- Email: [email protected]
Review of Natural Ventilation Models
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 78 (2015) 2700 – 2705
6th International Building Physics Conference, IBPC 2015
Review of natural ventilation models Zhiqiang (John) Zhaia, Mohamed El Mankibib*,Amine Zoubirb b
a University of Colorado at Boulder, Boulder, CO 80309-0428, USA ENTPE-University of Lyon, 3 rue Maurice Audin, Vaulx en Velin 69120, France
Abstract Natural ventilation (NV) is an important and efficient passive technique to reduce building cooling energy need and improve indoor air quality. NV design requires profound knowledge and accurate prediction of air flow and heat transfer in and around buildings. This paper reviews the important NV models and simulation tools and the comparisons of their prediction capabilities. In one hand, a review of the analytical models reveals that these models are generally only applicable to specific geometries and driving forces. In other hand, results of comparison and assessment between airflow models have shown that the current one can be used to model most NV mechanisms, with an exception of wind-driven single-sided ventilation. For the predictable cases, the most accuracy is achieved for cases with small and simple openings. For larger openings and especially complicated openings, the model’s predictions are less accurate. Furthermore, the model is heavily dependent on several somewhat ambiguous coefficients including: wind profile exponent, pressure coefficient, and discharge coefficient. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ©2015 2015Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL. Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL Keywords: Natural Ventilation; Modeling
1. Main text Natural ventilation (NV) is one of the most efficient techniques, when weather permits, to reduce building cooling energy usage and improve indoor air quality. Research has shown that the acceptable thermal comfort range for natural ventilated buildings is larger than for buildings with standard mechanical HVAC systems (De Dear and Brager [1]). Sepannen and Fisk [2], after reviewing 18 different studies on sick building syndrome (SBS) and ventilation systems,
* Corresponding author. Tel.: +33 (0) 6 42 45 64 75; fax: +33 (0) 4 72 04 70 41. E-mail address: [email protected]
1876-6102 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL doi:10.1016/j.egypro.2015.11.355
Zhiqiang (John) Zhai et al. / Energy Procedia 78 (2015) 2700 – 2705
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found that prevalence of SBS symptoms was 30 to 200% higher in air conditioned buildings as compared to naturally ventilated ones. NV design for buildings requires profound knowledge and accurate prediction of air flow and heat transfer in order to quantify the naturally driven ventilation rates as well as the associated effects on building space temperatures. Computational fluid dynamics (CFD) techniques can provide a robust prediction of NV. They have been used to simulate NV under a variety of conditions, including wind- and buoyancy-driven flows as well as those with combined forces (Zhai [3]). CFD is mostly used to perform simulations on portions of a building (Lomas et al. [4]), particularly where spatial temperature variations exist. Performing an annual CFD simulation of an entire building is impractical, due to the computational complexity and cost of CFD. Reduced-order airflow models such as network models have been developed to quickly predict airflows throughout a building. A variety of different network models have been developed, such as, MIX by Li et al. [5] and AIOLOS by Allard and Santamouris [6], many of which are used internally by the developer. Several studies comparing these models to each other are found in literature, including Dascalaki et al. [7], Haghighat and Li [8], and Furbringer et al. [9]. The general conclusion of these studies is that the models are generally similar, with minor functional differences separating the tools. This research conducted a comprehensive literature review on the state of NV modeling research. 2. Natural Ventilation Models A review of both analytical/empirical models and commonly used network airflow models was performed. Analytical models are only derived for simple geometries and almost entirely for single-zone geometries while network models are applicable for multi-zone structures. For NV, due to the dependency of temperature on stack-driven flow, airflow models are often solved in conjunction with thermal models. 2.1. Analytical and Empirical Models Most analytical models are developed by applying the mass and energy conservation equations to particular configurations. Most of these models have been verified experimentally. (1) Single Zone (a) One Opening Yamanaka et al. [10] experimentally investigated the validity of two single-sided wind-driven ventilation models: the pulsation theory (Cockroft and Robertson [11]) and the mixing layer theory (Warren, [12]). Pulsation theory assumes that air flow is quantified by the fluctuation of pressure across the opening. Yamanaka proved this model was inaccurate for all wind incidence angles except 0°. The mixing layer theory assumes a velocity and pollutant distribution inside the single opening, and ventilation rate is given by:
Q C AU w
(1)
where Q is the ventilation flow rate, C is the airflow coefficient (varies depending on geometry and wind incidence direction), A is the opening area and Uw is the local velocity (wind velocity along the wall at the outside edge of mixing layer). A semi-analytical model for single-sided ventilation driven by buoyancy alone has been developed, based on the fact that the volume flow rate is driven by the pressure difference across the opening and assuming a small temperature difference 'T (Alloca, [13]). The volume flow rate for this configuration, from Bernoulli principles, is: Q
'T Cd A g h Tout 3
(2)
where h is the height of the opening. The general form of the equation for airflow from both stack, wind, and other driving pressure differences is the power law for orifices: Q Cd A
(3)
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Phaff et al. [14] performed a detailed experimental study into the terms and coefficients comprising the Δp in the above equation. They considered contributions from wind, buoyancy, and also included a turbulence constant. Their empirical equation, based on meteorological wind speed rather than local wind speed, is:
Q
A 2 0, 001V Vmet 0, 0035h 'T 0, 01 2
(4)
(b) Multiple Openings – Buoyancy Driven Linden’s work (Linden et al [15]) on the fluid mechanics of both displacement and mixing ventilation forms the basis of much of the analytical modeling of NV. Linden considered steady-state filling and draining behavior of a room with high and low level openings, and point, horizontal line, and vertical line sources of buoyancy, using conservation of volume and buoyancy fluxes. Linden assumes that velocity of air through the vents is related to pressure drop across the vent, and that zones form within the space where the lowest zone’s temperature is equal to ambient. Also, the effect of thermal radiation between surfaces is neglected. For a single buoyancy source, this model uses the following equation for volume flow rate (Li et al [5]):
Q (C A*)2/3 (B (h h ))1/3 d
c
and
A* 2 At Ab At2 A Ab2
(5) where B is the buoyancy flux, h is the height between two vertical openings,
hc is the clean zone height and A* is
the effective area of the two openings (areas At and Ab). Cooper and Linden [16] extended this model to an enclosure with two buoyancy sources, investigating sources of unequal strength the same and opposite sign, and then extended the model to multiple sources (Linden et al. [15]). An approximation that the buoyancy in the plumes from each source remains unchanged though it is rising through stratified layers in the rooms results in some error, which is determined to be acceptable for design purposes, as the volume flow was determined to be strongly dependent on height of the ambient zone and only weakly dependent on buoyancy flux in the plume. Chen et al. [17] suggests a simple multi-layer stratification model of displacement ventilation in a single-zone building driven by a heat source distributed uniformly over a vertical wall. This model, an extension of Linden’s model (Linden et al. [15]), is derived from conservation of mass and Bernoulli’s theorem, with assumptions that the fluid is incompressible. The model shows close agreement with results from water-bath experiment using a fine-bubble technique. Chenvidyakarn and Woods [18] applies conservation of mass and energy at steady-state to a room with two stacks, a low-level opening, and a uniform source of buoyancy at floor level. Three ventilation regimes were investigated.vFor each regime, flow at each opening was found in terms of the pressure difference across the building at the level of the opening. Good agreement was found between the model and small-scale water-bath experiments. Fitzgerald and Woods [19] similarly investigated the NV of a room with distributed base heating and vents (lower, upper, and also intermediate) at different heights. The intermediate vent is found to act as either an inlet or an outlet, depending on its location relative to the height of neutral buoyancy. Water-bath analogue experiments validate the model. Because transient behavior is a major consideration in larger buildings like theatres, Fitzgerald and Woods [20], investigated the draining flows as affected by the initial temperature difference between interior and exterior. Three regimes were investigated, depending on the initial temperature of the room relative to the exterior temperature and the final equilibrium temperature. The models were developed using conservation of energy and verified using water-bath testing. Andersen [21] developed a fully mixed model for a zone with floor-level buoyancy source, a lower and upper level opening, and assumed adiabatic walls and uniform indoor air temperature. The flow rate defined by these assumptions is: Q (Cd A*)2/3 (B h)1/3
(6)
Li [22] developed two models, which he termed “emptying air-filling box” models, as improvements on Linden’s “emptying water-filling box” models and Andersen’s fully-mixed model. Li [22] retained convective and radiative heat transfer coefficients. He first proposed a model with two temperature zones, where the bottom zone air temperature is warmer than ambient. Volume flow rate is given by:
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Zhiqiang (John) Zhai et al. / Energy Procedia 78 (2015) 2700 – 2705
Q (C A*)2/3 (B (h h Oh ))1/3 d
c
and
c
O
ª Q U c p
1
« « Af
¨ § D ¨ f
¬
©
Where D is the convective heat transfer coefficient at floor, Dr f
1
Dr
1
1
(7)
¸1» · º Dc ¸ » ¹
¼
is the radiative heat transfer coefficient and D c is
the convective heat transfer coefficient at ceiling. Li also proposed a model with a vertical indoor temperature profile, rather than two separate temperature zones. Volume flow rate under this model is given by: 2/3 1 1/3 Q (Cd A*) ( B (1O)) 2
(8)
In comparing the four models, Li showed that Andersen’s model and Linden’s model are simply special cases of his model, for λ = 0 and λ = 1 respectively. He also found that the fully mixed model over-predicts the clean zone height and volume flow rate, while the “emptying water-filling box” model under-predicts the same two parameters. (C) Multiple Openings – Combined Driven Li and Delsante [23] presented analytical solutions for buoyancy driven flow in the presence of both fully assisting and fully opposing winds, also incorporating solar radiation and heat conduction loss through the building envelope. The volume flow rate is given by a cubic equation as a function of 3 terms: one related to heat loss (γ), one related to buoyancy (α), and one related to wind (β). The solutions to this equation result in three roots, and are presented graphically in terms of the described parameters and for different assisting winds case. A similar plot is given for the case of opposing wind, though Li determined that multiple steady-state solutions are possible with the system exhibiting hysteresis. Andersen [24] further investigated this situation and found that unambiguous solutions can be obtained if the initial temperature difference between indoor and outdoor temperature when vents are opened is known. Etheridge [25] also presented a detailed study on buoyancy flows in the presence of unsteady wind conditions. He investigated several transient models with varying levels of simplification, and determines relationships for both mean and instantaneous flow rate. His quasi-temporal inertia model, which approximates the flow as steady at each instant of time and includes an inertia term, is proven to be very accurate against previously published experimental data and is also validated later by Chiu and Etheridge [26]. (2) Multiple Zones The added complexity of multi-zone air flows means numerical methods are generally required to model the behavior. A very limited number of analytical solutions exist. Li [27] listed the governing equations for stack-only, wind-assisted, and wind-opposed two-zone NV. These situations result in cubic equations, for which analytical solutions do exist, but meaningful information is difficult to obtain. Holford and Hunt [28] derived a model for a single story zone connected to a ventilated atrium. The model is comprised of 6 non-linear algebraic equations and one integral equation, and thus must be solved numerically. Holford used the Newton-Raphson method. 2.2. Network Models The general principle behind network airflow modeling is the construction of a matrix of equations representing all airflow paths in a building. A “node” is used to describe each zone connected by one or more airflow paths, and external nodes characterize the external conditions on each façade of the structure. Each airflow path (window, path, etc.) is mathematically described using the Bernoulli equation. Properties including wind and temperature outside the building describe the external nodes. The resulting matrix is then solved numerically, typically by the NewtonRaphson method. El mankibi et al [29] compared the results of this method under different development environment (Matlab/Simulink, Spark and TRNSYS). Boundary nodes are also used to represent the environment outside the building. Those nodes are then interconnected by flow paths, such as crack or windows. Application of mass balance equation on a given zone i with j flow paths gives: N
0 ¦Ui Qik k 1
(9)
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where Qik is the volumetric flow from zone i to zone k and Ui is the air density in the direction of the flow. Air flow is attributed to pressure differences across the openings taking into account the air motion due to the wind and the temperature difference across the opening resulting to buoyancy driven flow. The wind pressure at the external node is calculated from Bernoulli’s equation as follows: 1 Cp UV 2 2
P w
(10) where Cp is the pressure coefficient and V is the wind speed at the height of the building. The reference pressure on the ground being Po,i and according to hydrostatic gradient, the pressure due to stack effect only at a height z, is: Pz ,i Po,i Ui g z
(11)
The pressure difference across an exterior opening at a height z is then equal to: 'Pz ,i
Po,i Po, j g Ui Ua z Pw
(12)
The air flow through large opening is assumed to be bi-directional. Thus, a level of zero pressure level (neutral level: 'Pz ,i 0 ) is located at height ZNL from the ground. The bi-directional flow is then calculated by integrating (15) between bottom or top of the opening and the neutral level: ZNL
QBellow Cd W
P dz 2 'P
Zb Air flow bellow neutral level
Zs
and
QAbove Cd W
2
'P P
dz
(13)
ZNL Air flow above neutral level
Newton-Raphson’s method is then used to solve the system obtained by applying equation (9). 3. Conclusions A review of the analytical models published in the literature reveals that these models are generally only applicable to specific geometries and specific driving forces. The complex interactions between combined driving forces and complex geometries results in sets of non-linear equations which must be solved numerically. For these situations, network airflow models are more appropriate. However, analytical models are capable of describing intra-zonal flow characteristics, while network airflow models typically treat each zone as well-mixed. A variety of commonly used network airflow models are found in studies. The most commonly described in literature is COMIS, CONTAM, and ESP-r. A version of CONTAM has also been recently implemented in to the DOE’s latest building energy simulation tool, EnergyPlus. The further review reveals that the COMIS and CONTAM airflow models are based on the same principles and are executed in an identical fashion. The Airflow Network Module incorporated into EnergyPlus was determined to be merely another version of the same network model. Results also prove that the coupling of the Airflow Network Module within EnergyPlus behaves almost identically to the network model coupled with ESP-r. Previous testing results [30] have shown that the current airflow model can be used to model various NV situations, with an exception in the case of single-sided ventilation. Wind-driven single-sided ventilation cannot be modeled with the current network models. Generally, the most accuracy is achieved for cases with small opening. For larger openings, the model’s predictions are less accurate. Furthermore, the model is heavily dependent on several somewhat ambiguous coefficients including: wind profile exponent, pressure coefficient and discharge coefficient. Adjustment of these coefficients can improve the model’s accuracy [31]. 4. References [1] De Dear, R. J., & G.S. Brager. 2002. Thermal comfort in naturally ventilated buildings: Revisions to ASHRAE standard 55. Energy and Buildings, 34(6):549-561. [2] Seppanen, O., & W. J. Fisk. (2002). Association of ventilation system type with SBS symptoms in office workers. Indoor Air, 12(2):98-112.
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[3] Zhai, Z. 2014. Computational Fluid Dynamics Applications in Green Building Design. Computational Fluid Dynamics Applications in [1] Green Design (Book), pp.1-22, ed. (IEEF). ISBN-13: 978-1494875756, ISBN-10: 1494875756. [4] Lomas, K. J., Eppel, H., Martin, C. J., & Bloomfield, D. P. 1997. Empirical validation of building energy simulation programs. Energy and Buildings, 26(3):253-75. [5] Li, Y., Delsante, A., & Symons, J. 2000. Prediction of natural ventilation in buildings with large openings. Building and Environment, 35(3):191206. [6] Allard, F., & Santamouris, M. (Eds.). 1998. Natural ventilation in buildings: A design handbook (1st ed.) Earthscan Publications, Ltd. [7] Dascalaki, E., M. Santamouris, A, Argiriou, C. Helmis, D.N. Asimakopoulos, K. Papadopoulos, et al. 1995. Predicting single sided natural ventilation rates in buildings. Solar Energy, 55(5):327-341. [8] Haghighat, F., & Li, H. 2004. Building airflow movement - validation of three airflow models. Journal of Architechtural and Planning Research, 21(4):331-349. [9] Furbringer, J., C. Roulet, C, and R. Borchellini. 1996. Annex 23: Evaluation of COMIS. International Energy Agency. [10] Yamanaka, T., Kotani, H., Iwamoto, K., & Kato, M. 2006. Natural, wind-forced ventilation caused by turbulence in a room with a single opening. International Journal of Ventilation, 5(1):179-187. [11] Cockroft, J. P., & Robertson, P. 1976. Ventilation of an enclosure through a single opening. Building and Environment, 11(1):29-35. [12] Warren, P. R. 1978. Ventilation through openings on the one wall only. Energy Conservation in Heating, Cooling, and Ventilation of Buildings, 1(1):186-206. [13] Allocca, C. 2001. Single-sided natural ventilation: Design analysis and general guidelines. MS thesis, MIT. [14] Phaff, J. C., de Gids, W. F., Ton, D.V. van der Ree, & Schijndel, L. L. M. (1980). The ventilation of buildings: Investigation of the consequences of opening one window on the internal climate of a room. Delft, Netherlands. [15] Linden, P. F., Lane-Serff, G. F. & Smeed, D. A. 1990. Emptying filling boxes: The fluid mechanics of natural ventilation. Journal of Fluid Mechanics, 212:309-35. [16] Cooper, P., & Linden, P. F. 1996. Natural ventilation of an enclosure containing two buoyancy sources. Journal of Fluid Mechanics,153-176. [17] Chen, Z. D., Li, Y., & Mahoney, J. 2001. Natural ventilation in an enclosure induced by a heat source distributed uniformly over a vertical wall. Building and Environment, 36(4):493-501. [18] Chenvidyakarn, T., & Woods, A. W. 2005. Multiple steady states in stack ventilation. Building and Environment, 40(3):399-410. [19] Fitzgerald, S. D., & Woods, A.W.2004.Natural ventilation of a room with vents at multiple levels. Building and Environment,39(5):505-521. [20] Fitzgerald, S. D., & Woods, A. W. 2007. Transient natural ventilation of a room with a distributed heat source. Journal of Fluid Mechanics, 591:21-42. [21] Andersen, K. T. 1995. Theoretical considerations on natural ventilation by thermal buoyancy. Proceedings of the 1995 ASHRAE Annual Meeting, 101(1):1103-1117. [22] Li, Y. 2000. Buoyancy-driven natural ventilation in a thermally stratified one-zone building. Building and Environment, 35(3):207-214. [23] Li, Y., & Delsante, A. 2001. Natural ventilation induced by combined wind and thermal forces. Building and Environment, 36(1):59-71. [24] Andersen, K. T. 2007. Airflow rates by combined natural ventilation with opposing wind-unambiguous solutions for practical use. Building and Environment, 42(2):534-542. [25] Etheridge, D. W. 2000. Unsteady flow effects due to fluctuating wind pressures in natural ventilation design - mean flow rates. Building and Environment, 35(2):111-133. [26] Chiu, Y. & Etheridge, D. W. 2004. Experimental technique to determine unsteady flow in natural ventilation stacks at model scale. Journal of Wind Engineering and Industrial Aerodynamics, 92(3-4):291-313. [27] Li, Y. 2002. Analysis of natural ventilation - A summary of existing analytical solutions. IEA ECBCS. [28] Holford, J. M., & G. R. Hunt. 2003. Fundamental atrium design for natural ventilation. Building and Environment, 38(3):409-426. [29] EL Mankibi. M, Cron. F, Michel. P, and Inard C 2006. Prediction of hybrid ventilation performance using two simulation tools. Solar Energy, 80(8): 908-926. [30] Johnson MH, Zhai Z and Krarti M. 2012. Performance Evaluation of Network Airflow Models for Natural Ventilation. HVAC&R Research, 18(3): 349-365. [31] Zhai Z, Johnson MH, Krarti M. 2011. Assessment of Natural and Hybrid Ventilation Models in Whole-Building Energy Simulations. Energy and Building, 43(9):2251-2261.
ScienceDirect Energy Procedia 78 (2015) 2700 – 2705
6th International Building Physics Conference, IBPC 2015
Review of natural ventilation models Zhiqiang (John) Zhaia, Mohamed El Mankibib*,Amine Zoubirb b
a University of Colorado at Boulder, Boulder, CO 80309-0428, USA ENTPE-University of Lyon, 3 rue Maurice Audin, Vaulx en Velin 69120, France
Abstract Natural ventilation (NV) is an important and efficient passive technique to reduce building cooling energy need and improve indoor air quality. NV design requires profound knowledge and accurate prediction of air flow and heat transfer in and around buildings. This paper reviews the important NV models and simulation tools and the comparisons of their prediction capabilities. In one hand, a review of the analytical models reveals that these models are generally only applicable to specific geometries and driving forces. In other hand, results of comparison and assessment between airflow models have shown that the current one can be used to model most NV mechanisms, with an exception of wind-driven single-sided ventilation. For the predictable cases, the most accuracy is achieved for cases with small and simple openings. For larger openings and especially complicated openings, the model’s predictions are less accurate. Furthermore, the model is heavily dependent on several somewhat ambiguous coefficients including: wind profile exponent, pressure coefficient, and discharge coefficient. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ©2015 2015Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL. Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL Keywords: Natural Ventilation; Modeling
1. Main text Natural ventilation (NV) is one of the most efficient techniques, when weather permits, to reduce building cooling energy usage and improve indoor air quality. Research has shown that the acceptable thermal comfort range for natural ventilated buildings is larger than for buildings with standard mechanical HVAC systems (De Dear and Brager [1]). Sepannen and Fisk [2], after reviewing 18 different studies on sick building syndrome (SBS) and ventilation systems,
* Corresponding author. Tel.: +33 (0) 6 42 45 64 75; fax: +33 (0) 4 72 04 70 41. E-mail address: [email protected]
1876-6102 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the CENTRO CONGRESSI INTERNAZIONALE SRL doi:10.1016/j.egypro.2015.11.355
Zhiqiang (John) Zhai et al. / Energy Procedia 78 (2015) 2700 – 2705
2701
found that prevalence of SBS symptoms was 30 to 200% higher in air conditioned buildings as compared to naturally ventilated ones. NV design for buildings requires profound knowledge and accurate prediction of air flow and heat transfer in order to quantify the naturally driven ventilation rates as well as the associated effects on building space temperatures. Computational fluid dynamics (CFD) techniques can provide a robust prediction of NV. They have been used to simulate NV under a variety of conditions, including wind- and buoyancy-driven flows as well as those with combined forces (Zhai [3]). CFD is mostly used to perform simulations on portions of a building (Lomas et al. [4]), particularly where spatial temperature variations exist. Performing an annual CFD simulation of an entire building is impractical, due to the computational complexity and cost of CFD. Reduced-order airflow models such as network models have been developed to quickly predict airflows throughout a building. A variety of different network models have been developed, such as, MIX by Li et al. [5] and AIOLOS by Allard and Santamouris [6], many of which are used internally by the developer. Several studies comparing these models to each other are found in literature, including Dascalaki et al. [7], Haghighat and Li [8], and Furbringer et al. [9]. The general conclusion of these studies is that the models are generally similar, with minor functional differences separating the tools. This research conducted a comprehensive literature review on the state of NV modeling research. 2. Natural Ventilation Models A review of both analytical/empirical models and commonly used network airflow models was performed. Analytical models are only derived for simple geometries and almost entirely for single-zone geometries while network models are applicable for multi-zone structures. For NV, due to the dependency of temperature on stack-driven flow, airflow models are often solved in conjunction with thermal models. 2.1. Analytical and Empirical Models Most analytical models are developed by applying the mass and energy conservation equations to particular configurations. Most of these models have been verified experimentally. (1) Single Zone (a) One Opening Yamanaka et al. [10] experimentally investigated the validity of two single-sided wind-driven ventilation models: the pulsation theory (Cockroft and Robertson [11]) and the mixing layer theory (Warren, [12]). Pulsation theory assumes that air flow is quantified by the fluctuation of pressure across the opening. Yamanaka proved this model was inaccurate for all wind incidence angles except 0°. The mixing layer theory assumes a velocity and pollutant distribution inside the single opening, and ventilation rate is given by:
Q C AU w
(1)
where Q is the ventilation flow rate, C is the airflow coefficient (varies depending on geometry and wind incidence direction), A is the opening area and Uw is the local velocity (wind velocity along the wall at the outside edge of mixing layer). A semi-analytical model for single-sided ventilation driven by buoyancy alone has been developed, based on the fact that the volume flow rate is driven by the pressure difference across the opening and assuming a small temperature difference 'T (Alloca, [13]). The volume flow rate for this configuration, from Bernoulli principles, is: Q
'T Cd A g h Tout 3
(2)
where h is the height of the opening. The general form of the equation for airflow from both stack, wind, and other driving pressure differences is the power law for orifices: Q Cd A
(3)
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Phaff et al. [14] performed a detailed experimental study into the terms and coefficients comprising the Δp in the above equation. They considered contributions from wind, buoyancy, and also included a turbulence constant. Their empirical equation, based on meteorological wind speed rather than local wind speed, is:
Q
A 2 0, 001V Vmet 0, 0035h 'T 0, 01 2
(4)
(b) Multiple Openings – Buoyancy Driven Linden’s work (Linden et al [15]) on the fluid mechanics of both displacement and mixing ventilation forms the basis of much of the analytical modeling of NV. Linden considered steady-state filling and draining behavior of a room with high and low level openings, and point, horizontal line, and vertical line sources of buoyancy, using conservation of volume and buoyancy fluxes. Linden assumes that velocity of air through the vents is related to pressure drop across the vent, and that zones form within the space where the lowest zone’s temperature is equal to ambient. Also, the effect of thermal radiation between surfaces is neglected. For a single buoyancy source, this model uses the following equation for volume flow rate (Li et al [5]):
Q (C A*)2/3 (B (h h ))1/3 d
c
and
A* 2 At Ab At2 A Ab2
(5) where B is the buoyancy flux, h is the height between two vertical openings,
hc is the clean zone height and A* is
the effective area of the two openings (areas At and Ab). Cooper and Linden [16] extended this model to an enclosure with two buoyancy sources, investigating sources of unequal strength the same and opposite sign, and then extended the model to multiple sources (Linden et al. [15]). An approximation that the buoyancy in the plumes from each source remains unchanged though it is rising through stratified layers in the rooms results in some error, which is determined to be acceptable for design purposes, as the volume flow was determined to be strongly dependent on height of the ambient zone and only weakly dependent on buoyancy flux in the plume. Chen et al. [17] suggests a simple multi-layer stratification model of displacement ventilation in a single-zone building driven by a heat source distributed uniformly over a vertical wall. This model, an extension of Linden’s model (Linden et al. [15]), is derived from conservation of mass and Bernoulli’s theorem, with assumptions that the fluid is incompressible. The model shows close agreement with results from water-bath experiment using a fine-bubble technique. Chenvidyakarn and Woods [18] applies conservation of mass and energy at steady-state to a room with two stacks, a low-level opening, and a uniform source of buoyancy at floor level. Three ventilation regimes were investigated.vFor each regime, flow at each opening was found in terms of the pressure difference across the building at the level of the opening. Good agreement was found between the model and small-scale water-bath experiments. Fitzgerald and Woods [19] similarly investigated the NV of a room with distributed base heating and vents (lower, upper, and also intermediate) at different heights. The intermediate vent is found to act as either an inlet or an outlet, depending on its location relative to the height of neutral buoyancy. Water-bath analogue experiments validate the model. Because transient behavior is a major consideration in larger buildings like theatres, Fitzgerald and Woods [20], investigated the draining flows as affected by the initial temperature difference between interior and exterior. Three regimes were investigated, depending on the initial temperature of the room relative to the exterior temperature and the final equilibrium temperature. The models were developed using conservation of energy and verified using water-bath testing. Andersen [21] developed a fully mixed model for a zone with floor-level buoyancy source, a lower and upper level opening, and assumed adiabatic walls and uniform indoor air temperature. The flow rate defined by these assumptions is: Q (Cd A*)2/3 (B h)1/3
(6)
Li [22] developed two models, which he termed “emptying air-filling box” models, as improvements on Linden’s “emptying water-filling box” models and Andersen’s fully-mixed model. Li [22] retained convective and radiative heat transfer coefficients. He first proposed a model with two temperature zones, where the bottom zone air temperature is warmer than ambient. Volume flow rate is given by:
2703
Zhiqiang (John) Zhai et al. / Energy Procedia 78 (2015) 2700 – 2705
Q (C A*)2/3 (B (h h Oh ))1/3 d
c
and
c
O
ª Q U c p
1
« « Af
¨ § D ¨ f
¬
©
Where D is the convective heat transfer coefficient at floor, Dr f
1
Dr
1
1
(7)
¸1» · º Dc ¸ » ¹
¼
is the radiative heat transfer coefficient and D c is
the convective heat transfer coefficient at ceiling. Li also proposed a model with a vertical indoor temperature profile, rather than two separate temperature zones. Volume flow rate under this model is given by: 2/3 1 1/3 Q (Cd A*) ( B (1O)) 2
(8)
In comparing the four models, Li showed that Andersen’s model and Linden’s model are simply special cases of his model, for λ = 0 and λ = 1 respectively. He also found that the fully mixed model over-predicts the clean zone height and volume flow rate, while the “emptying water-filling box” model under-predicts the same two parameters. (C) Multiple Openings – Combined Driven Li and Delsante [23] presented analytical solutions for buoyancy driven flow in the presence of both fully assisting and fully opposing winds, also incorporating solar radiation and heat conduction loss through the building envelope. The volume flow rate is given by a cubic equation as a function of 3 terms: one related to heat loss (γ), one related to buoyancy (α), and one related to wind (β). The solutions to this equation result in three roots, and are presented graphically in terms of the described parameters and for different assisting winds case. A similar plot is given for the case of opposing wind, though Li determined that multiple steady-state solutions are possible with the system exhibiting hysteresis. Andersen [24] further investigated this situation and found that unambiguous solutions can be obtained if the initial temperature difference between indoor and outdoor temperature when vents are opened is known. Etheridge [25] also presented a detailed study on buoyancy flows in the presence of unsteady wind conditions. He investigated several transient models with varying levels of simplification, and determines relationships for both mean and instantaneous flow rate. His quasi-temporal inertia model, which approximates the flow as steady at each instant of time and includes an inertia term, is proven to be very accurate against previously published experimental data and is also validated later by Chiu and Etheridge [26]. (2) Multiple Zones The added complexity of multi-zone air flows means numerical methods are generally required to model the behavior. A very limited number of analytical solutions exist. Li [27] listed the governing equations for stack-only, wind-assisted, and wind-opposed two-zone NV. These situations result in cubic equations, for which analytical solutions do exist, but meaningful information is difficult to obtain. Holford and Hunt [28] derived a model for a single story zone connected to a ventilated atrium. The model is comprised of 6 non-linear algebraic equations and one integral equation, and thus must be solved numerically. Holford used the Newton-Raphson method. 2.2. Network Models The general principle behind network airflow modeling is the construction of a matrix of equations representing all airflow paths in a building. A “node” is used to describe each zone connected by one or more airflow paths, and external nodes characterize the external conditions on each façade of the structure. Each airflow path (window, path, etc.) is mathematically described using the Bernoulli equation. Properties including wind and temperature outside the building describe the external nodes. The resulting matrix is then solved numerically, typically by the NewtonRaphson method. El mankibi et al [29] compared the results of this method under different development environment (Matlab/Simulink, Spark and TRNSYS). Boundary nodes are also used to represent the environment outside the building. Those nodes are then interconnected by flow paths, such as crack or windows. Application of mass balance equation on a given zone i with j flow paths gives: N
0 ¦Ui Qik k 1
(9)
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where Qik is the volumetric flow from zone i to zone k and Ui is the air density in the direction of the flow. Air flow is attributed to pressure differences across the openings taking into account the air motion due to the wind and the temperature difference across the opening resulting to buoyancy driven flow. The wind pressure at the external node is calculated from Bernoulli’s equation as follows: 1 Cp UV 2 2
P w
(10) where Cp is the pressure coefficient and V is the wind speed at the height of the building. The reference pressure on the ground being Po,i and according to hydrostatic gradient, the pressure due to stack effect only at a height z, is: Pz ,i Po,i Ui g z
(11)
The pressure difference across an exterior opening at a height z is then equal to: 'Pz ,i
Po,i Po, j g Ui Ua z Pw
(12)
The air flow through large opening is assumed to be bi-directional. Thus, a level of zero pressure level (neutral level: 'Pz ,i 0 ) is located at height ZNL from the ground. The bi-directional flow is then calculated by integrating (15) between bottom or top of the opening and the neutral level: ZNL
QBellow Cd W
P dz 2 'P
Zb Air flow bellow neutral level
Zs
and
QAbove Cd W
2
'P P
dz
(13)
ZNL Air flow above neutral level
Newton-Raphson’s method is then used to solve the system obtained by applying equation (9). 3. Conclusions A review of the analytical models published in the literature reveals that these models are generally only applicable to specific geometries and specific driving forces. The complex interactions between combined driving forces and complex geometries results in sets of non-linear equations which must be solved numerically. For these situations, network airflow models are more appropriate. However, analytical models are capable of describing intra-zonal flow characteristics, while network airflow models typically treat each zone as well-mixed. A variety of commonly used network airflow models are found in studies. The most commonly described in literature is COMIS, CONTAM, and ESP-r. A version of CONTAM has also been recently implemented in to the DOE’s latest building energy simulation tool, EnergyPlus. The further review reveals that the COMIS and CONTAM airflow models are based on the same principles and are executed in an identical fashion. The Airflow Network Module incorporated into EnergyPlus was determined to be merely another version of the same network model. Results also prove that the coupling of the Airflow Network Module within EnergyPlus behaves almost identically to the network model coupled with ESP-r. Previous testing results [30] have shown that the current airflow model can be used to model various NV situations, with an exception in the case of single-sided ventilation. Wind-driven single-sided ventilation cannot be modeled with the current network models. Generally, the most accuracy is achieved for cases with small opening. For larger openings, the model’s predictions are less accurate. Furthermore, the model is heavily dependent on several somewhat ambiguous coefficients including: wind profile exponent, pressure coefficient and discharge coefficient. Adjustment of these coefficients can improve the model’s accuracy [31]. 4. References [1] De Dear, R. J., & G.S. Brager. 2002. Thermal comfort in naturally ventilated buildings: Revisions to ASHRAE standard 55. Energy and Buildings, 34(6):549-561. [2] Seppanen, O., & W. J. Fisk. (2002). Association of ventilation system type with SBS symptoms in office workers. Indoor Air, 12(2):98-112.
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