Aalborg Universitet. Stochastic Prediction of Ventilation System Performance. Haghighat, F.; Brohus, Henrik; Frier, Christian; Heiselberg, Per

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1 Aalborg Universitet Stohasti Predition of Ventilation System Performane Haghighat, F.; Brohus, Henrik; Frier, Christian; Heiselberg, Per Publiation date: 2 Doument Version Publisher's PDF, also known as Version of reord Link to publiation from Aalborg University Citation for published version (APA): Haghighat, F., Brohus, H., Frier, C., & Heiselberg, P. (2). Stohasti Predition of Ventilation System Performane. Aalborg: Dept. of Building Tehnology and Strutural Engineering, Aalborg University. Indoor Environmental Engineering, No. 122, Vol.. R47 General rights Copyright and moral rights for the publiations made aessible in the publi portal are retained by the authors and/or other opyright owners and it is a ondition of aessing publiations that users reognise and abide by the legal requirements assoiated with these rights.? Users may download and print one opy of any publiation from the publi portal for the purpose of private study or researh.? You may not further distribute the material or use it for any profit-making ativity or ommerial gain? You may freely distribute the URL identifying the publiation in the publi portal? Take down poliy If you believe that this doument breahes opyright please ontat us at providing details, and we will remove aess to the work immediately and investigate your laim. Downloaded from vbn.aau.dk on: January 14, 22

2 Stohasti Predition of Ventilation System Performane F. Haghighat, H. Brohus, C. Frier, P Heiselberg N N "t"""" z ~ Cl. CO.. Ol ;:: o, w ro... E e :::;: w... 't:l E ro :;:::; Cll E N 1- z w > :2 ::.._ (/) Ol '5 (.) e.. ~ ::> ) '5 Cll :: ui E v :: Ll) CO,!; I > v.q CO '5 i.. ;:: Cl. (;) -... ~ ~ N (.) N!!:!..- I ~ > >. 'S (.)...,

3 ..,;. The Indoor Environmental Engineering papers are issued for early dissemination of researh results from the Indoor Environmental Engineering Group at the Department of Building Tehnology and Strutural Engineering, Aalborg University. These papers are generally submitted to sientifi meetings, onferenes or journals and should therefore not be widely distributed. Whenever possible, referene should be given to the final publiations (proeedings, journals, et.) and not to the Indoor Environmental Engineering papers. Printed ataalborg University

4 Stohasti Predition of Ventilatio~ System Performane F. Haghighat, H. Brohus, C. Frier, P Heiselberg

5

6 STOCHASTIC PREDICTION OF VENTILATION SYSTEM PERFORMANCE F. Haghighat 1, H. Brohus 2, C. Frier 2 and P. Heiselberg 2 1 Department of Building, Civil and Environmental Engineering Conordia University, Montreal, Quebe H3G 1M8, Canada 2 Department of Building Tehnology and Strutural Engineering Aalborg University, DK-9 Aalborg, Denmark ABSTRACT Traditionally, predition of ventilation systems performane has been based on deterministi approah, whih implies that the spread of the input parameters values is zero. The deterministi approah is valid if the effet of flutuations in the foring funtions (wind speed and diretion, temperature, radiation, oupants' behavior, et.) is negligible when ompared to the mean value. When random flutuations of the foring funtions are signifiant, the variane of response an no longer be negleted, as for example, for a hybrid-ventilated building, where a part of or the entire required ventilation load is supplied naturally. Most of the parameters influening the performane of a hybrid-ventilated building are inherently stohasti in nature. The paper briefly reviews the existing tehniques for prediting the airflow rate due to the random nature of foring funtions, e.g. wind speed. The effort is to establish the relationship between the statistis of the output of a system and the statistis of the random input variables and parameters of a model. INTRODUCTION Predition of the air infiltration and ventilation of buildings is an essential element in the design of energy effiient buildings. Air infiltration in buildings due to wind-indued pressure is a omplex proess that is highly influened by the turbulent nature of wind. The turbulent wind an be expressed as a stohasti proess omposed by a mean value of the wind veloity superimposed by a flutuating omponent (Haghighat et al., 1988). In addition to the gustiness of the wind, the turbulene in wind-indued pressure is also a result of the interation of the wind and the building envelope. In most of the urrent multi-zone air flow models, air infiltration is alulated by means of a deterministi approah where the omplex wind flutuations are disregarded and the predition of the infiltration rate of the building is based solely on average wind veloity (as well as stak and mehanial fores). However, several measurements and detailed analysis of air infiltration reveals a substantial influene of wind flutuations, espeially when the root mean square of the flutuations is relatively large ompared

7 with the average wind pressures. At the same time there is an inreasing demand for proper infiltration models for the purpose of improved predition of energy onsumption, building safety (fire propagation, transport of smoke and other pollutants), indoor air quality and thermal omfort. Several tehniques have been proposed to alulate the resultant flutuating infiltration. The wind flutuation has two effets: 1) the pulsation flow and 2) the penetration eddies. The pulsation flow has a variation in pressure at the opening, that will indue a flutuation flow due to the ompressibility of the air in the internal spae. Thus, a pulsation flow is produed through the opening whih depends on the magnitude of the flutuating pressure and the size of the enlosure. The penetration eddies have higher frequeny flutuations that enable air exhange at the opening due to smaller sale turbulene with eddy sizes omparable with, or smaller than the opening size. Thus, a turbulent diffusion of air through the opening is produed, and it depends less on the ompressibility effets. Pulsation Model Cokroft & Robertson (1976) studied the single-opening pulsation flow of an enlosure with a single opening, subjeted to a turbulent impinging air stream, and derived a simple theoretial pulsation model to assist in understanding the physial phenomena ausing airflow through the opening. In this model, pulsation flow, q, of a single.,ppening enlosure was aused by longitudinal flutuations of wind, and the ompressibility of air within the enlosure. This was related to the flutuating pressure differene,!:::,p, between the external wind pressure and the internal room pressure in: (1) where CD is the disharge oeffik:j.t, pis the air density and A is the opening area. Assuming an adiabati proess, it was proposed that the flutuating omponent of the pulsation flow into a simple opening enlosure an be obtained by: (2) where y is the polytrophi exponent whih is equal to 1.4 to 1., respetively for adiabati and isothermal flows, Pais the atmospheri pressure, V is the volume of the enlosure, u is the flutuating omponent of the wind veloity, and v is the derease in volume of the original air inside the enlosure. Cokroft & Robertson (1976) further argued that all the air flowing into the enlosure, Q; 11, does not neessarily ontribute to the effetive ventilation of the enlosure. Some of the inflowing pulsations of air are exhausted before mixing with the interior air ours. The net mean effetive flow rate of ventilation air, Qeffi into the enlosure is obtained by: (3) The proportion of air mixed,j;,, depends on the frequeny spetrum of the turbulent air stream. The J;, value is determined from results of their experiments as.37. Mehanial-System-Simulation Model Sasaki et al. (1987) onsidered the flutuation of the airflow through the raks to be influened not only by the stati resistane of the rak but also by the depth of the rak, the air volume behind the rak, and 2

8 the dynami feature of the wind pressure. A building was modelled by a orresponding mehanial system onsisting of mass, resistane, and elasti fores. The airflow is simulated assuming: 1) air in the rak moves as the mass, 2) spae behind the rak works as the spring, and 3) dynami resistane of airflow an be measured by statistial measurement. For an enlosure with a single opening, the orresponding mehanial system an be represented by: d 2 x dx M-+ C- + Kx=f::..pA dt 2 dt (4) where x is the displaement of air in the rak, M is the mass of air in the rak, C is the airflow resistane of the rak, and K is a onstant aounting for the ompressibility of air. By solving the above seond order differential equation, the movements of the air mass displaement x an be obtained for a given frequeny f of flutuating wind veloity. The air infiltration through the rak at frequeny f an be written as (assuming inside pressure is onstant): (5) where x is the magnitude of the x, and l is the depth of the opening. Comparison of the theoretial solutions and the measurements resulj.ing from a speially designed experiment shows that the differenes were within 2%. However, the input needs for detailed temporal pressure profiles of all the exterior openings and the omputation requirement for solving linear differential equations prevent the model be used in realisti appliations. Correlation Models Phaff & De Gidds (198) proposed an empirial orrelation whih desribes a general definition of the ventilation rate through an open window as a funtion of the temperature differene, wind veloity, and flutuating terms. Etheridge & Stanway (1988), and Etheridge & Alexander (198) developed a multi-zone model for prediting air infiltration whih takes into aount the turbulene effet of flutuating wind. Numerial Simulation Model Kazi & Novak (1989) developed a dynami model to simulate the airflow in multi-room buildings subjeted to wind pulsation. Their model was based on the steady flow equation, and attempted to alulate the additional airflow due to low frequeny variation in the pressure field around the building. Governing equations were derived from several equations, inluding ontinuity, energy, Bemoulli's, and the ideal gas equations. Input data must inlude pressures as funtions of time on boundary surfaes of the building. Solutions are obtained by solving a set of non-linear, first-order differential equations in time domain. Resonator Model Holmes (198) studied the flutuating internal pressure mainly for the purpose of wind loading design of building struture and ladding. The ase of a single windward opening was modelled as a damped Helmholtz resonator: 3

9 (6) w h ere C p,- - P; - /(1 2) d -/(I 2) h... 1 d 1 2 p U H an C P, - p 2 p U H are t e time varymg mterna an externa pressure oeffiients, and UH is the mean wind veloity at the roof height. Power Spetrum Analysis Approah A power spetrum analysis approah to model the pulsating air flows due to turbulent wind-indued pressures was developed and applied to single-opening and two-opening ases (Haghighat et al., 1991). The total air flow is divided into mean and flutuating omponents. The equations that govern the flutuating omponents were linearized in order to benefit from the spetral analysis methods. Haghighat et al. (1991) showed that for a given Fourier transform of the external wind-indued pressure pw( w), the resultant Fourier transform of the airflow through a single opening an be expressed by: jaw q(w)= A Pw(w)= H(w)p,Jw) I._!_::_ - pi w 2 + j kw V (7) where)= (-1l 5 is the imaginary unit, k is a flutuating airflow parameter, wis the frequeny, and H(w) is the transfer funtion. The airflow spetrum an be alulated for a given wind pressure spetrum, SP'v( w): (8) The root-mean-square value (RMS) of the flutuating infiltration an be alulated by integrations of the spetra over the frequeny (see Haghighat et al., 1999). The wind pressure spetrum, as input, an be obtained either experimentally or by means of empirial formulae. The internal pressure of this singleopening enlosure, in frequeny domain an be expressed as: (9) The RMS value of internal pressure, p;, an be alulated in similar fashion, as for the infiltration rate, by integration of the spetrum funtion. The results of ase studies showed that, for a single-opening ase, the turbulene in the airflow rate was onentrated in the higher frequeny range (around.1 Hz), while for the two-opening ase, the flutuating airflow rates were mainly aused by the instantaneous pressure differenes, and the frequeny ranges of their turbulene were lower (around the same frequeny range of the wind pressure, at about.8 Hz) (Haghighat et al., 1991). The predited RMS values of flutuating airflow rates are theoretial, and a onversion is required to obtain the effets on the total air exhange rates. Three fators influene the onversion: the "residue" (or "hidden") air in the openings, the mixing proess inside rooms, and the possibility of flow reversal. In the single-opening ase, only the first two fators have effets. For the two-openings ase, the third fator has a major influene while the other two fators have only negligible effets (Haghighat et al., 1992). Further theoretial and experimental efforts are required to better understand and qualify these phenomena. 4

10 SUMMARY AND CONCLUSION The importane of onsidering the flutuating omponents of the wind veloity of air infiltration is disussed. Main features of turbulent wind are desribed together with the physis of flutuation, espeially the two main effets of pulsation flow and penetrating eddies. The different approahes to flutuating infiltration modelling are reviewed, a summary is found in Table 1. Important main topis for further researh in flutuating infiltration modelling are identified in the following. TABLE 1 APPROACHES TO MODELLING Model Pulsation (Cokroft & Robertson, 1976) Mehanial-System-Simulation (Sasaki et al., 1987) Correlation (Phaff & De Gidds, 198) (Etheridge & Alexander, 1986) Numerial Simulation (Kazi & Novak, 1989) Resonator (Holmes, 198) Power Spetrum Analysis (Haghighat et al., 1991)... Features Longitudinal flutuations of wind and ompressibility of air within enlosure ause pulsation flow of single opening enlosure. Airflow through openings is modelled as a mehanial system. Infiltration an be alulated for pressures of single frequeny. Empirial orrelation expressing mean airflow rate through an open window as a funtion of temperature differene, wind veloity, and flutuating terms. Flutuating infiltration assumed proportional to RMS value of wind pressure. The oeffiients depend on opening harateristis and empirial onstants. Governing equations derived from fundamentals are solved numerially. Flutuating internal pressures are obtained numerially from seondorder non-linear differential equation. Power spetrum analysis is used to model pulsating airflow due to turbulent wind-indued pressures. Applied for a single-opening ase and a two-opening ase. Some of the models are ready for use in pratial engineering design, for instane the orrelation models, provided that their range of appliations are properly aknowledged. Other models require greater skills among users in terms of understanding and omputing. Future inorporation of the models in ommerial software for building simulation or as stand alone software demands a higher degree of generalization, i.e. an extension to n openings and m enlosures inside an arbitrary oriented building, et. Simple guidelines for the use of flutuating models would be highly benefiial, like rules of thumb stating when it is appropriate to use the simple deterministi average wind veloity approah, et. An important area is to extend the models to inlude turbulene in flutuating pressure differenes aused by thermal buoyany and unsteady operation of mehanial ventilation. In this respet a signifiant question is whether it is possible to deouple the effet of thermal loads in shape of solar radiation and internal gains from the flutuations aused by wind, or if there will be substantial mutual interations that should be aknowledged. The main purpose of the different tehniques reviewed in this paper is to predit the airflow rate. However, as pointed out by Cokroft and Robertson (1976), some of the inoming air is exhausted before mixing with the room air. They found that less than 4% of the airflow rate ontributed to the "effetive ventilation". This fat raises a ruial need for a kind of ventilation effetiveness that determines the ratio of infiltration air atually ontributing to the air hange rate and the total air flow rate, where part of the air "short-iruits". 5

11 ACKNOWLEDGEMENTS This work is part of the Canadian and Danish ontribution to the work of Annex 35 of the International Energy Ageny "Hybrid Ventilation in New and Retrofitted Offie Buildings". Funding for the Canadian author partiipation was made possible through a ontrat provided by the CANMET - Energy Tehnology Centre of Natural Resoures Canada. The Danish ontribution was supported finanially by the Danish Tehnial Researh Counil (STVF). Their supports are highly appreiated. REFERENCES Cokroft and Robertson (1976). Ventilation of an Enlosure through a Single Opening. Building and Environment 11, Etheridge D. W. and Alexander D. K. (198). The British Gas Multi-Cell Model for Calulating Ventilation. ASHRAE Trans. 86:2, Etheridge D.W. and Stanway R. J. (1988). A Parametri Study of Ventilation as a Basis for Design. Building and Environment 23:2, Haghighat F.,..Brohus, H. and Rao, J. (1999). Modelling Air Infiltration due to Wind Flutuations -A Review. Building and Environment (aepted for publiation). Haghighat F., Fazio P. and Unny T. E. (1988). A Preditive Stohasti Model for Indoor Air Quality. Building and Environment 23:3, Haghighat F., Rao J. and Riberon J. (1992). Modelling Flutuating Airflow through Large opening. Pro. of the 13th A/VC Conferene, pp , Nie, Frane. Haghighat F., Rao J. and Fazio P. (1991). The Influene of Turbulent Wind on Air Change Rates - a Modelling Approah. Building and Environment 26:2, Hill J. F. and Kusuda T. (1975). Dynami Charateristis of Air Infiltration. ASHRAE Trans. 81: 1, Holmes J. D. (198). Means and Flutuating Internal Pressure Indued by Wind. In: Cermak J.E., Editor. Wind Engineering, Pro. of the 5th Intl. Conf., Fort Collins. USA. Kazi N. and Novak P. (1989). A Dynami Model of Air Movement in a Building, Pro. ofclima 2, The 2nd World Congress on Heating, Ventilating, Refrigerating and Air Conditioning, ISBN , Vol. 1, pp , Sarajevo, Yugoslavia. PhaffH. and De Gidds W. (198). Building Ventilation, Investigation ofthe Consequene of Opening one Window on the Internal Climate of a Room, IMG-TNO Report C448, Delft, Netherlands. Sasaki T., Hayashi M. and Aratani N. (1987). On the Ventilating Charateristis of the Spae under the Flutuating Wind Pressure. Pro. of ROOMVENT '87, Air Distribution in Ventilated Spaes, Session 4a. 6

12 RECENT PAPERS ON INDOOR ENVIRONMENTAL ENGINEERING PAPER NO. 19: E. Bjrn: Simulation of Human Respiration with Breathing Thermal Manikin. ISSN R9944. PAPER NO. 11: P. Heiselberg: Hybrid Ventilation and the Consequenes on the Development of the Faade.ISSN R33. PAPER NO. 111 : P. Heiselberg, M. Pedersen, T. Plath: Loal Exhaust Optimization and WorkerExposure. ISSN R34. PAPER NO. 112: K. Svidt, P. Heiselberg: Push-Pull Ventilation in a Painting Shop for Large Steel Construtions. I SS N R35. PAPER NO. 113: P. Heiselberg: Design Priniples for Natural and Hybrid Ventilation. ISSN R36 PAPER NO. 114: A. Andersen, M. Bjerre, Z.D. Chen, P. Heiselberg, Y. Li: Experimental Study of Wind-Opposed Buoyany-Driven Natural Ventilation. ISSN R37 PAPER NO. 115: P. Heiselberg, K. Svidt, P.V. Nielsen: Windows- Measurements of AirFlow Capaity.ISSN R4 PAPER NO. 116 ~ K. Svidt. P. Heiselberg, P.V. Nielsen: Charaterization of the Airflow from a Bottom Hung Window under Natural Ventilation. ISSN R41 PAPER NO. 117: Z. Yue, P.V. Nielsen: Flow Pattern in Ventilated Rooms with Large Depth and Width.ISSN R42. PAPER NO. 118: P.V. Nielsen, H. Dam, L.C. Srensen, K. Svidt, P. Heiselberg: Charateristis of Buoyant Flow from Open windows in Naturally Ventilated Rooms. ISSN R43. PAPER NO. 119: P.V. Nielsen, C. Filholm, C. Topp, L. Davidson: Model Experiments with Low Reynolds Number Effets in a Ventilated Room. ISSN R44. PAPER NO. 12: P. Lengweiler, P.V. Nielsen, A. Moser, P. Heiselberg, H. Takai: Experimental Method for Measuring Dust Load on Surfaes in Rooms. ISSN R45. PAPER NO. 121 : L. Davidson, P.V. Nielsen, C. Topp: Low-Reynolds Number Effets in Ventilated Rooms: A Numerial Study R46. PAPER NO. 122: F. Haghighat, H. Brohus, C. Frier, P. Heiselberg: Stohasti Predition of Ventilation System Performane. ISSN R47. PAPER NO. 123: H. Brohus, F. Haghighat C. Frier, P. Heiselberg: Quantifiation of Unertainty in Thermal Building Simulation. Part 1: Stohasti Building Model. ISSN R48. PAPER NO. 124: H. Brohus, F. Haghighat C. Frier, P. Heiselberg: Quantifiation of Unertainty in Thermal Building Simulation. Part 2: Stohasti Loads. ISSN R49. Complete list of papers:

13 ISSN R47 Dept. of Building Tehnology and Strutural Engineering Aalborg University, Deember 2 Sohngaardsholmsvej 57, DK-9 Aalborg, Denmark Phone: Fax:

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