flow rate, the predicted heat transfer coefficient in narrow cavities (width < 0.3 m) was higher using the smaller domain than that using the larger domain but generally lower in wide cavities as seen from Fig. 9b. However, the difference in the predicted heat transfer coefficient using two different domains was smaller than that in the flow rate, particularly for cavities with asymmetrical heating. 3.2. Effect of cavity height The variations in the flow rate from the maximum in cavities with horizontal inlet and with different heights but the same aspect ratio of 10 are compared in Fig. 10. The maximum flow rate for all cavity heights was achieved when the heat distribution ratio was about 65% and 70% using Domains L and S, respectively. The difference in the variations of the flow rate from the maximum
Fig. 10. Effect of cavity height on the variation from maximum of flow rate with heat distribution ratio in cavities with horizontal inlet and aspect ratio of 10: (a) using Domain L and (b) using Domain S.
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Fig. 11. Variations from maxima of flow rate and heat transfer coefficient with heat distribution ratio in cavities with vertical inlet and aspect ratio of 10.
asymmetrical heating were 16% and 13% using Domains L and S, respectively. Fig. 12 shows that the difference in the variation of the heat transfer coefficient for cavities with horizontal inlet was negligible using Domain L for cavity heights between 3 and 6 m; for short cavities, the difference was large probably due to less air turbulence than in tall and wide cavities. In addition to less variation in heat transfer coefficient with heat distribution ratio, the effect of the cavity height on the variation in heat transfer coefficient was much smaller using Domain S with a maximum difference between tallest and shortest cavities investigated of less than 3% for heat distribution ratios less than or equal to 90% and within 6% for heat distribution ratios larger than 90%. The maximum difference in the predicted heat transfer coefficient in cavities with vertical inlet was also small using both domains; it was about 3% between cavities 1 and 4 m tall using Domain L and 5% between the shortest and tallest cavities using Domain S (Fig. 11). The predicted flow rate in cavities with horizontal inlet using Domain S was generally higher than that using Domain L for heat distribution ratios between 15% and 98% as shown in Fig. 13a. For heat distribution ratios less than 15% or greater than 98%, the predicted flow rate using Domain S was also higher for short cavities but lower for tall cavities than that using Domain L. For example, for a 6 m tall cavity with only one (inlet) wall heated, the predicted
Fig. 13. Effect of domain size on the variations in air flow rate and heat transfer coefficient with heat distribution ratio in cavities with horizontal inlet and aspect ratio of 10: (a) air flow rate and (b) heat transfer coefficient.
flow rate using Domain L was as much as 22% higher than that using Domain S. This was again the consequence of over-prediction of reverse flow at the outlet using Domain S. The effect of cavity height on the magnitude of heat transfer coefficient was similar to the effect of cavity width as seen from Fig. 13b and Fig. 9b. The predicted heat transfer coefficient using Domain S was slightly higher than that using Domain L for a 1 m tall cavity. For cavities of 2–3 m tall, the heat transfer coefficient was lower for heat distribution ratios up to about 50% and 70% for 2 and 3 m tall cavities, respectively, but higher for larger ratios using Domain S than Domain L. For cavities taller than 3 m, the predicted heat transfer coefficient using Domain S was lower than that using Domain L. For cavities shorter than 3 m, the maximum difference in heat transfer coefficient using the two domains was less than 4%. The difference increased with height with a maximum difference of 15% for the 6 m tall cavity at a heat distribution ratio of 10%. Therefore, a large domain should be used where possible to predict accurately the flow rate and heat transfer coefficient for tall cavities with horizontal inlet. 3.3. Effect of total heat flux
Fig. 12. Effect of cavity height on the variation from maximum of heat transfer coefficient with heat distribution ratio in cavities with horizontal inlet and aspect ratio of 10: (a) using Domain L and (b) using Domain S.
Fig. 14 shows that there was hardly any variation in flow rate from maximum (attained at a heat distribution ratio between 60% and 65%) predicted using Domain L when the total heat flux imposed on the two vertical walls increased by 10-fold. The variation of the predicted flow rate using Domain S from the maximum (attained at a heat distribution ratio of about 70%) increased slightly with the total heat flux with a maximum difference of about 10%. By contrast, the variation of the heat transfer coefficient from the maximum (occurred when only the opposite wall was heated) decreased with increasing total heat flux as shown in Fig. 15. The variation in heat transfer coefficient with heat distribution ratio was smaller than that in flow rate particularly using Domain S but the effect of total heat flux on the variation from the maximum of heat transfer coefficient was relatively large compared with the magnitude of variation. For the range of total heat fluxes inves-
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Fig. 14. Effect of total heat flux on the variation from maximum of flow rate with heat distribution ratio in a 3 m tall and 0.3 m wide cavity with horizontal inlet: (a) using Domain L and (b) using Domain S.
tigated, the maximum difference was not more than 3% (at 50% heat distribution ratio) and 6% (at 65% heat distribution ratio) using Domains L and S, respectively. Fig. 16 shows the differences resulting from using the two domains in air flow rate and heat transfer coefficient in the 3 m tall and 0.3 m wide cavity with horizontal inlet under a range of heat fluxes from 100 to 1000 W/m2 together with the differences for the cavity with vertical inlet under the minimum and maximum heat fluxes. It is seen that the effect of total heat flux on the maximum
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Fig. 16. Effect of domain size on the variations in air flow rate and heat transfer coefficient with heat distribution ratio in two 3 m tall and 0.3 m wide cavities for different total heat fluxes: (a) air flow rate and (b) heat transfer coefficient.
differences in air flow rate and heat transfer coefficient using the two domains was larger in the cavity with horizontal inlet (occurred with asymmetrical heating) than that with vertical inlet (occurred with symmetrical heating). The difference in the flow rate using the two domains for different total heat fluxes increased with the asymmetry of heat input on the two vertical walls of the cavity with horizontal inlet but decreased with the asymmetry for the cavity with vertical inlet. The difference for a 10-fold increase in total heat flux for the cavity with horizontal inlet was less than 3% for heat distribution ratios between 20% and 95% and the maximum difference was about 10% when only one wall was heated. However, the difference in the heat transfer coefficient for different total heat fluxes increased with the proportion of heat input from the opposite wall of the cavity with horizontal inlet and again decreased with the asymmetry for the cavity with vertical inlet. The maximum difference in heat transfer coefficient for the 10-fold increase in total heat flux for the cavity with horizontal inlet was 8% when only the opposite wall was heated whereas the maximum differences in both flow rate and heat transfer coefficient for the cavity with vertical inlet were about 3%, occurred when both walls were equally heated. It follows that using a large domain than a ventilation cavity would not only reduce the effect of using a representative amount of heat input say 100 W/m2 on the accuracy for general analysis of simulation results but also provide more accurate simulation of flow in similar enclosures with horizontal inlet, typical of solar-assisted naturally ventilated spaces and other types of buoyancy-driven naturally ventilated building such as atrium buildings.
4. Naturally ventilated buildings
Fig. 15. Effect of total heat flux on the variation from maximum of heat transfer coefficient with heat distribution ratio in a 3 m tall and 0.3 m wide cavity with horizontal inlet: (a) using Domain L and (b) using Domain S.
To demonstrate further the importance of using a larger domain than the size of a ventilated space in the simulation of buoyancy-driven natural ventilation, ventilation rates were predicted for a room integrated with a solar chimney and an atrium building with internal heat gains at an ambient temperature of 20 ◦ C.
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4.1. Room ventilation Bouchair [16] conducted experimental measurements of buoyancy-driven air flow in a 2 m tall solar chimney for room ventilation. The cavity width of the chimney varied from 0.1 to 0.5 m. The chimney had a horizontal inlet of 0.1 or 0.4 m high and shared the storage wall with a room of the same height where a window on the opposite wall allowed air to flow into the room and then to the chimney. The wall surfaces of the cavity were symmetrically heated to temperatures from 30 to 60 ◦ C. Simulation of buoyancy-driven air flow was performed for the room integrated with the solar chimney with a 0.5 m wide cavity and 0.4 m high inlet using two two-dimensional domain sizes – one the same as the space for the combined room and chimney structure (Domain S) and another larger than the combination (Domain L) – at a chimney temperature of 60 ◦ C for both the exterior wall and insulated storage wall. In addition, the air flow rate was also predicted using a third domain of the same size as the chimney cavity with a horizontal inlet which had a length the same as the thickness of the storage wall (Domain C), with which the flow resistance of the window opening was ignored. It was assumed that the room was 3 m deep and the window opening size was the same as the chimney inlet. The predicted mass flow rate using Domain L was 0.127 kg/s-m which was close to the measured value of approximately 0.124 kg/s-m. The predicted flow rate using Domain S was approximately 8% less than the prediction using Domain L. The predicted flow rate using Domain C was even lower (about 10% lower than that predicted using Domain L) even though the flow resistance of the window opening was neglected. The difference in the predicted ventilation rate using Domains L and S for the combination of the room and chimney was consistent with the results discussed in the previous section for similar cavities. Fig. 9 indicates that the predicted ventilation rate for a symmetrically heated cavity of 3 m tall would be higher for a 0.5 m cavity width but lower for a 0.6 m cavity width using Domain S than using Domain L. The aspect ratio of the chimney cavity of 2 m tall and 0.5 m wide was 4. Therefore, in terms of aspect ratio, the cavity width comparable with the 3 m tall cavity should be 0.6 m or larger for which the predicted ventilation rate using Domain L was higher. A practical solar chimney with glazing as the exterior wall would rarely be symmetrically heated during operation. When the temperature of the exterior wall of the chimney was reduced but the temperature of the interior (storage) wall remained at 60 ◦ C (all referring to the wall surfaces facing the chimney cavity), the predicted flow rates using all the three domains decreased as shown in Fig. 17. It is also seen that the rate of decrease predicted using Domains L and S increased with decreasing exterior wall temperature whereas the rate of decrease predicted using Domain C was constant for the exterior wall temperatures from 30 to 60 ◦ C. The predicted flow rate was lower using Domain C than using either Domain L or Domain S for exterior wall temperatures between 25 and 60 ◦ C but higher for the temperatures below 25 ◦ C. The difference in the flow rates between using Domains C and S partly represented the influence of the window opening but more importantly could result from different flow patterns in the chimney–similar to the differences presented in Figs. 3 and 4. The higher flow rate predicted using Domain S suggests that the effect of flow resistance (dependent on the flow rate) due to the window opening was stronger than that of the flow pattern in the chimney when its exterior wall temperature was over 5 ◦ C higher than the room air temperature. However, when the exterior wall temperature was low, leading to more asymmetrical air flow and heat transfer, the flow pattern in the chimney would have a larger influence than the flow resistance of the window opening. The predicted flow rate was slightly lower using Domain S than using Domain L but the difference between the flow rates using
Fig. 17. Comparison of predicted mass flow rates in the solar chimney for room ventilation using three types of domain.
Domains L and S decreased from 8% to less than 1% when the temperature of the exterior wall decreased from 60 to 25 ◦ C. For the exterior wall temperature between 21 and 25 ◦ C, the predicted flow rate using Domain S was more or less the same as predicted using Domain L. When the exterior wall was at the same temperature as room air, leading to varying degrees of reverse flow away from the storage wall depending on the size of domain, the predicted flow rates using Domains S and C were as much as 44% and 39%, respectively, lower than the predicted value of 0.0367 kg/s-m using Domain L which was itself a massive 70% drop from the flow rate for symmetrical heating. The decrease of the predicted flow rate with the exterior wall temperature was gradual using Domain L, but a sharp decrease in the flow rate was predicted using Domain S or Domain C when the wall temperature was reduced from a small value above the room air temperature to the same as the room temperature. For example, when the exterior wall temperature was reduced from 1 ◦ C above to the same temperature as room air, the predicted flow rates using Domains S and C decreased by approximately 58% and 63%, respectively, compared with a decrease of 25% using Domain L. In other words, using Domain S or Domain C would significantly over-predict the effect on the ventilation rate of buoyancy along the exterior wall of a solar chimney when its temperature approaches the room air temperature. The predicted ventilation rates in the room and chimney using three different domains can be correlated with the exterior wall temperature as follows: Using Domain L: Q = 0.012T + 0.037 Q = 0.0485T 0.262
0K = T < 1K 1K ≤ T ≤ 40K
(R2 = 0.996) (R2 = 0.999)
(4a) (4b)
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transfer from the storage wall, therefore the difference in the predicted flow rate using two types of domain (Domains L and S) would be within 10%. For heating seasons, however, because of the heat loss to the ambient from the solar chimney in particular with single glazing, the glazing temperature could be the same as or even lower than the room air temperature and the ventilation potential of a solar chimney would be significantly under-predicted using a computational domain of the same size as the chimney cavity or in combination with the ventilated space. 4.2. Atrium ventilation
Fig. 18. Predicted air flow patterns and temperature distribution in the atrium building using Domain L: (a) air flow patterns and (b) temperature contours.
Using Domain S: Q = 0.0496T 0.24
0.5K ≤ T ≤ 40K
(R2 = 0.999)
(5)
Using Domain C: Q = 0.06T 0.135
0.5K ≤ T ≤ 10K
Q = 0.00106T + 0.0716
(R2 = 0.999)
10K ≤ T ≤ 40K
(6a)
(R2 = 0.999) (6b)
where Q is the ventilation rate (m3 /s-m), T is the temperature difference between the exterior wall and room air. For solar-assisted natural ventilation of a similar space in summer, the glazing temperature is likely to be higher than the temperature of room air due to solar absorption and radiation heat
The air flow and temperature distribution were also predicted using both small and large domains for a hypothetical office building with a central atrium to assist natural ventilation. The building (Fig. 18) consisted of two wings of three floors of open plan offices 12 m deep and 3 m high separated by an atrium 8 m deep and 15.9 m high at the top of roof. There were two balconies of 3 m long in the atrium attached to the first and second floors on the left wing. The ceilings and external fac¸ade walls of the building were 0.3 m thick and internal walls 0.1 m thick. The width of the building was assumed large enough to allow simplification as two-dimensional flow along the depth and height directions. The size of window openings in both the external fac¸ade and atrium wall for natural ventilation of offices was 0.5 m high and the vent opening at the atrium top was 2 m wide. The internal space and structure of the building was defined as Domain S whereas Domain L included both the building and a large extended external area (over five times the building height, set up for simulation of both wind- and buoyancydriven flow) surrounding the building. It was assumed that heat gains in the building were equivalent to 40 W/m2 on the floors of offices and atrium. Fig. 18 shows the predicted air flow patterns and temperature distribution in the building using the large domain. The predicted air movement in a lower floor was larger than that in an upper floor due to the higher buoyancy effect. The indoor air would be thermally comfortable with air temperatures in the offices varying between 20 and 22 ◦ C. The predicted ventilation rates for the offices of the building using Domains L and S (QL and QS , respectively) are compared in Table 1. The ventilation rate for an office on the left wing was similar to or lower than that on the right wing at the same floor level for the ground and first floors due to the additional flow resistance from the balconies but higher for the top floor because these balconies reduced disruption of the outgoing flow from the offices by the upward flow from below. The predicted total ventilation rate
Table 1 Predicted ventilation rates for the atrium building using two types of domain. Inlet position (see Fig. 18)
QS (Domain S) (m3 /s-m)
QL (Domain L) (m3 /s-m)
(QL − QS )/QL (%)
Inlet height = 0.5 m L1 L2 L3 R1 R2 R3
0.266 0.214 0.150 0.263 0.232 0.154
0.249 0.214 0.163 0.248 0.214 0.156
−6.97 −0.03 7.98 −6.22 −8.42 1.55
1.280
1.245
−2.84
0.320 0.252 0.114 0.377 0.285 0.119
0.318 0.244 0.129 0.349 0.256 0.108
−0.53 −3.46 11.23 −8.23 −11.58 −9.58
1.467
1.403
−4.59
Total Inlet height = 1 m L1 L2 L3 R1 R2 R3 Total
1300
G. Gan / Energy and Buildings 42 (2010) 1290–1300
for the building was about 3% higher using the small domain than using the large domain. Larger differences between the ventilation rates were predicted using the two domains for some of the offices because the flow rate and velocity distribution across an inlet opening varied with its vertical position. Using the small domain would over-predict the ventilation rates by approximately 6–8% for the offices at ground floor on the left wing and the ground and first floors on the right wing but under-predict the rate by nearly 8% for the office at the top floor on the left wing. Hence, simulation using a domain the same as the physical size of a multi-storey atrium building would give rise to larger uncertainty in ventilation rates for individual office spaces than that in the overall ventilation rate. This was confirmed with another simulation for larger window openings (1 m high in both external and internal walls) but the same outlet opening size. Increasing the window opening size lowered the neutral pressure level and consequently increased the relative differences in the ventilation rates from bottom to top floors. The difference in the overall ventilation rate for the building using the two domains increased to over 4% and larger differences in the ventilation rates for individual spaces between 8% and 12% would occur at the top floor on the left wing (QS < QL ) and all floors on the right wing (QS > QL ). Therefore, a larger domain than the physical size should be used to predict more accurately the ventilation rates in naturally ventilated multi-storey buildings with multiple inlets and single common or multiple ventilation outlets.
A larger computational domain than the physical size of a cavity can provide more accurate simulation of buoyancy-driven natural ventilation. Therefore, such large computational domains should be used for accurate prediction of heat transfer and flow rate in ventilation cavities or enclosures with large openings for natural ventilation, particularly with multiple inlets and outlets, asymmetrical heat distribution on opposing walls, or asymmetrical flow distribution at openings unless a known flow profile is prescribed at each opening. For an enclosure with multiple openings at different heights, varying flow distribution at the openings could create another source of uncertainty in flow prediction. Using a domain of the same as physical size to simulate flow through a multi-storey building with multiple ventilation inlet or outlet openings would give rise to larger uncertainty in ventilation rates for individual spaces or zones than that in the overall ventilation rate for the building. For a ventilation cavity with either horizontal or vertical inlet using either large or small domain, the air flow rate and heat transfer coefficient increase with cavity size and total heat input if reverse flow at the cavity outlet can be prevented. In general, the more evenly heat is distributed on the two vertical walls, the larger the flow rate in a ventilation cavity with either vertical or horizontal inlet but smaller heat transfer coefficient in a cavity with vertical inlet.
5. Conclusions
[1] M. Cook, Y. Ji, G.R. Hunt, CFD modelling of natural ventilation: combined wind and buoyancy forces, International Journal of Ventilation 1 (3) (2003) 169–179. [2] R. Letan, V. Dubovsky, G. Ziskind, Passive ventilation and heating by natural convection in a multi-storey building, Building and Environment 38 (2003) 197–208. [3] G. Gan, Simulation of buoyancy-induced flow in open cavities for natural ventilation, Energy and Buildings 38 (5) (2006) 410–420. [4] Y. Ji, M. Cook, V. Hanby, CFD modelling of natural displacement ventilation in an enclosure connected to an atrium, Building and Environment 42 (3) (2007) 1158–1172. [5] S. Baskaya, M.K. Aktas, N. Onur, Numerical simulation of the effects of plate separation and inclination on heat transfer in buoyancy driven open channels, International Journal of Heat and Mass Transfer 35 (1999) 273–280. [6] A.M. Rodrigues, A. Canha da Piedade, A. Lahellec, J.Y. Grandpeix, Modelling natural convection in a heated vertical channel for room ventilation, Building and Environment 35 (2000) 455–469. [7] C. Allocca, Q. Chen, L.R. Glicksman, Design analysis of single-sided natural ventilation, Energy and Buildings 35 (2003) 785–795. [8] K. Vafai, J. Ettefagh, Thermal and fluid flow instabilities in buoyancy-driven flows in open-ended cavities, International Journal of Heat and Mass Transfer 43 (1990) 2329–2344. [9] S.K.S. Boetcher, E.M. Sparrow, Buoyancy-induced flow in an open-ended cavity: assessment of a similarity solution and of numerical simulation models, International Journal of Heat and Mass Transfer 52 (2009) 3850–3856. [10] G. Gan, Impact of computational domain on the prediction of buoyancy-driven ventilation cooling, Building and Environment 45 (2010) 1173–1183. [11] FLUENT User’s Guide, Fluent Inc., New Hampshire, USA, 2005. [12] V. Yakhot, S.A. Orzsag, Renormalization group analysis of turbulence. I. Basic theory, Journal of Scientific Computing 1 (1986) 1–51. [13] G. Gan, Prediction of turbulent buoyant flow using an RNG k- model, Numerical Heat Transfer Part A: Applications 33 (2) (1998) 169–189. [14] Z.D. Chen, P. Bandopadhayay, J. Halldorsson, C. Byrjalsen, P. Heiselberg, Y. Li, An experimental investigation of a solar chimney model with uniform wall heat flux, Building and Environment 38 (2003) 893–906. [15] B. Moshfegh, M. Sandberg, Flow and heat transfer in the air gap behind photovoltaic panels, Renewable and Sustainable Energy Reviews 2 (1998) 287–301. [16] Bouchair, Solar chimney for promoting cooling ventilation in southern Algeria, Building Services Engineering Research and Technology 15 (2) (1994) 81–93.
CFD has been used to simulate the buoyancy-driven air flow and heat transfer in vertical cavities with horizontal inlet for natural ventilation of buildings using two different sizes of computational domain and results have been compared with those with vertical inlet. There are differences in the predicted air flow rate and heat transfer coefficient through the cavities between using a small domain of the same size as the cavity and using a large extended domain. The degree of difference varies with cavity size and heat distribution ratio—larger difference in flow rate than in heat transfer coefficient and larger difference for wider cavities with asymmetrical heating. The large extended domain is suitable for predicting buoyancy-driven flow in any ventilation cavities whereas the small domain can be used for flow simulation in very tall ventilation cavities where friction resistance is dominant. The differences in the predicted air flow rate and heat transfer coefficient for a ventilation cavity is also influenced by the position of inlet opening. Apart from extreme asymmetrical heating (heat distribution ratios not more than 5% or not less than 95%), the differences in flow rate and heat transfer coefficient increase with the level of symmetry in heat distribution on two vertical walls of a ventilation cavity with vertical inlet but decrease in a cavity with horizontal inlet. As a result, e.g. for the same cavity height and total heat flux, the differences are larger for more symmetrical heat distribution in cavities with vertical inlet but for more asymmetrical heat distribution in cavities with horizontal inlet particularly for wide cavities. For the same cavity size at different total heat fluxes or for cavities with the same aspect ratio but different heights, the difference is slightly larger for cavities with horizontal inlet than those with vertical inlet.
References
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Simulation of buoyancy-driven natural ventilation of buildings—Impact of computational domain Guohui Gan ∗ Department of the Built Environment, University of Nottingham, University Park, Nottingham NG7 2RD, UK
a r t i c l e
i n f o
Article history: Received 8 January 2010 Accepted 25 February 2010 Keywords: CFD Computational domain Solar chimney Buoyancy Natural ventilation Ventilation rate Heat transfer coefficient Heat flux Heat distribution ratio
a b s t r a c t Two computational domains have been used for simulation of buoyancy-driven natural ventilation in vertical cavities for different total heat fluxes and wall heat distributions. Results were compared between cavities with horizontal and vertical inlets. The predicted ventilation rate and heat transfer coefficient have been found to depend on the domain size and inlet position as well as the cavity size and heat distribution ratio. The difference in the predicted ventilation rate or heat transfer coefficient using two domains is generally larger for wider cavities with asymmetrical heating and is also larger for ventilation cavities with a horizontal inlet than those with a vertical inlet. The difference in the heat transfer coefficient is generally less than that in the ventilation rate. In addition, a ventilation cavity with symmetrical heating has a higher ventilation rate but generally lower heat transfer coefficient than does an asymmetrically heated cavity. A computational domain larger than the physical size should be used for accurate prediction of the flow rate and heat transfer in ventilation cavities or naturally ventilated buildings with large openings, particularly with multiple inlets and outlets. This is demonstrated with two examples for natural ventilation of buildings. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Natural ventilation is an energy efficient means of delivering fresh air to occupants of a building. Cavity structures such as solar chimneys and Trombe walls rely on the storage wall to induce thermal buoyancy for passive solar heating and natural ventilation of buildings. The air flow and heat transfer in the cavity of such a structure with one wall heated are asymmetrical. Integration of photovoltaic (PV) devices into the exterior skin of the structures leads to redistribution of heat on the two cavity walls due to absorption of solar heat by PV cells. The proportion of heat distribution on the two walls depends on various factors such as the type, transparency and coverage of PV cells as well as operating time. The resulting air flow and heat transfer in the cavity become more complex ranging from laminar to turbulent local flow and symmetrical to asymmetrical global variation patterns. The accuracy of simulation of buoyancy-driven natural ventilation in the cavity or other types of enclosure is influenced by the boundary conditions at the cavity openings in addition to other factors such as turbulence modelling. In most numerical studies of buoyancy-driven natural ventilation of enclosures or buildings, the main concerns are the internal
∗ Tel.: +44 115 9514876; fax: +44 115 9513159. E-mail address: [email protected]. 0378-7788/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2010.02.022
air flow and resulting indoor environmental quality and so the internal space is defined as the computational domain for simulation [1–4]. When a computational domain of the same size as the ventilation cavity or naturally ventilated enclosure is used for flow simulation, uniform pressures are generally prescribed for the inlet and outlet openings. The assumption of a uniform pressure would result in a nearly uniform distribution of velocity at an inlet [5,6] and so could lead to significant errors when the actual flow at the inlet as well as outlet openings deviates from uniform distribution. Allocca et al. [7] used a small computational domain for the indoor space and a large extended domain including both the indoor and outdoor spaces to predict the ventilation rate for a three-storey building with single-sided natural ventilation, each room with a lower inlet opening and upper outlet opening. It was found that the predicted ventilation rate using the small domain was much lower than that using the large domain. An extended computational domain is often used for simulation of buoyancy-driven flow through an open-ended horizontal cavity [8,9]. The author [10] has recently analysed the effect of computational domain on the prediction of natural ventilation through vertical cavities of various sizes and heat distribution ratios. It has been found that using the domain of the same size as a cavity would result in over-prediction of the degree of reverse flow at the top outlet of a wide cavity and consequently under-prediction of the ventilation rate. The problem can be overcome using an extended computational domain larger than the physical size of the cavity
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Fig. 2. Variation of the predicted air flow rate with domain extension size for two 3 m tall and 0.6 m wide cavities one with horizontal inlet and another with vertical inlet.
in an asymmetrically heated cavity. It is also seen that the effect of domain size on the flow rate in the cavity with horizontal inlet was approximately twice that in the cavity with vertical inlet. Air flow in a solar heated tall cavity would likely be turbulent and the RNG k- turbulence model [12] was used for modelling. The model equations for buoyancy-driven flow are represented by the following expression [13]:
∇ • (V៝ ϕ − ϕ ∇ ϕ) = Sϕ
Fig. 1. Schematic diagram of two types of computational domain for simulation of cavity flow.
such that flow patterns at inlet and outlet openings are established naturally from the flow within the cavity and without. This paper aims to demonstrate the importance of using such a large extended domain for accurate simulation of air flow and heat transfer in open vertical cavities with horizontal inlet for natural ventilation of buildings. 2. Methodology A commercial computational fluid dynamics (CFD) software package FLUENT [11] was used for simulation of steady-state air flow and heat transfer through two-dimensional ventilation cavities with a horizontal inlet for different proportions of heat distribution on two vertical walls ranging from heat transfer from either of the walls to heat transfer equally from both walls. Two sizes of computational domain – one larger than the physical size of a ventilation cavity (defined as Domain L) and the other the same size as the cavity (Domain S) – were used for simulation. Fig. 1 shows the schematic diagram of the two domains for a ventilation cavity with a horizontal inlet and a vertical outlet. The required extension (L) from Domain S to create Domain L depends on the cavity width and heat distribution ratio; it varies from about five times the cavity width for symmetrically heated to 10 times the width for asymmetrically heated cavities with a vertical inlet [10]. A similar domain extension would be required for cavities with a horizontal inlet. Fig. 2 shows the variation of the predicted flow rate with extension size for two 3 m tall and 0.6 m wide cavities with asymmetrical heating, where QL and QS are the flow rates from the simulations using Domains L and S, respectively. It is seen that the flow rate increased with the size of extension up to about 3 m or five times the cavity width. The increase became much less when the extension size increased further and there was little difference between the predicted flow rates in the cavities with domain extensions of 5.4 and 6 m, i.e., nine and 10 times the cavity width. Therefore, an extension of 10 times the cavity width would be sufficient to create Domain L for the simulation of flow
(1)
where ϕ is variables representing the mean velocity V, mean enthalpy, turbulent kinetic energy and its dissipation rate, ϕ is the diffusion coefficient and Sϕ is the source for ϕ. In the simulation, the heat flux was used as the wall boundary condition and equal uniform pressure was prescribed as the conditions at the inlet and outlet either as cavity openings for Domain S or the domain boundary for Domain L. The wall with the inlet is referred to as the inlet wall and the heated section of the opposing vertical wall as the opposite wall. The height of the opposite wall was the same as that of inlet wall and the inlet size (height) was equal to the cavity width. To compare with a similar cavity with a vertical inlet (which consists of two parallel walls—the inlet and opposite walls in Fig. 1), the rate of heat transfer from or distribution on the inlet (right) wall is defined as the heat flux q2 and that on the opposite (left) wall as heat flux q1 . The heat distribution ratio (qr ) is the ratio of uniform heat flux from the inlet wall to the total heat flux from both walls: q2 qr = (2) q1 + q2 Determination of the effect of computational domain was based on the predicted air flow and heat transfer rates in a ventilation cavity. The air flow rate (Q) through the cavity is the product of average velocity and opening area of the inlet, with a unit of m3 /s-m for two-dimensional flow. The heat transfer rate is expressed in terms of heat transfer coefficient or Nusselt number which is defined as Nu =
hc b qw b = k (tw − ta )k
(3)
where hc is the convective heat transfer coefficient, b is the cavity width, qw (=((q1 +q2 )/2) is the average heat flux for the inlet and opposite walls, and k is the thermal conductivity of air based on the average temperature of the inlet and opposite walls, tw , and ambient air temperature, ta . Validation of the model for buoyancy-driven natural ventilation was carried out through comparison with experimental data from literature for vertical cavities. Chen et al. [14] measured air flow rates through an asymmetrically heated 1.5 m tall and up to 0.6 m wide vertical cavity. A comparison with the measurements indicated that more accurate simulation of natural ventilation was achieved using a computational domain larger than the cavity [10]. The effect of domain size would be less where the friction loss in
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Fig. 3. Predicted air flow patterns near the horizontal inlet and vertical outlet of a 3 m tall cavity with 100% heat distribution ratio using Domain L.
the cavity was much larger than the influences of flow resistance and velocity variation at inlet and outlet openings, as shown for a much taller cavity (6.5 m tall and 0.23 m wide [15]) with horizontal inlet. In addition to providing more accurate simulation, Domain L is more universal for predicting buoyancy-driven ventilation than Domain S. Domain L is suitable for use in predicting the buoyancydriven flow rates in any ventilation cavities or combination of ventilated spaces whereas Domain S can provide reasonable predictions of ventilation rates for limited circumstances such as in very tall and/or narrow ventilation cavities where flow is unidirectional.
The similarities and differences between the results using the two domains are further examined in the following two sections. 3. Ventilation cavities Simulation was carried out for vertical ventilation cavities of different heights ranging from 1 to 6 m and widths from 0.05 m (for cavity heights up to 3 m and from 0.1 m for taller cavities) to 0.6 m under the entire range of heat distribution ratios from 0% for heat from the opposite wall only, to 50% for heat equally distributed on both the inlet and opposite walls and to 100% for heat from the inlet
Fig. 4. Predicted air flow patterns near the horizontal inlet and vertical outlet of a 3 m tall cavity with 100% heat distribution ratio using Domain S.
G. Gan / Energy and Buildings 42 (2010) 1290–1300
wall only. The variations of cavity width and height gave aspect ratios (height/width) between 5 and 60. In the simulation, the total heat gain by the two vertical walls of a ventilation cavity was generally fixed at 100 W/m2 but the effect of total heat flux was also investigated. The ambient air temperature was fixed at 20 ◦ C. Discussion of the simulation results is here focused on cavities with a horizontal inlet. Nevertheless, the results are also briefly compared between cavities with a horizontal inlet and those with a vertical inlet; details for the latter are presented elsewhere [10]. The predicted flow patterns of air through the horizontal inlet and vertical outlet of a 3 m tall ventilation cavity of three different widths and with a heat distribution ratio of 100% are shown in Figs. 3 and 4 using Domains L and S, respectively. The air flowed along the opposite wall after turning from horizontal at the inlet to vertical direction. A large recirculation zone was formed above the inlet and near the inlet wall. The two domains resulted in different flow patterns in the bottom corner and near the outlet of the cavity. Using the large domain, incoming air is seen from Fig. 3 to detach from the bottom wall and be deflected upwards, forming another large recirculation zone in the corner between the bottom wall and opposite wall. By comparison, using the small domain, horizontal incoming air flowed along part of the bottom wall and then turned upwards along the opposite wall with very little air movement in the corner, see Fig. 4. Reverse flow at the outlet of 0.3 m wide cavity disappeared using Domain L but would still occur using Domain S. Therefore, Domain S could over-predict the possibility of reverse flow at the outlet of a wide cavity with horizontal inlet. Similar flow patterns were observed at the outlet of a cavity with vertical inlet [10]. However, deflection of incoming air towards the opposite wall of a cavity with horizontal inlet led to less or no reverse flow at the outlet than a cavity with vertical inlet, depending on the cavity width and computational domain. Because of reduced reverse flow, the predicted flow rate in an asymmetrically heated cavity with horizontal inlet was higher than that with vertical inlet for wide cavities (width ≥ 0.3 m) as seen from Fig. 5 (where H and V denote horizontal and vertical inlets, respectively), even though the flow resistance of the horizontal inlet would be larger resulting from flow turning from horizontal to vertical direction. The additional flow resistance of the horizontal inlet would however reduce the flow rate compared with the cavities with vertical inlet where the cavity size and the heat distribution on two walls were such that no reverse flow would occur at the outlet. This is seen for both the wide cavities (e.g. the 0.5 m wide cavity in Fig. 5c) with symmetrical heating and narrow cavities (0.1 m wide in Fig. 5a) with any heat distribution ratio. Consequently, using Domain L, the predicted variation in flow rate with heat distribution ratio in the cavity with horizontal inlet was less than that with vertical inlet, due to generally a higher flow resistance with more symmetrical heating but less reverse flow with asymmetrical heating. By comparison, because the flow resistance at the inlet could not be fully taken into account using Domain S, the difference in the flow rate through the 0.3 m wide cavity with vertical inlet and that with horizontal inlet was less clear-cut as shown in Fig. 5b. Apart from asymmetrical heating (qr = 0 or qr = 100%) which resulted in a higher flow rate through the cavity with horizontal inlet, the predicted flow rate was lower for heat distribution ratios below 40% but higher for higher heat distribution ratios in the cavity with horizontal inlet than that with vertical inlet. The predicted flow rate in the 0.5 m wide cavity with horizontal inlet was generally much higher than that with vertical inlet. These variations suggest that there was significant uncertainty using Domain S for predicting buoyancy-driven flow in a very wide cavity because real flow would not be uniform at such large inlet and outlet openings and that the uncertainty resulting from using Domain S would be larger for a cavity with vertical inlet than that with horizontal inlet.
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Fig. 5. Comparison between the flow rate in a 3 m tall cavity with horizontal inlet (H) and that with vertical inlet (V): (a) cavity width = 0.1 m, (b) cavity width = 0.3 m and (c) cavity width = 0.5 m.
3.1. Effect of cavity width Fig. 6 shows the variation of the air flow rate with heat distribution ratio in a 3 m tall cavity with horizontal inlet and different widths. Unlike a cavity with vertical inlet where flow is symmetrical along the equal heat flux value (qr = 50%), the variation with heat distribution ratio of the flow rate through the cavity with horizontal inlet was not symmetrical. The flow rate was slightly higher when more heat flowed from the inlet wall than when heat flowed from the opposite wall. The highest predicted flow rate using Domain L for the cavity with the horizontal inlet was obtained when the heat distribution ratio was between 60% and 65%, compared with 50% for the cavity with vertical inlet (see Fig. 5). It is also seen from Fig. 6a or b that when heat flow from the inlet wall was 2% or more, or heat flow from the opposite wall was 10% or more of the total heat flux, the flow rate increased with cavity width. For heat flow from one wall only, the flow rate in the cavity still increased with cavity width up to 0.5 m. Besides, the effect of heat distribution on the variation in flow rate increased with cavity width. A comparison between Fig. 6c and b shows that the variation patterns of the flow rate from the maximum with heat distribution ratio were similar using two different sizes of domain although the maximum flow rate was attained at different heat distribution ratios—about 70% using Domain S compared with 60–65% using Domain L.
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Fig. 6. Effects of heat distribution ratio and cavity width on the flow rate in a 3 m tall cavity with horizontal inlet: (a) air flow rate Q predicted using Domain L, (b) variation from maximum Q predicted using Domain L and (c) variation from maximum predicted using Domain S.
The variation with heat distribution ratio of the heat transfer coefficient for the 3 m tall cavity with horizontal inlet is shown in Fig. 7 for different cavity widths. The heat transfer coefficient was generally higher when heat flowed from one wall only and the highest heat transfer coefficient was obtained when heat flowed only from the opposite wall. The variations with heat distribution ratio of the heat transfer coefficient for the 3 m tall cavity with horizontal inlet and vertical inlet are compared in Fig. 8 for three selected cavity widths. The predicted heat transfer coefficient was lower for narrow cavities but higher for wide cavities with horizontal inlet than vertical inlet particularly using Domain L. Unlike for the cavity with vertical inlet where the lowest heat transfer coefficient was obtained when heat was equally distributed on both walls, the lowest heat transfer coefficient in a cavity with horizontal inlet generally occurred at a point when more heat flowed from the inlet wall than from the opposite wall. The effect of heat distribution on the variation in heat transfer coefficient and the lowest heat transfer coefficient depended on the cavity width (Fig. 7b). The largest variation in heat transfer coefficient with heat distribution ratio from the predictions using Domain L was 19% for flow in a cavity with an aspect ratio of 10 at a heat distribution ratio of about 98% compared with 12% variation at 60% heat distribution ratio for the 0.6 m wide cavity with an aspect ratio of 5 or negligible variation for a very narrow cavity (width = 0.06 m and aspect ratio = 50).
Fig. 7. Effects of heat distribution ratio and cavity width on the heat transfer coefficient in a 3 m tall cavity with horizontal inlet: (a) heat transfer coefficient Nu predicted using Domain L, (b) variation from maximum Nu predicted using Domain L and (c) variation from maximum predicted using Domain S.
In contrast with similar variation patterns of the flow rate from the maximum with heat distribution ratio, large differences were found in the variation patterns of heat transfer coefficient particularly for wide cavities with horizontal inlet using two different domains. The heat transfer coefficient reached minimum in cavities wider than 0.065 m when the heat distribution ratio was about 50% or slightly over using Domain S (Fig. 7c) rather than close to 100% for wide cavities using Domain L, shown in Fig. 7b. The heat transfer coefficient became independent of the heat distribution ratio for 3 m tall cavities of 0.065 and 0.06 m wide, respectively, using Domain S and Domain L, or the variation trend inverted when the cavity widths decreased further, i.e., the heat transfer coefficient increased with heat distribution from asymmetrical to symmetrical heating. Fig. 9a shows that the predicted flow rate in cavities with horizontal inlet was higher using Domain S than that using Domain L for cavity widths less than 0.3 m and also for cavity widths between 0.3 and 0.5 m and with heat distribution ratios between 20% and 95%. The reason for the higher predicted flow rate using the smaller domain was disregarding the flow resistance through the horizontal inlet where flow had to turn at a right angle from the ambient to the cavity. For very low or high heat distribution ratios or for the widest cavity (0.6 m wide and 3 m tall), the predicted flow rate
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Fig. 9. Effect of domain size on the variations in air flow rate and heat transfer coefficient with heat distribution ratio in a 3 m tall cavity with horizontal inlet: (a) air flow rate and (b) heat transfer coefficient.
with cavity height was small (less than 4%) using Domain L but the variations from the maximum increased considerably using Domain S with a maximum difference of about 20% between the variations from about 20% to 40% when the cavity height increased from 1 to 6 m. By contrast, the variations of the predicted flow rate through cavities with vertical inlet were larger using Domain L than using Domain S as shown in Fig. 11 for comparison between two cavities with minimum and maximum variations. The maximum differences that occurred between 0.1 and 0.6 m wide cavities with Fig. 8. Comparison of the heat transfer coefficient in a 3 m tall cavity with horizontal inlet (H) with that with vertical inlet (V): (a) cavity width = 0.1 m, (b) cavity width = 0.3 m and (c) cavity width = 0.5 m.
using the larger domain was higher due to reduced reverse flow at the outlet which outweighed the effect of additional inlet flow resistance. The maximum difference in flow rate using the two domains was generally within 10% (and less than 2% for a symmetrically heated 0.5 m wide cavity) but much higher for asymmetrically heated cavities wider than 0.3 m and with heat distribution ratios less than 5% or greater than 98%, with the largest differences of about 40% and 43%, respectively, for 0.5 and 0.6 m wide cavities with only the opposite wall heated. Similar to the flow rate, the predicted heat transfer coefficient in narrow cavities (width < 0.3 m) was higher using the smaller domain than that using the larger domain but generally lower in wide cavities as seen from Fig. 9b. However, the difference in the predicted heat transfer coefficient using two different domains was smaller than that in the flow rate, particularly for cavities with asymmetrical heating. 3.2. Effect of cavity height The variations in the flow rate from the maximum in cavities with horizontal inlet and with different heights but the same aspect ratio of 10 are compared in Fig. 10. The maximum flow rate for all cavity heights was achieved when the heat distribution ratio was about 65% and 70% using Domains L and S, respectively. The difference in the variations of the flow rate from the maximum
Fig. 10. Effect of cavity height on the variation from maximum of flow rate with heat distribution ratio in cavities with horizontal inlet and aspect ratio of 10: (a) using Domain L and (b) using Domain S.
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Fig. 11. Variations from maxima of flow rate and heat transfer coefficient with heat distribution ratio in cavities with vertical inlet and aspect ratio of 10.
asymmetrical heating were 16% and 13% using Domains L and S, respectively. Fig. 12 shows that the difference in the variation of the heat transfer coefficient for cavities with horizontal inlet was negligible using Domain L for cavity heights between 3 and 6 m; for short cavities, the difference was large probably due to less air turbulence than in tall and wide cavities. In addition to less variation in heat transfer coefficient with heat distribution ratio, the effect of the cavity height on the variation in heat transfer coefficient was much smaller using Domain S with a maximum difference between tallest and shortest cavities investigated of less than 3% for heat distribution ratios less than or equal to 90% and within 6% for heat distribution ratios larger than 90%. The maximum difference in the predicted heat transfer coefficient in cavities with vertical inlet was also small using both domains; it was about 3% between cavities 1 and 4 m tall using Domain L and 5% between the shortest and tallest cavities using Domain S (Fig. 11). The predicted flow rate in cavities with horizontal inlet using Domain S was generally higher than that using Domain L for heat distribution ratios between 15% and 98% as shown in Fig. 13a. For heat distribution ratios less than 15% or greater than 98%, the predicted flow rate using Domain S was also higher for short cavities but lower for tall cavities than that using Domain L. For example, for a 6 m tall cavity with only one (inlet) wall heated, the predicted
Fig. 13. Effect of domain size on the variations in air flow rate and heat transfer coefficient with heat distribution ratio in cavities with horizontal inlet and aspect ratio of 10: (a) air flow rate and (b) heat transfer coefficient.
flow rate using Domain L was as much as 22% higher than that using Domain S. This was again the consequence of over-prediction of reverse flow at the outlet using Domain S. The effect of cavity height on the magnitude of heat transfer coefficient was similar to the effect of cavity width as seen from Fig. 13b and Fig. 9b. The predicted heat transfer coefficient using Domain S was slightly higher than that using Domain L for a 1 m tall cavity. For cavities of 2–3 m tall, the heat transfer coefficient was lower for heat distribution ratios up to about 50% and 70% for 2 and 3 m tall cavities, respectively, but higher for larger ratios using Domain S than Domain L. For cavities taller than 3 m, the predicted heat transfer coefficient using Domain S was lower than that using Domain L. For cavities shorter than 3 m, the maximum difference in heat transfer coefficient using the two domains was less than 4%. The difference increased with height with a maximum difference of 15% for the 6 m tall cavity at a heat distribution ratio of 10%. Therefore, a large domain should be used where possible to predict accurately the flow rate and heat transfer coefficient for tall cavities with horizontal inlet. 3.3. Effect of total heat flux
Fig. 12. Effect of cavity height on the variation from maximum of heat transfer coefficient with heat distribution ratio in cavities with horizontal inlet and aspect ratio of 10: (a) using Domain L and (b) using Domain S.
Fig. 14 shows that there was hardly any variation in flow rate from maximum (attained at a heat distribution ratio between 60% and 65%) predicted using Domain L when the total heat flux imposed on the two vertical walls increased by 10-fold. The variation of the predicted flow rate using Domain S from the maximum (attained at a heat distribution ratio of about 70%) increased slightly with the total heat flux with a maximum difference of about 10%. By contrast, the variation of the heat transfer coefficient from the maximum (occurred when only the opposite wall was heated) decreased with increasing total heat flux as shown in Fig. 15. The variation in heat transfer coefficient with heat distribution ratio was smaller than that in flow rate particularly using Domain S but the effect of total heat flux on the variation from the maximum of heat transfer coefficient was relatively large compared with the magnitude of variation. For the range of total heat fluxes inves-
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Fig. 14. Effect of total heat flux on the variation from maximum of flow rate with heat distribution ratio in a 3 m tall and 0.3 m wide cavity with horizontal inlet: (a) using Domain L and (b) using Domain S.
tigated, the maximum difference was not more than 3% (at 50% heat distribution ratio) and 6% (at 65% heat distribution ratio) using Domains L and S, respectively. Fig. 16 shows the differences resulting from using the two domains in air flow rate and heat transfer coefficient in the 3 m tall and 0.3 m wide cavity with horizontal inlet under a range of heat fluxes from 100 to 1000 W/m2 together with the differences for the cavity with vertical inlet under the minimum and maximum heat fluxes. It is seen that the effect of total heat flux on the maximum
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Fig. 16. Effect of domain size on the variations in air flow rate and heat transfer coefficient with heat distribution ratio in two 3 m tall and 0.3 m wide cavities for different total heat fluxes: (a) air flow rate and (b) heat transfer coefficient.
differences in air flow rate and heat transfer coefficient using the two domains was larger in the cavity with horizontal inlet (occurred with asymmetrical heating) than that with vertical inlet (occurred with symmetrical heating). The difference in the flow rate using the two domains for different total heat fluxes increased with the asymmetry of heat input on the two vertical walls of the cavity with horizontal inlet but decreased with the asymmetry for the cavity with vertical inlet. The difference for a 10-fold increase in total heat flux for the cavity with horizontal inlet was less than 3% for heat distribution ratios between 20% and 95% and the maximum difference was about 10% when only one wall was heated. However, the difference in the heat transfer coefficient for different total heat fluxes increased with the proportion of heat input from the opposite wall of the cavity with horizontal inlet and again decreased with the asymmetry for the cavity with vertical inlet. The maximum difference in heat transfer coefficient for the 10-fold increase in total heat flux for the cavity with horizontal inlet was 8% when only the opposite wall was heated whereas the maximum differences in both flow rate and heat transfer coefficient for the cavity with vertical inlet were about 3%, occurred when both walls were equally heated. It follows that using a large domain than a ventilation cavity would not only reduce the effect of using a representative amount of heat input say 100 W/m2 on the accuracy for general analysis of simulation results but also provide more accurate simulation of flow in similar enclosures with horizontal inlet, typical of solar-assisted naturally ventilated spaces and other types of buoyancy-driven naturally ventilated building such as atrium buildings.
4. Naturally ventilated buildings
Fig. 15. Effect of total heat flux on the variation from maximum of heat transfer coefficient with heat distribution ratio in a 3 m tall and 0.3 m wide cavity with horizontal inlet: (a) using Domain L and (b) using Domain S.
To demonstrate further the importance of using a larger domain than the size of a ventilated space in the simulation of buoyancy-driven natural ventilation, ventilation rates were predicted for a room integrated with a solar chimney and an atrium building with internal heat gains at an ambient temperature of 20 ◦ C.
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4.1. Room ventilation Bouchair [16] conducted experimental measurements of buoyancy-driven air flow in a 2 m tall solar chimney for room ventilation. The cavity width of the chimney varied from 0.1 to 0.5 m. The chimney had a horizontal inlet of 0.1 or 0.4 m high and shared the storage wall with a room of the same height where a window on the opposite wall allowed air to flow into the room and then to the chimney. The wall surfaces of the cavity were symmetrically heated to temperatures from 30 to 60 ◦ C. Simulation of buoyancy-driven air flow was performed for the room integrated with the solar chimney with a 0.5 m wide cavity and 0.4 m high inlet using two two-dimensional domain sizes – one the same as the space for the combined room and chimney structure (Domain S) and another larger than the combination (Domain L) – at a chimney temperature of 60 ◦ C for both the exterior wall and insulated storage wall. In addition, the air flow rate was also predicted using a third domain of the same size as the chimney cavity with a horizontal inlet which had a length the same as the thickness of the storage wall (Domain C), with which the flow resistance of the window opening was ignored. It was assumed that the room was 3 m deep and the window opening size was the same as the chimney inlet. The predicted mass flow rate using Domain L was 0.127 kg/s-m which was close to the measured value of approximately 0.124 kg/s-m. The predicted flow rate using Domain S was approximately 8% less than the prediction using Domain L. The predicted flow rate using Domain C was even lower (about 10% lower than that predicted using Domain L) even though the flow resistance of the window opening was neglected. The difference in the predicted ventilation rate using Domains L and S for the combination of the room and chimney was consistent with the results discussed in the previous section for similar cavities. Fig. 9 indicates that the predicted ventilation rate for a symmetrically heated cavity of 3 m tall would be higher for a 0.5 m cavity width but lower for a 0.6 m cavity width using Domain S than using Domain L. The aspect ratio of the chimney cavity of 2 m tall and 0.5 m wide was 4. Therefore, in terms of aspect ratio, the cavity width comparable with the 3 m tall cavity should be 0.6 m or larger for which the predicted ventilation rate using Domain L was higher. A practical solar chimney with glazing as the exterior wall would rarely be symmetrically heated during operation. When the temperature of the exterior wall of the chimney was reduced but the temperature of the interior (storage) wall remained at 60 ◦ C (all referring to the wall surfaces facing the chimney cavity), the predicted flow rates using all the three domains decreased as shown in Fig. 17. It is also seen that the rate of decrease predicted using Domains L and S increased with decreasing exterior wall temperature whereas the rate of decrease predicted using Domain C was constant for the exterior wall temperatures from 30 to 60 ◦ C. The predicted flow rate was lower using Domain C than using either Domain L or Domain S for exterior wall temperatures between 25 and 60 ◦ C but higher for the temperatures below 25 ◦ C. The difference in the flow rates between using Domains C and S partly represented the influence of the window opening but more importantly could result from different flow patterns in the chimney–similar to the differences presented in Figs. 3 and 4. The higher flow rate predicted using Domain S suggests that the effect of flow resistance (dependent on the flow rate) due to the window opening was stronger than that of the flow pattern in the chimney when its exterior wall temperature was over 5 ◦ C higher than the room air temperature. However, when the exterior wall temperature was low, leading to more asymmetrical air flow and heat transfer, the flow pattern in the chimney would have a larger influence than the flow resistance of the window opening. The predicted flow rate was slightly lower using Domain S than using Domain L but the difference between the flow rates using
Fig. 17. Comparison of predicted mass flow rates in the solar chimney for room ventilation using three types of domain.
Domains L and S decreased from 8% to less than 1% when the temperature of the exterior wall decreased from 60 to 25 ◦ C. For the exterior wall temperature between 21 and 25 ◦ C, the predicted flow rate using Domain S was more or less the same as predicted using Domain L. When the exterior wall was at the same temperature as room air, leading to varying degrees of reverse flow away from the storage wall depending on the size of domain, the predicted flow rates using Domains S and C were as much as 44% and 39%, respectively, lower than the predicted value of 0.0367 kg/s-m using Domain L which was itself a massive 70% drop from the flow rate for symmetrical heating. The decrease of the predicted flow rate with the exterior wall temperature was gradual using Domain L, but a sharp decrease in the flow rate was predicted using Domain S or Domain C when the wall temperature was reduced from a small value above the room air temperature to the same as the room temperature. For example, when the exterior wall temperature was reduced from 1 ◦ C above to the same temperature as room air, the predicted flow rates using Domains S and C decreased by approximately 58% and 63%, respectively, compared with a decrease of 25% using Domain L. In other words, using Domain S or Domain C would significantly over-predict the effect on the ventilation rate of buoyancy along the exterior wall of a solar chimney when its temperature approaches the room air temperature. The predicted ventilation rates in the room and chimney using three different domains can be correlated with the exterior wall temperature as follows: Using Domain L: Q = 0.012T + 0.037 Q = 0.0485T 0.262
0K = T < 1K 1K ≤ T ≤ 40K
(R2 = 0.996) (R2 = 0.999)
(4a) (4b)
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transfer from the storage wall, therefore the difference in the predicted flow rate using two types of domain (Domains L and S) would be within 10%. For heating seasons, however, because of the heat loss to the ambient from the solar chimney in particular with single glazing, the glazing temperature could be the same as or even lower than the room air temperature and the ventilation potential of a solar chimney would be significantly under-predicted using a computational domain of the same size as the chimney cavity or in combination with the ventilated space. 4.2. Atrium ventilation
Fig. 18. Predicted air flow patterns and temperature distribution in the atrium building using Domain L: (a) air flow patterns and (b) temperature contours.
Using Domain S: Q = 0.0496T 0.24
0.5K ≤ T ≤ 40K
(R2 = 0.999)
(5)
Using Domain C: Q = 0.06T 0.135
0.5K ≤ T ≤ 10K
Q = 0.00106T + 0.0716
(R2 = 0.999)
10K ≤ T ≤ 40K
(6a)
(R2 = 0.999) (6b)
where Q is the ventilation rate (m3 /s-m), T is the temperature difference between the exterior wall and room air. For solar-assisted natural ventilation of a similar space in summer, the glazing temperature is likely to be higher than the temperature of room air due to solar absorption and radiation heat
The air flow and temperature distribution were also predicted using both small and large domains for a hypothetical office building with a central atrium to assist natural ventilation. The building (Fig. 18) consisted of two wings of three floors of open plan offices 12 m deep and 3 m high separated by an atrium 8 m deep and 15.9 m high at the top of roof. There were two balconies of 3 m long in the atrium attached to the first and second floors on the left wing. The ceilings and external fac¸ade walls of the building were 0.3 m thick and internal walls 0.1 m thick. The width of the building was assumed large enough to allow simplification as two-dimensional flow along the depth and height directions. The size of window openings in both the external fac¸ade and atrium wall for natural ventilation of offices was 0.5 m high and the vent opening at the atrium top was 2 m wide. The internal space and structure of the building was defined as Domain S whereas Domain L included both the building and a large extended external area (over five times the building height, set up for simulation of both wind- and buoyancydriven flow) surrounding the building. It was assumed that heat gains in the building were equivalent to 40 W/m2 on the floors of offices and atrium. Fig. 18 shows the predicted air flow patterns and temperature distribution in the building using the large domain. The predicted air movement in a lower floor was larger than that in an upper floor due to the higher buoyancy effect. The indoor air would be thermally comfortable with air temperatures in the offices varying between 20 and 22 ◦ C. The predicted ventilation rates for the offices of the building using Domains L and S (QL and QS , respectively) are compared in Table 1. The ventilation rate for an office on the left wing was similar to or lower than that on the right wing at the same floor level for the ground and first floors due to the additional flow resistance from the balconies but higher for the top floor because these balconies reduced disruption of the outgoing flow from the offices by the upward flow from below. The predicted total ventilation rate
Table 1 Predicted ventilation rates for the atrium building using two types of domain. Inlet position (see Fig. 18)
QS (Domain S) (m3 /s-m)
QL (Domain L) (m3 /s-m)
(QL − QS )/QL (%)
Inlet height = 0.5 m L1 L2 L3 R1 R2 R3
0.266 0.214 0.150 0.263 0.232 0.154
0.249 0.214 0.163 0.248 0.214 0.156
−6.97 −0.03 7.98 −6.22 −8.42 1.55
1.280
1.245
−2.84
0.320 0.252 0.114 0.377 0.285 0.119
0.318 0.244 0.129 0.349 0.256 0.108
−0.53 −3.46 11.23 −8.23 −11.58 −9.58
1.467
1.403
−4.59
Total Inlet height = 1 m L1 L2 L3 R1 R2 R3 Total
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for the building was about 3% higher using the small domain than using the large domain. Larger differences between the ventilation rates were predicted using the two domains for some of the offices because the flow rate and velocity distribution across an inlet opening varied with its vertical position. Using the small domain would over-predict the ventilation rates by approximately 6–8% for the offices at ground floor on the left wing and the ground and first floors on the right wing but under-predict the rate by nearly 8% for the office at the top floor on the left wing. Hence, simulation using a domain the same as the physical size of a multi-storey atrium building would give rise to larger uncertainty in ventilation rates for individual office spaces than that in the overall ventilation rate. This was confirmed with another simulation for larger window openings (1 m high in both external and internal walls) but the same outlet opening size. Increasing the window opening size lowered the neutral pressure level and consequently increased the relative differences in the ventilation rates from bottom to top floors. The difference in the overall ventilation rate for the building using the two domains increased to over 4% and larger differences in the ventilation rates for individual spaces between 8% and 12% would occur at the top floor on the left wing (QS < QL ) and all floors on the right wing (QS > QL ). Therefore, a larger domain than the physical size should be used to predict more accurately the ventilation rates in naturally ventilated multi-storey buildings with multiple inlets and single common or multiple ventilation outlets.
A larger computational domain than the physical size of a cavity can provide more accurate simulation of buoyancy-driven natural ventilation. Therefore, such large computational domains should be used for accurate prediction of heat transfer and flow rate in ventilation cavities or enclosures with large openings for natural ventilation, particularly with multiple inlets and outlets, asymmetrical heat distribution on opposing walls, or asymmetrical flow distribution at openings unless a known flow profile is prescribed at each opening. For an enclosure with multiple openings at different heights, varying flow distribution at the openings could create another source of uncertainty in flow prediction. Using a domain of the same as physical size to simulate flow through a multi-storey building with multiple ventilation inlet or outlet openings would give rise to larger uncertainty in ventilation rates for individual spaces or zones than that in the overall ventilation rate for the building. For a ventilation cavity with either horizontal or vertical inlet using either large or small domain, the air flow rate and heat transfer coefficient increase with cavity size and total heat input if reverse flow at the cavity outlet can be prevented. In general, the more evenly heat is distributed on the two vertical walls, the larger the flow rate in a ventilation cavity with either vertical or horizontal inlet but smaller heat transfer coefficient in a cavity with vertical inlet.
5. Conclusions
[1] M. Cook, Y. Ji, G.R. Hunt, CFD modelling of natural ventilation: combined wind and buoyancy forces, International Journal of Ventilation 1 (3) (2003) 169–179. [2] R. Letan, V. Dubovsky, G. Ziskind, Passive ventilation and heating by natural convection in a multi-storey building, Building and Environment 38 (2003) 197–208. [3] G. Gan, Simulation of buoyancy-induced flow in open cavities for natural ventilation, Energy and Buildings 38 (5) (2006) 410–420. [4] Y. Ji, M. Cook, V. Hanby, CFD modelling of natural displacement ventilation in an enclosure connected to an atrium, Building and Environment 42 (3) (2007) 1158–1172. [5] S. Baskaya, M.K. Aktas, N. Onur, Numerical simulation of the effects of plate separation and inclination on heat transfer in buoyancy driven open channels, International Journal of Heat and Mass Transfer 35 (1999) 273–280. [6] A.M. Rodrigues, A. Canha da Piedade, A. Lahellec, J.Y. Grandpeix, Modelling natural convection in a heated vertical channel for room ventilation, Building and Environment 35 (2000) 455–469. [7] C. Allocca, Q. Chen, L.R. Glicksman, Design analysis of single-sided natural ventilation, Energy and Buildings 35 (2003) 785–795. [8] K. Vafai, J. Ettefagh, Thermal and fluid flow instabilities in buoyancy-driven flows in open-ended cavities, International Journal of Heat and Mass Transfer 43 (1990) 2329–2344. [9] S.K.S. Boetcher, E.M. Sparrow, Buoyancy-induced flow in an open-ended cavity: assessment of a similarity solution and of numerical simulation models, International Journal of Heat and Mass Transfer 52 (2009) 3850–3856. [10] G. Gan, Impact of computational domain on the prediction of buoyancy-driven ventilation cooling, Building and Environment 45 (2010) 1173–1183. [11] FLUENT User’s Guide, Fluent Inc., New Hampshire, USA, 2005. [12] V. Yakhot, S.A. Orzsag, Renormalization group analysis of turbulence. I. Basic theory, Journal of Scientific Computing 1 (1986) 1–51. [13] G. Gan, Prediction of turbulent buoyant flow using an RNG k- model, Numerical Heat Transfer Part A: Applications 33 (2) (1998) 169–189. [14] Z.D. Chen, P. Bandopadhayay, J. Halldorsson, C. Byrjalsen, P. Heiselberg, Y. Li, An experimental investigation of a solar chimney model with uniform wall heat flux, Building and Environment 38 (2003) 893–906. [15] B. Moshfegh, M. Sandberg, Flow and heat transfer in the air gap behind photovoltaic panels, Renewable and Sustainable Energy Reviews 2 (1998) 287–301. [16] Bouchair, Solar chimney for promoting cooling ventilation in southern Algeria, Building Services Engineering Research and Technology 15 (2) (1994) 81–93.
CFD has been used to simulate the buoyancy-driven air flow and heat transfer in vertical cavities with horizontal inlet for natural ventilation of buildings using two different sizes of computational domain and results have been compared with those with vertical inlet. There are differences in the predicted air flow rate and heat transfer coefficient through the cavities between using a small domain of the same size as the cavity and using a large extended domain. The degree of difference varies with cavity size and heat distribution ratio—larger difference in flow rate than in heat transfer coefficient and larger difference for wider cavities with asymmetrical heating. The large extended domain is suitable for predicting buoyancy-driven flow in any ventilation cavities whereas the small domain can be used for flow simulation in very tall ventilation cavities where friction resistance is dominant. The differences in the predicted air flow rate and heat transfer coefficient for a ventilation cavity is also influenced by the position of inlet opening. Apart from extreme asymmetrical heating (heat distribution ratios not more than 5% or not less than 95%), the differences in flow rate and heat transfer coefficient increase with the level of symmetry in heat distribution on two vertical walls of a ventilation cavity with vertical inlet but decrease in a cavity with horizontal inlet. As a result, e.g. for the same cavity height and total heat flux, the differences are larger for more symmetrical heat distribution in cavities with vertical inlet but for more asymmetrical heat distribution in cavities with horizontal inlet particularly for wide cavities. For the same cavity size at different total heat fluxes or for cavities with the same aspect ratio but different heights, the difference is slightly larger for cavities with horizontal inlet than those with vertical inlet.
References