A survey of airflow models for multizone structures

Energy and Buildings, 18 (1992) 79-100

79

A survey of airflow models for multizone structures H e l m u t E. F e u s t e l a n d J u e r g e n Dieris Indoor Environment Program, Applied Science Division, Lawrence Berkeley Laboratory, Berkeley, CA 94720 (USA)

(Received December 14, 1990; accepted February 6, 1991; revised paper received March 1, 1991)

Abstract Airflow models are used to simulate the rates of incoming and outgoing airflows for a building with known leakage under given weather and shielding conditions. Additional information about the flow paths and air-mass flows inside the building can only be made by using multizone airflow models. In order to obtain more information on multizone airflow models, a literature review was performed in 1984. A second literature review and a questionnaire survey performed in 1989 revealed the existence of 50 multizone airflow models, all developed since 1966, two of which are still under development. All these programs use similar flow equations for crack flow, but differ in the versatility to describe the full range of flow phenomena and the algorithm provided for solving the set of nonlinear equations. This literature review has found that newer models are able to describe and simulate the ventilation systems and interrelation of mechanical and natural ventilation.

Introduction Airflow m o d e l s are u s e d t o simulate t h e r a t e s o f i n c o m i n g a n d o u t g o i n g airflows f o r a building with k n o w n l e a k a g e u n d e r given w e a t h e r a n d shielding conditions. Airflow m o d e l s c a n b e divided into t w o main c a t e g o r i e s , single-zone m o d e l s a n d m u l t i z o n e models. Single z o n e m o d e l s a s s u m e t h a t t h e s t r u c t u r e can b e d e s c r i b e d b y a single, well-mixed zone. T h e m a j o r a p p l i c a t i o n f o r this m o d e l t y p e is t h e singlestory, single-family h o u s e with n o internal p a r t i t i o n s (e.g., all internal d o o r s axe o p e n ) . A large n u m b e r o f buildings, h o w e v e r , h a v e s t r u c t u r e s t h a t w o u l d c h a r a c t e r i z e t h e m m o r e a c c u r a t e l y as m u l t i z o n e structures. T h e r e f o r e m o r e detailed m o d e l s h a v e b e e n d e v e l o p e d , w h i c h also take internal p a r t i t i o n s into a c c o u n t . F i g u r e 1 s h o w s a simple m u l t i z o n e n e t w o r k [ 1 ]. Multizone airflow n e t w o r k m o d e l s deal with t h e c o m p l e x i t y o f flows in a building b y r e c o g n i z i n g the effects o f internal flow restrictions. T h e y r e q u i r e e x t e n s i v e i n f o r m a t i o n a b o u t flow c h a r a c t e r i s t i c s a n d p r e s s u r e distributions and, in m a n y cases, are t o o c o m p l e x to justify t h e i r u s e in p r e d i c t i n g flow f o r simple s t r u c t u r e s s u c h as single-family r e s i d e n c e s [2]. As f o r t h e i r single-zone c o u n t e r p a r t s , t h e s e m o d e l s are b a s e d on the m a s s - b a l a n c e equation. Unlike t h e single-zone a p p r o a c h , w h e r e t h e r e is o n l y o n e in-

0378-7788/92/$5.00

Fig. 1. Simple multizone network.

t e r n a l p r e s s u r e to b e d e t e r m i n e d , the m u l t i z o n e models must determine one pressure for each of t h e zones. This a d d s c o n s i d e r a b l y to the c o m p l e x i t y o f t h e n u m e r i c a l solving algorithm, b u t b y t h e s a m e t o k e n , t h e m u l t i z o n e a p p r o a c h offers great p o t e n t i a l in analyzing infiltration and ventilation airflow distribution. T h e a d v a n t a g e of m u l t i z o n e models, b e s i d e s b e i n g able to simulate infiltration in l a r g e r buildings, is t h e i r ability t o calculate m a s s flow i n t e r a c t i o n s bet w e e n the different zones. U n d e r s t a n d i n g the airm a s s flow in buildings is i m p o r t a n t for several reasons: • e x c h a n g e o f outside a i r w i t h inside air is n e c e s s a r y f o r building ventilation;

© 1992- Elsevier Sequoia. All rights reserved

80

• energy consumed to heat or cool the incoming air to inside comfort temperature; • air needed for combustion; • airborne particles and germs transported by airflow in buildings; • smoke distribution in case of fire. The air-mass flow distribution for a given building is caused by pressure differences, whether evoked by wind, thermal buoyancy, mechanical ventilation systems or a combination of those. The distribution of openings in the building shell and the inner paths also influence the airflow. The openings can be varied by the inhabitants. This can lead to significant differences in the pressure distribution inside the building. Figure 2 shows in detail the influence of pressure distribution on the air-mass flow distribution. In terms of air-mass flow, buildings are complicated interlacing systems of flow paths. In this grid system the joints are the rooms of the building and the connections between the joints simulate the flow paths including the flow resistances caused by open or closed doors and windows or background leakage of the partitions. The boundary conditions for the pressure can be described by the grid points outside the building. The wind pressure distribution depends on the velocity and the direction of the wind, the terrain surrounding the building, and the shape of the building. If the physical interrelationship between

-velocity Wind

Mechanical

-direction Temperature

Ventilation

I

Differences

Systems

Surroundings

I

I

Vertical Flow

I Fan- and Duct

Shape of the

Resistance

C.haracteristics

Windpressure

Thermal

Imposed

Distribution

Buoyancy

Pressure

Building

Building .... ]Inhabitants Behaviour

]-

Leakage ] Configuration~ Inside Pressure Distribution Air Flow Distribution

Fig. 2. Influence of pressure distribution on the air-mass flow in buildings.

the flow resistance and the airflow is known for all flow paths, the airflow distribution for the building can be calculated, as long as there is no density difference between outside and inside air. Differences in density of the air, due to differences between outside and inside air temperatures or moisture content, cause further pressures in the vertical direction, again influencing the air-mass flow. Mechanical ventilation can also be included in this network. The duct system can be treated like the other flow paths in the building. The advantage for calculating airflow distribution effects of mechanical ventilation systems is that the duct pathways, as well as their connections with the building, are known. In the case of mechanical ventilation systems the fan can be described as the source of pressure differences, lifting the pressure level between two joints according to the characteristic curve of the fan. Because of the nonlinear dependency of the volume flow rate on the pressure difference, the pressure distribution for a building can be calculated only by using a method of iterations. Large quantities of computer storage were necessary for the early models to describe buildings with arbitrary floor plans and to solve the set of nonlinear equations.

Literature review and questionnaire survey A literature review undertaken in 1984 [3 ] revealed 26 papers describing 15 different multizone infiltration models which had been developed in eight countries. A recent questionnaire survey produced additional information about the status of network models. One of the first models we found was Jackman's model LEAK [4] which was published in 1970. In 1974 it was followed by the NRCC model [5], which was the first one available to interested parties. Indeed, this numerical tool is probably still the most widely used multizone infiltration model. Several multizone models were developed in the aftermath of the oil price crises. Between 1975 and 1977 a series of steps were taken at Technische Universitaet, Berlin, to develop such a model. This resulted in the program STROM [6] which was later extended to handle HVAC systems and has recently been rewritten to improve the solver and to be combined with a thermal building simulation model [7]. Concurrent with STROM, ELA 4 [8] was developed. The models VENT 1 and VENT 2 [9] as well as BREEZE [10] were developed in the late 1970s by researchers from British Gas and the Building Research Establishment. In the early 1980s,

81 the first versions of Nantka's INFILTRATION & VENTILATION [11], Walton's AlRNET [12], and Herrlin's MOVECOMP [ 13 ] appeared. The latter two programs were the first to address the mathematical problem of solving the set of nonlinear equations for zones with very different leakage characteristics. Open doorways in otherwise tight constructions are the main cause of significant problems in convergence. This has been solved by introducing underrelaxation factors to the well-known Newton method. KGVCP from Hayakawa dates back to 1979 [14]. More recent work done in Japan has been published by Ishida and Udagowo [15], as well as Hayashi and Urano [16], Sasaki [17], Okuyama [18], and Matsumoto and Yoshino [ 19]. France has also developed several multizone models; the recent survey unveiled models from CSTD, 1NSA [20] and EDF. From Brazil, Melo's model FLOW2 [21] has been discovered. The latest development in infiltration modeling is the COMIS model [22 ]. In a twelve-month period, ten scientists from nine countries, working together at Lawrence Berkeley Laboratory, developed a multizone model on a modular base. Because of its modular structure, COMIS is designed to expand its capability to simulate buildings. To accomplish a user-friendly program, special emphasis was given to input and output routines. Support of the international group by IEA's Air Infiltration and Ventilation Centre will help the wide distribution of this model to all interested parties. COMIS can be used as a stand-alone infiltration model with input and output features, or as an infiltration module for thermal building simulation programs. It also serves as a module library. One of the major tasks for the program user is to find a method of determining the wind pressure distribution for a building. This can be done by measuring the wind pressure distribution on a scale model in a wind tunnel or by using measured data from available literature. Only few attempts have been made to calculate the wind pressure distribution. In order to calculate the Cp distribution for buildings, the COMIS group worked on a method based on a parametrical study, to determine the C, values [23]. Crack flow, large openings and mechanical ventilation systems can be simulated by some of the models. Furthermore, additional flows, i.e., simultaneous two-way flow at large openings and wind turbulence effect at single-sided windows, etc., were studied. Airflow rates through doorways, windows and other c o m m o n large openings are significant ways in which air, pollutants and thermal energy are

transferred from one zone of a building to another. In the previous survey of multizone infiltration models, however, none of the described codes were able to solve this problem in any other way than to divide the large opening into a series of small ones described by crack flow equations. Therefore, COMIS's contribution to this fundamental problem was to describe the physical problem, review the various solutions developed in the literature and compare these solutions using both a numerical and a physical point of view. In most cases the temperature of the air in a crack is quite different from the temperatures of the zones on either side of the crack. Furthermore, air leakage performance measurements are usually performed in a certain temperature condition, but results are used at different temperatures. The temperature variation, however, has a big influence on the air leakage flow due to changes in the air viscosity and air density. Unfortunately, almost all the models dealing with air leakage characteristics ignore this phenomenon. Heating, ventilating and air-conditioning (HVAC) systems are composed of ducts, duct fittings, junctions, fans, air filters, heating and cooling coils, airto-air heat exchangers, flow controllers, etc. Several modeling programs for ventilating systems were developed. Calculating the infiltration and ventilation flow rates requires the solution of a nonlinear system of equations. The main task is to find an efficient solving method. The starting point is the Newt o n - R a p h s o n method, with derivatives, operating on a node-oriented network which, in most cases, quickly brings about the convergence of the system of equations. Although network computer models are available, there is an obvious need for simplified multichamber infiltration models capable of providing the same accuracy as the established single-cell models. The extended crack model is the simplest multizone model. It is used to design conditioning loads and size the conditioning equipment [24]. The method is based on the single-zone crack model and has been refined to multizone applications by also taking into consideration the crack flow through internal partitions. Buildings are characterized according to their cross flow and stack flow capabilities. The stack pressures of the core zones for multistory structures are pre-calculated for design weather conditions and published in reference tables. Together with pressures due to the effect of wind and permeability distribution, this enables a user to calculate the infiltration for each of the outside zones.

82 The simplified multizone infiltration model developed at LBL [25] is able to calculate the airflow distribution for arbitrary structures in any given weather condition. The basic idea is to determine the flow network and to calculate the resultant air permeability of a zone from the combination of flow paths arranged in series a n d / o r parallel. The use of these equations assumes that all permeabilities have the same flow characteristics and, therefore, the same exponent, n. Airflows caused by separate mechanisms (such as wind and thermal buoyancy) are not able to be added because the flow rates are n o t linearly propo.rtional to the pressure differences. To superimpose the flows, it is ne c e s s a r y to add the pressures. Several lumped parameters reflecting the different permeability distributions of the building's envelope and the flow resistances inside the building were introduced to describe the airflow distribution. To keep the model simple, no mass-balance equation is used to predict the airflows. Because of the precalculation of the simplified network, the model gives a comprehensive understanding of the flow characteristics of the structure under investigation. The model is simple to use and requires only simple mathematical tools, e.g., p o c k e t calculator. In terms o f t he total n u m b e r of returned questionnaires, this r e c e nt survey represents the most comprehensive review of current r e s ear c h in developed multizone infiltration models. The questionnaires were mailed to addresses provided by the Air Infiltration and Ventilation Centre [26, 27]. Fifty multizone infiltration models developed in 16 countries are r e pr e s ent ed in this survey. In addition to the general references, m o r e than 60 papers describing the programs in detail are listed in Appendix B to g ethe r with the names and addresses of the authors. Of those models for which questionnaires were not returned, information was collected from the reviewed literature. In cases where the reviewed p a p e r did not give a reasonable answer to a certain pr obl e m or where information was missing from a r e t u r n e d questionnaire, a question mark was entered in the list of models. The summarized list of multizone airflow m o d e l s found in the literature is r e p r o d u c e d in Appendix A. The current addresses of the authors including their r e f e r e n c e s are shown in Appendix B. Equations are r e p r o d u c e d separately in Appendix C.

Discussion T h e s u r v e y o f m u l t i z o n e n e t w o r k m o d e l s is s u m m a r i z e d in Table 1. It s h o w s that 3 4 m o d e l s h a v e

been written in FORTRAN (FORTRAN IV (F IV), FORTRAN V (F V), and FORTRAN 77 (F 77). The program m i ng language BASIC has been used four times; followed by HPL with three and C with two applications. PASCAL and dBaseIV have been' used for the development of one mQdel each. Among the analyzed models it appeared that 14 were developed on mainframe computers, 15 on PCs and 11 on workstations. In the past, large amounts of c o m p u t e r storage were necessary when calculating the airflow distribution of more complicated buildings. Nowadays m ost progr a m s use solvers which reduce the space requirement, e.g., band matrices or the skyline method. The Newton m e t h o d is the m ost c o m m o n tool used to solve the set of nonlinear equations. The majority of the program s use a technique based on Newt o n - R a p h s o n . Other algorithms are used less frequently. The limits of zones and openings per zone a model can handle depends on c o m p u t e r storage. Due to the limited availability of c o m p u t e r storage, most of the earlier models were not able to handle more than 100 zones. Models developed later are able to handle an unlimited n u m b e r of zones. Approximately one third of the models do not have an interactive input option and the output features listed show that only few models use graphical output or statistical functions rather than files comparable to the arrays used by the model. These features are an indication of a user-unfriendly model. CAD input and 3-D building description are not necessary to run the program, but would increase the user-friendliness. Unfortunately, these input features belong to the class of "special design", and are rarely integrated in these kinds of models. Only 19 models take into consideration o c c u p a n t schedules which can lead to significant differences in the pressure distribution. The output features show that the graphical output and the statistical functions are less applied than files used by the model. Twenty-four of the models use a separate input p r o g r a m and twenty models are based on a modular structure. A modular structure might b e m o r e advantageous for further development, because the m o d e l would be easier to expand. A combination with ot her models would also be easier to implement. Fifteen of the models allow a combination with a thermal model and thirteen m o d e l s are coupled with a pollution model. Less than one third (15) of t he m o d e l s are available to third parties. S o m e m o d e l s are n o t available before completing and testing. Fifteen m o d e l s are n o t available to the public and axe written as research

83 TABLE 1. Review of multizone airflow infiltration network models

Program

Language

:

34 4 1 2 3

FORTRAN BASIC PASCAL iC HPL dBaseIV

1

Computer

Type :

Main Frame Computer Work Station Personal Computer Solver

14

11 15

:

H a r d y - Cross - M e t h o d Newton - Raphson M e t h o d Levenberg - M a r q u a r d - M e t h o d Drown - C o n t e - M e t h o d Secant - M e t h o d R u l e "falsi" Gaussian - Elimination B e t a - Method by N e w m a r k Limits

max. max. max. max.

1

25 1 1

3 1 1 1

:

<~ 1 0 0

number number number number

of of of of

zones opening/zone shafts/corridors/floors mechanical v e n t i l a t i o n system

Input Features

:

interactive input CAD input w e a t h e r d a t a from w e a t h e r files 3 - D building description schedules (e.g., occupants) ! Output

Features

:

file of a r r a y s used by the model graphical output s t a t i s t i c a l functions Structure

:

separate input program modular structure Combination

with other models

100

unlimited

7 3 2 2

18 23 23 20

yes

no

15 1 24 10 lg

21 30 14 26 17

14 19 13 14 14

yes

no

not specified

29 12 5

6 23 29

15 15 16

yes

no

not specified

24 20

14 14

12 16

not specified

!not specified

yes

no

combined w i t h t h e r m a l model combined w i t h pollution model

15 13

24 26

11 II

Availability

no

yes

yes, but

15

15

:

p r o g r a m a v a i l a b l e to t h i r d parties

:

>

18 17 17 18

tools, r ath er than for the use of professional engineers or architects.

Conclusions This literature review and the questionnaire survey s h o w that an extensive research effort has been made in the last five years to develop an airflow model for multizone structures. Especially the maximum number of z o n e s the models can handle has been increased due to reduced computer storage requirements. Some of the models have been extended with special input and output features. Fifteen of the models are available to third parties and fifteen models have been written as research tools, and are dimcult to use. This might be the reason t h e y are not available to third parties.

12

The development of multizone infiltration and ventilation models shows a relatively slow evolution. Lack of exchange of information, restricted distribution of models, p o o r documentation, and lack of a flexible structure are probably the reasons why models developed in the early seventies are n o t v e r y different from those developed in the late eighties. Although several of the models discovered during this survey serve a particular purpose, t h e y could have b e e n developed using existing models. The COMIS workshop was trying to o v e r c o m e these p r o b l e m s by creating a multizone infiltration model with a modular structure which will allow modules t o be c h a n g e d easily. The availability of the p r o g r a m and its d o c u m e n t a t i o n t o g e t h e r with the international authorship should help to establish COMIS as an

84 infiltration standard on which specific applications can be built.

Future outlook Along with stand-alone infiltration models, network models will also find their way into thermal building simulation models. With the expected advances in the development of the next generation of building simulation programs, infiltration modules will be needed for implementation in the program libraries. Future tasks include the development of methods to determine the required input parameters, especially the wind pressure distribution. Further work must be done through sensitivity studies to reduce the input requirement and to increase user-friendliness by using the output features of the PCs. Validation of the models is another essential task. In order to understand physical p h e n o m e n a related to transport mechanism in buildings and to develop numerical descriptions, measurements must first be performed under steady-state conditions. It is necessary, in order to measure mass flow transport mechanism accurately, to be able to control the pressure level and its fluctuation for each of the outside walls. This is only possible if the test building itself is located in a building. Such a test facility would not only validate airflow models as a whole, but would also help to validate the tracer-gas techniques used to validate infiltration models in field experiments. Recent developments in measurement techniques open new possibilities to study physical phenomena and use the results for comparison with results from the model. Some data sets for evaluation purposes have been produced based on i n s i t u measurements of heavy instrumented buildings. Before these data sets can be used for model evaluation, however, internal model comparisons based on benchmark buildings have to be performed. The Energy Conservation in Buildings and Community Systems Program of the International Energy Agency adopted a new working group (Annex 23) to study physical p h e n o m e n a causing airflow and pollutant transport (e.g., moisture) in multizone buildings and to develop modules to be integrated in a multizone airflow modeling system. The system itself shall be user-friendly and structured to be incorporable in thermal building simulation models. Furthermore, special emphasis shall be given to provide data necessary to use the system (e.g., wind pressure distribution, default values for leakage of building components, material properties like ab-

sorption and desorption). The comparison between results from the model and from i n s i t u tests is an important part of this Annex. Close cooperation is envisaged, with regard to state-of-the art reviews, data collection, coordi_r/ation of work, e.g., defining cases for eyaluation purposes with other pertinent projects. The work to be carried out will be complementary with the above-mentioned Annexes. The Air Infiltration and Ventilation Centre will, as part of its on-going work plan, act as a vehicle for disseminating the results of this particular Annex. A data base for evaluation purposes is going to be prepared by AIVC. The Centre has already started to collect wind pressure data and leakage data. Acknowledgements We would like to acknowledge the program authors for their cooperation in responding to our questionnaires, for without this information the different programs could not have been summarized. This work was jointly supported by the Carl-Duisberg-Gesellschaft, K61n, FRG, and the Assistant Secretary for Conservation and Renewable Energy, Office of Building and Community Systems, Building Systems Division of the US Department of Energy under Contract No. DE-AC03-76SF00098.

References 1 M. Liddament,A i r Infiltration Calculation Techniques -An Applications Guide, Air Infiltration and Ventilation Centre, Warwick, UK, June 1986. 2 ASHRAE 1985 Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1985, Ch. 22. 3 H. E. Feustel and V. M. Kendon, Infiltration models for multicellularstructures -- a literaturereview,Energy Build., 8 (2) (1985) 123-136, I_,BL-Rep. No. 17588, Lawrence Berkeley Laboratory, Apr. 1985. 4 P. J. Jackman, A study of natural ventilation of tall office buildings, J. Inst. Heat. Vent. Eng., 38 (1970). 5 D. M. Sander, FORTRAN/V Program to calculate Air Infiltration in Buildings, DBR Computer Program No. 37, National Research Council Cax~la, 1984.

6 H. E. Feustel, Entwicklungeines FORTRANProgrmmnszur Bestimmung der Luftstromverteilungin Geb~uden, Thes/s, Teclmische Universit~t, Berlin, 1977. 7 Jiaaxiong Guo, Weiterenturicklung des Programms mit dem Ergelmis einer Beracksichtigung thermischer Dm,ckd ~ e r e n z e n auch innerhalb vine~ Geschosses und einer spfirbaren Verrinoerung des R e c h e n z e i t ~ Interner Institutsbericht, Technische Universit~t, Berlin, 1988. 8 W. F. de Gids, Calcul~ion Method f o r the Natural Ventilation o f Buildings, TNO Research Institute for Environ-

mental Hygiene, Delft, 1977.

85 9 D.W. Etheridge and D. K. Alexander, The British Gas multicell model for calculating ventilation, ASHRAE Trans., 86 (Part II) (1980). 10 E. Evers and A. Waterhouse, A Computer Model f o r Analysing Smoke Movement in Buildings, Building Research Establishment, 1978. 11 M. Nantka, A numerical method for air change rate of buildings calculated, Proc. 5th Int. Conf. on HVAC, Praha, 1981. 12 G. N. Walton, T h e n n a / A n a l y s i s Research Program Reference Manual~ NBSIR 83-2555, US Department of Commerce, 1983. 13 M. K. Herrlin, MOVECOMP: a static multicell air flow model, ASHRAE Trans., 91 (Part 2B) (1985). 14 S. Hayakawa and S. Togari, F/mz Rate Variation of Air Conditioning Systems due to Stack Effect and Opening a Window, Rep. No. 30, Kajima Institute of Construction Technology, Japan, 1979. 15 K. Ishida and M. Udagowo, Validation of the Ventilation Net Work Model for the Estimation of Room Temperatures and Heat Load of Residential Buildings with Measured Data, Trans. Archit. Inst. J p ~ , (1988). 16 T. Hayashi, Y. Urano, T. Watanabe and Y. Ryu, Passive system simulation program PSSP and its applications, Proc. Building Energy Simulation Conf., Seattle, WA, 1085. 17 T. Sasaki, Der Lueftungszustand von der Luftschicht durch Wind-Unruhe, Trans. Archit. Inst. Jpn., (372) (1987). 18 H. Okuyama, Network numerical analysis method for heat transfer and air flow in buildings, Proc. 17th Syrup. Committee of Building Heat Transfer, Building Environment Committee of Architectural Institute of Japan, 1987. 19 M. Matsumoto and H. Yoshino, A calculation method for predicting air ponution in multi-celled buildings, Proc. Meet. of the Tohoku Branch of the Architectural Institute of Japan, 1088. 20 D. Cacavelli, J. J. Roux and F. Allard, A simplified approach of air infiltration in multizone buildings, Proc. 9th AIVC Co~fi., Gent, 1988, Air Infiltration and Ventilation Centre. 21 C. Melo, FLOW - an algorithm for calculating air infiltration into buildings, Proc. ICBEM '87 Int. Cong~ss Building Energy Management, Lausanne, Switzerland, 1987.

22 H. E. Feustel et aL, The COMIS infiltration model, Proc. Building Simulation '80, Int. Building Performance Simulation Assoc., Vancouver, 1989. 23 H. E. Feustel and A. Raynor-Hoosen (eds.), Fundamentals of the Multizone A i r Flow Model -- COMIS, Tech. Note 20, Air Infiltration and Ventilation Centre, Warwick, UK, May, 1990. 24 German Standard DIN 4701: Regeln fi~r die Berechnung des Wdrmebedarfs van Gebduden~ Tell 1: Grundlagen der Berechnung, Teil 2: Tabellen, Bilder, Algorithmen Beuth Verlag Berlin, Berlin, 1983. 25 H. E. Feustel and M. H. Sherman, A simplified model for predicting air flow in multizone structures, Energy Build., 13 (3) (1989) 217-230. 26 P. Charlesworth, 1086 Survey of Current Research into Air I~fdtration and Related Air Quality Problems in Buildings, Tech. Note 19, Air Infiltration and Ventilation Centre, Warwick, UK, Dec. 1986. 27 J. Blacknell, A Subject Analysis of the AIVC's Bibliographic Database -- AIRBASE (6th edn.), Tech. Note 25, Air Infiltration and Ventilation Centre, Warwick, UK, Jan. 1989.

Appendices The following appendices describe the reviewed literature and the results of the questionnaire survey in a tabular form. Fifty different multizone airflow models are listed in Appendix A. A question mark was entered in the Table of models where the reviewed p a p e r did not give a reasonable answer to a certain probl em or where information was missing from the r e t u r n e d questionnaire. The authors of the models can be found in Appendix B. T o g e th e r with the authors of the c o m p u t e r models and their current addresses, m o r e than 60 papers describing the models in detail are listed in Appendix B. Equations used by the models as well as a Nomenclature are shown separately in Appendix C.

N o t e s u s e d in A p p e n d i x A o.1

Abbreviations used for the computer language: Fortran F F 77 Fortran 77 MS MicroSoft FIV Fortran IV program language C C HP Basic 4.0 Hewlett Packard Basic 4.0 FV Fortran V dBaseIV Data Base Language HPL Hewlett Packard Language HP-Special Hewlett Packard Special

0.2

Abbreviations used for the computer type: PC personal computer M mainframe WS workstation VAX virtual address extension IBM International Business Machines (continued on p. 91)

A

--

11o

Program Availability -program available to third parties yes, but z3

t3o no

yes yes

Combination With Other Models -combined with thermal model -combined with pollution model

uo uo no

no rio /to no rio

2or3 2or3

Iteration 13D

? ? ? ? ?

6D

2_2

ID ID ID

~lg:2-1 ? ? ?

no uo

no no

?

no uo no rio

?

unlimited

lO0

13C

N-R

yes

IG 2D 3B 4E 5C 6D constant yes yes yes

F + Basic PC MS-DOS/DOS

Structure -separate input program -modular structtre

Output -file of arrays used by the model -graphical output -statistical functions

Input -interactive input -CAD-input -weather data from weal/wr tiles -3-D building description -schedules (e.g., occupants)

Limits -max. number of zones -max. number of oponings/zon~ -max. number of shafts/corridors/floors -max. number of mech~ical ventilation systems

Algorithm To Solve Nonlinear Set Of Equations °4 -name of algorithm°s -equation

Equations °.s -flow tlrough cracks -flow through large openings -flow through duct work -fan flow characteristics -wind pressure -thermal buoyancy -outside pressure fluctuation -circulation flow on lmge openings -single sided ventilation -cross ventilatien -presanre coefficient (only if calculated) -temperature gradient

General -name -progr~n-langange°'1 -written for computer typen2 -written for o ~ g system so~ I.I

List of multizone airflow models

Number (for authors see Appendix B)

Appendix

?

uo

no

yes

yes no

yes no no

no no yes rlo yes

20

20 20 ?

N-R 13C

12A

yes4.5

yes no

yes rio

yes no no

no no yes no yes

unlimited unlimited unlimited unlimited

Newton 4.4 13F

8D yes

y~s yes4.3

collstant 5C 6D

4A 5D 6B ? 9 .9 ?

IE 2D

PSSP/MV14a F77 M / P C 4"2 94.2

IE 2D

F77 + MS M/PC ?

yes,but s.7

no no

yes yes

yes no no

yes no y e s / ~ s.6 yes yes

sees .5 ? ? ?

see5.4 ?

constant

yes5.3

yess-2

1E 2D 3C 4B 5B 6B

ETIMCELL Pascal PC MS-DOS 3.3

5~a

yes

no no

yes no

yes no no

no no yes no no

8 12 2

13A

?

5E

IB 2D ? .9

VENT F 77 M

no

nO

nO

no yes

yes no no

no yes no no

no

rule "falsi" 13D

5C 6D

IE 2G 3E

sees.~ F M ?

no

no yes

yes nO no

yes yes yes yes yes

N-R 13 B

? ? ? ?

IE 2D 3E 4E 5D 6B 7A

see ~.1 Basic PC ?

yes, but 9 2

yes yes

yes yes

yes yes no

no no yes yes yes

300 900 300 900

MNR see9.!

constant

IK 21 3G 4G 5C 6J

NETS F M

yes llo

yes yes

yes yes no

yes no no no yes

10 33 unlimited 1O0

13A

see lo.I

IlA

4C 5B 6B

1E 2D

S3PAS F 77 WS VMS

10

no yes

yes yes

yes yes yes

yes no yes

7

unlimited unlimited unlimited unlimited

Newton 13E

conslarR ?

? ?

3E 4C 5C 6B constant

1A

GAINE FIV WS VMS

11

0O

yes yes

Structure -separateinput wogram -modulK structure

Program Availability -program available to third parties

yes

no

yes no no

Output -file of arrays used by the model -graphical output -statistical functions

Combhtatkm With Other Models -combincd with thermal model .combined with pollution model

yes no yes

7

40 unlimited 1 unlimited

Limits -max. number of zones -max. number o f openings/zone* -max. number of shafts/corridorstn nors -max. number of mechanical ventilation systems

Input -interactive input -CAD-input -weather data from weather files -3-D building descrilxion -schedules(e.g., occupants)

Lev - Mar 13F

constant .9

? ?

1A 2A 3B 4C 5C 6B constant

SIREN2 F IV WS VMS

12

Algorithm To Solve Nonlinear Set Of Equations°'4 -name of algorithm o's -eq,mfino

Equations°a -flow tlmmgh cracks -flow t l u ~ g h large openings -flow through duct work -fan flow chaructefistics -wind p~.asore -thermal buoyancy -outside ~ fluctuation -circulatitm flow on large openings -single sided ventilation -cross veatilslJon -iZl'essu~ coefficient (only if calculated) -temperature gradient

Geueeal -name -p¢ogrnmqanguage °a -writ~n for computer typeu2 -writleat for operating systean

N u m b e r (for enthors see Appendix B)

, yes

nO no

no no

yes no no

BO no no no no

unlimited unlimited unlimited unlimited

Gauss 13G

5B constant

31-I

IG 2K

JKCIRCUS F WS/PC VMS/MS-DOS

13

no

yes no

ycs ?

yes yes ?

yes ? yes ? yes

unlimited unlimited unlimited unlimited

Bro - Con See14.2

4B 5C 6B ? ? ? ? ? ?

IE 2D

see ~4a F 77 ? ?

14

no no

yes no

yes no rio

yes no no no no

N-R ?

IA 2A ? ? 5B ? ? ? ? .9 ? ?

no J ~

no no 16"2

no no

? ? ?

no no yes yes no

30 20 20 10

1A 2D 3B 4A 5A 6H ? ? ? ? ? 12 B

MS-DOS

F PC

16

limited

no no

yes ?

yes ? ?

? ? yes ? ?

un~mited unlimited unfimited unlimited

Beta ?

IB ? ? ? ? ? ? ? ? ? ? ?

F WS VAX

flo~17.1

no

yes yes

no no

yes no no

no no yes yes yes

unlimited unlimited unlimited unlimited

N-R 13B

I1B

4B 5B 6B

IG 2D

SSPV-7 F77 ? ?

18

yes

no no

yes yes

no no no

yes no no no nO

unlimited unlimited unlimited unlimited

N - Steff 13Eorl3H

yes

yes

1 A + l j19.1 2 A + 2 H 19a 3F 4F 5C 6A

AIRNET C PC MS-DOS

19

yes

no no

yes yes

yes no yes

no no yes no no

unlimited unlimited unlimited unlimited

N.R2O.2 13H

constant 12C

IA 2A 3H yes2oA 5D 6D

MOVECOMP-PC F 77 M/PC MS-DOS

20

no

no no

no no

no no no

yes no no yes no

unlimited unlimited unlimited

N-R 13E

no

IA

1A

5B 6B

1A 2A

F M/PC NCOS/DOS

21

no

no yes

no yes

yes yes yes

no no no no yes

unlimited unlimited unlimiwA 4OO

Sec - Met see22-1

y~

1G+2F IG+2F 3E 4A 5B 6G 7B yes y~ y~

VENCON HP Basic 4.0 series 200 HP Basic 4.0

22

OO

? 13 B

200 3500 ---

no no no yes no yes no no

yes yes

no no ?

Limits -max. number of zones -max. number of openings/zouet, -max. number of shafts/corridors/floors -max. number of mechanical ventilation

Input -interactive input -CAD-inlmt -weatbea- data from weather files -3-I) beilding dteseriptiou -schedules (e.g., occupants)

Output -lil~of arrays used by the model -gral~ical output -statistical functions

Structure -sepem~ input program -modular structme

Cembimttioa With Other Models -combined with thermal model -combined with ImUutiou model

Program Availability -program available to third parties

1L 2J 31 -5B 6B . . . . constant constant ? ?

1NFILTR F 77 PC MS-DOS

23

Algorithm To Solve Nonlinear Set Of Equations °'4 -name of algorithm°'5 -equation

Eqaatioas °.3 -flow tlMough cracks -flow tlmmgh large openings -flow tlmmgh dnot work -fun flow cl'mrmacristic* -wind ptessmc ~ Imoyuney -outside pressure fluctuation -¢irculaliun flow on large openings -single sided ventilation -cross ventilation -pressure coefficient (only if calculated) -temperature gradieat

-written for operating system

-written for computer type°'2

-progrmn-lungougo °'I

General -name

Number (for authors see Appendix B)

4 E

4 E

yes

yes no

yes yes

yes yes yes

yes no yes no yes

4 -5 5

Newton 13 D

yes

yes no

yes yes

yes no no

no no yes no yes

unlimited unlimited unlimited unlimited

Newton 13 D

5D 5D 6A 6B . . . . . . . . . . . . . . yes yes yes . . . . . . .

1G 2D --

VMS-DOS

TONY F 77

25

1G -3C

ICARE Basic HP-series 200 l i p Basic 3.0

24

. .

. .

.

. .

no

yes no

yes yes

yes no no

yes no no yes ?

150 unlimited unlimited 6

Newton 13B

5D 6B . . ? -9

4 B

1E 2D 3B

STROM-II FV M ?

26

yes

? ?

? ?

? ? ?

? ? ? ? ?

unlimited unlimited unlimited unlimited

HCR 13 C

? ? ? ?

5B 6C

--

1C 2C --

? F M ?

27

yes,but 2~2

yes yes

yes yes

yes yes no

yes

no no 292

no yes

yes no no

no

yes,but 3°l

no no

no no

no no no

no

no

no

no

no

4 7 -2

Newton ?

IB 2D 3J 4H

PAFDPIM Basic PC DOS

30

yes no no

25 4 8 ?

Newton 13 D

5F 6D

IF 2E

CP 3729'1 F M/]~ ?

29

no no no

no no yes

unlimited unlimited unlimited unlimited

SOLVP 13 D

yes~.! 12D

5B 6C constant 8A

1B 2D

FLOW2 F 77 VAX/IBM VMS

28

no

yes no

no no

? yes yes

?

no

? ? yes

25 10 ? 4

Sec-Met 13 1

12A

8B

5G 6I

IM 2K 9 9

CLIM F 77 ? ?

31

?

? ?

? ?

? ? ?

? ? ? ? ?

60 unlimited 10 unlimited

Newton ._32a

? ? ? ?

IH 2D 3D 4D 5B 6F

? F 77 M/WS Uluix

32

unclear yet

no yes

yes yes

yes yes no

yes no yes no yes

unlimited unlimited unlimited unlimited

..

see 334

constant

IA 2L 3J 4E 5C 6J constant 8C yes 33-2 yes33.2 yes33,3

COMERL dBaselV PC DOS

3333~

00 OQ

? ? ? .9 ? ? ? limited

Output -file of arrays used by the model -graphicaloutput -slatistkal functions

Structure -separate input program -modular sWuctum

Combination With Other Models -combined with tlgtmal model -combined with poUution model

Prowma Availability -program available to third parties

725 unlimited 5,720,720 20

? ? ? ? ?

of zones of openings/zones of shafts/conidors/floors of mechanical ventilation

-13A

.9 ? ? .9

consUmt

3A yes 5E 6B yes

yes

? ?

? ?

? ? ?

? ? ? ? ?

25 4 1 8

? 13D

.9 ? ? ?

yes 6D

IF 2E

? F IV M ?

35

IG

? F 77 VAX ?

34

Input -interactive input -CAD-input -weather data from weather files -3-D building description -schedules (e.g,, occupants)

-max. number -max. number -max. number -max. number

Limits

Algorithm T o Solve Nonlinear Set O f Equations 0.4 -name of algorithm ~5 -equation

Equations°-s -flow through cracks -flow through large openings -flow through duct wodk -fan flow chat~t~ristics -wind Wcssure ahermal buoylmcy -outside pressure fluctuation -circulation flow on large openings -single sided veatilation -cross ventilation -wessure coefficient -tempumtme gradient

General -name -wogrmn-language °-I -wriuea for compute~r type°'2 -written for operating system

Number ( f ~ authors see Appendix B)

limited

yes yes

yes no

----

--yes yes yes

see~s'1 see~sl see 36a see 36"~

N - Steff 13E

yes

5A 6A conslant yes

IA 2A

TARP F 77 ? ?

36

limited

? ?

? ?

? ? ?

? ? ? ? ?

300 120 unlimited unlimited

N -R 13B

4A 5B 6B

IB 2B

? F IV M ?

37

yes,but 38"2

no yes

yes yes

yes .9 ?

yes no . ? ?

100 100 ? I00

N -R 13C,13E,13H,131

5F 6B, 6C, 6J ? ? ? ? ? ?

IM 2B ? sec 31.!

Vent F 77 IBM compatible MS DOS

38

.

no

? ?

? ?

? ? ?

? .9 ? ? ?

S e e 39'1

no

.9 ?

? ?

? ? ?

? ? ? ? ?

.

.

40"I

~d~:39-I

.

sec4°2 see4°3 unlimited

S~

*9 *9 .9

?

5D 6B

1E _.

? HP-Special PC ?

40

50 see39.1

Sec - Met 13D

? ? ? ?

IE 2F 3E 4E 5B 6G 7B

.9 HPL PC ?

39

.

.

.

.

yes

no no

no no

no no no

no no no no no

unlimited unlimited unlimited

--

I1C

5H 6K

1B

SAFM4H ---

41

?

? ?

? ?

? ? ?

*9 ? ? ? ?

? 4 1, 0, ? .9

? ?

*9 .9 ? .9

3C 4C 5B 6E

IE

? ? ? ?

42

?

*9 ?

.9 ?

*9 ? ?

*9 .9 ? ? ?

? ? ? .9

? ?

IE ? ? ? ? ? ? ? ? ? ? ?

? ? ? ?

43

yes

*9 ?

.9 ?

? ? ?

.9 ? ? ? ?

211 4 1, ?, 10 .9

? ?

*9 ?

*9 .9 ? ? ?

IE ? ? ? ?

? F ICL 1907 ?

44

00 ~,D

limited

Program Availability -program available to third parties 7

yes yes

yes ?

Slruch,re -sepura~ input program -modular sm~tm~

C o m b i u t i e a With Other Models -combined with thermal model -combined with pollution model

no yes no

Output -file of arrays used by the program -graphical output -statistical functions

40 unlimited 40, 40, 40 l/opening

see 46.1 ?

limited

no

no

no ~.

no yes no

yes ? no no no

2 40 0 1

see 47.1 ?

constant 5C 6B 7A

constant 5C 6B 7A

yes .9 yes no no

? ?

150 ? ? ?

New~n ?

1D 2D

VENT 2 Basic PC ?

47

1D 2D

VENT 1 F 77 M ?

46

-interactive input CAD-input -weather data from weather files -3-D building -schedules (e.g., oceupunts)

Input

Limits -max. number of zones -max. number of openings/zones -max. number of shafts/corridors/floors -max. number of mechanical ventilation systems

Algorithm To Solve Nonlinear Set Of Equations °4 -name of algorithm °'s -equation

-circulation flow on large openings -single sided ventilation -cross V~ltilation -pressure coefficient (only if calculated) -temlm'atore grndiem

-thermal buoyancy -outside pressure fluctuation

ID 2G 2G ? ? ? ? ? ? ? ? ?

? ? ? ?

General -name -program-lauguage °1 -wriUea for computer type °'2 -written for operating system

Equations0.3 -flow through o'acks -flow through Imge openings -flow through duet work -fan flow characteristics -wind pressure

45

Number (for authors see Appendix B)

yes4s'4

no yes

yes yes

yes yes no

yes no yes no yes

unlimited unlimited unlimited unlimited

13B

se~48.3

IA 2L 3J 4E 5C 6J constant 8C yes~.] yes~-] yests.2 constant

COMIS F 77 MicroVAX,PC Unix, MS-DOS

48

yes49.2

no yes

yes yes

yes no no

no no yes yes yes

unlimited unlimited unlimited ~limited

yesSO.2

yes no

no yes

yes rio no

no no yes yes yes

unlimited unlimited unlimited unlimited

N-R ?

? ? uniform

N-R ?

yes

? ? uniform

Se~50.1 See5o.1 see 5o.1 see 50.1 ? ?

DTFAM F 77 IBM comp MS-DOS

50

yes

See49.1 s~e49,l see49.1 ? ?

See49.L

CONTAM88 C IBM comp MS-DOS

49

e.D

91 0.3 0.4 0.5

1.1 2.1 2.2 2.3 4.1 4.2 4.3 4.4 4.5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 7.1 8.1 9.1

9.2 10.I 14.1 14.2 16.1 18.2 16.3 17.1 19.1 20.1 20.2 22.1 28.1 28.2 29.1 29.2

30.1 32.1

33.1 33.2 33.3 33.4

for equations see Tables 1 - 1 2 , Appendix C for algorithm to solve nonlinear set of equations see Table 13, Appendix C Abbreviations used for the name of algorithm to solve nonlinear set of equations: N - R N e w t o n - R a p h s o n method MNR modified N e w t o n - R a p h s o n method Lev - Mar Levenberg-Marquardt method Gauss Gaussian elimination Bro - Con B r o w n - C o n t e method Beta beta method by Newmark N - Steff Newton method with Steffensen acceleration Sec - Met Secant method Kajima general ventilation calculation program calculation of infiltration under consideration not so useful passive system simulation program/Multiroom Version 1 not in particular integration of 1 E or 2 D transformed Newton method for the system of nonlinear equations using Jacobian matrix under revision for new version still under development by dividing them into horizontal equidistant strips linear interpolation from CPBANK internal reference pressure adjusted until flow errors negligible not fully tested optional after completing and testing infiltration and ventilation AIR calculation numerically derived Jacobian matrix is inversed and calculated pressure correction vector is multiplied b y 0.5 for avoiding oscillation only in Japanese reference pressures adjusted until flow errors negligible simultaneous heat, moisture and ventilation predicting program multirooms revised N e w t o n - R a p h s o n method modified Walton (NBS) algorithm not yet not yet (used at user's risk) model for fluctuating wind pressure alternate linear interpolation b e t w e e n given points method with optimized acceleration secant and u / L decomposition harmonic analysis [3] and Lagrange interpolation [1] with some restrictions Fortran program to calculate air infiltration in buildings -- May 1974 but a second program, named CP 46, is combined with pollution model (smoke concentration) its applicability is very limited iterative technique using linear approximation to set of nonlinear equations including Q and P still under development treated like large openings calculated by CPCALC, calculation program, see ref. 23 optimized Newton, Newton with given relaxation, Newton--Steffensen

92 36.1

it is i n t e n d e d t h a t the p r o g r a m be c o m p i l e d with the a p p r o p r i a t e values o f a few p a r a m e t e r s t a t e m e n t s to m a t c h the p r o g r a m to the p r o b l e m still u n d e r d e v e l o p m e n t still u n d e r d e v e l o p m e n t total n u m b e r o f c o n n e c t i o n s smaller t h a n 2 0 0 the e x a c t n o n l i n e a r e q u a t i o n s w e r e s o l v e d t o d e t e r m i n e the v o l u m e flow rate. The b a l a n c e o f in- and o u t f l o w i n g air w a s d e t e r m i n e d b y iteration (variation o f the neutral p r e s s u r e level NPL). In h o r i z o n t a l d i r e c t i o n ( p e r floor): t h r e e g r o u p s o f r o o m s ; outside g r o u p divided in w i n d w a r d a n d l e e w a r d flats, i n n e r g r o u p (shafts), middle g r o u p ( c o r r i d o r s ) c o m b i n e the different g r o u p s . In vertical direction: 30. o n e to e a c h a t t a c h e d r e g i o n simplified airflow m o d e l internal r e f e r e n c e p r e s s u r e a d j u s t e d until flow e r r o r s negligible internal r e f e r e n c e s p r e s s u r e a d j u s t e d until flow e r r o r s negligible t r e a t e d like large o p e n i n g s c a l c u l a t e d b y CPCALC, c a l c u l a t i o n p r o g r a m , see ref. 23 o p t i m i z e d N e w t o n , N e w t o n with g i v e n relaxation, N e w t o n - S t e f f e n s o n as s o o n as fully d e b u g g e d e q u a t i o n to be specified b y t h e u s e r available at the N a t i o n a l Institute o f S t a n d a r d s a n d T e c h n o l o g y e q u a t i o n to be specified b y the u s e r available at the National Institute of S t a n d a r d s a n d T e c h n o l o g y

38.1 38.2 39,1 40.1

40.2

40.3 41.1 46.1 47.1 48.1 48.2 48.3 48.4 49.1 49.2 50.1 50.2

Appendix

B -

Model number Author Reference

Model number Author

The

authors

and references

of the computer

programs

1 S. Hayakawa, Building Environmental Engineering Department, Kajima Institute of Construction Technology, Kajima Corporation, 2-19-21 Chofu-City, Tokyo, Japan 1 S. Hayakawa, S. Togari and M. Hioki, Air flow rate variation of HVAC caused by stack effect and opening a window, Proc. Third Int. Symposium on the Use of Computers for Environmental Engineering related to Building, Banff, Canada, May 1978, pp. 627--636. 2 H. Yamazaki, Department of Architecture, Faculty of Engineering, Oita University, 700, Dan-noharu, Oita-shi 870-11, Japan

References Model number

3

Author

M. Udagawa, Department of Architecture, Kogakuln University, 1-24-2, Nishi-Shinjyuku, Shi~yukuku, Tokyo 160, Japan

References

1 K.-I. Ishida and M. Udagawa, A practical method for calculation of room temperature variation considering natural ventilation and radiant heat exchange among room surfaces in multi-room buildings, Trans. AIJ (Archit. Inst. Japan), (Nov.) (1987). 2 K.-I. Ishida and M. Udagawa, Validation of the ventilation net work model for the estimation of room temperatures and heat load of residential buildings with measured data, Trans. A/J (Archit. Inst. Japan), (Oct.) (1988). 3 K.-L Ishida and M. Udagawa, Ventilation of simulation program for the estimation of thermalperformance of residential houses using the data from the year round monitoring, Proc. CL/MA 2000, 1985.

93 Model number Author References

Model number Author

4 T. Hayashi, Department of Thermal Energy System, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Kouen, Kasuga-Shi, Fukuoka-Ken 816, Japan 1 T. Hayashi, Y. Urano, T. Watanabe and Y. Ryu, Passive system simulation program PSSP and its applications, Proc. Building Energy Simulation Conference 1985, Seattle, USA. 2 T. Hayashi et al., Prediction of air distribution in multiroom buildings, Proc. Roomvent 87, A i r Distribution in Ventilated Space, Stockholm, Sweden, 1987.

5 K. Balazs, Hungarian Institute for Building Science (eti) P.O.B. 71, XI. David F.u.6., Budapest 1113, Hungary

References Model number Author

6 I. C. Ward, University of Sheffield, Department of Building Science, Sheffield S10 2TN, UK

References Model numbers Author

7, 8 M. B. Nantka, Institute of Heating, Ventilating and Air Protection, Silesian Technical University, Pstrowski 5, Room 23, 44 100 Gliwice, Poland

References

1 Effectiveness of ventilation functioning in multi-story residential houses, District Heating, Heating & Ventilation, (6) (1981) 154 (in Polish). 2 A numerical method for air-change rate of buildings calculated, Proc. 5th Int. Conj,. on HVAC, Czechoslovakia, Nov. 24-25, 1081. 3 Mathematical Method for Natural and Mechanical Air Flows Calculated, (in Polish).

Model number

9

Author

H. Okuyama, Division of Environmental Technique, Shimizu Corporation, Institute of Technology, 4-17-, Etchujima 3-chome, Koto-ku, Tokyo, Japan

References

1 H. Okuyama, Theoretical study on the thermal network model in buildings, Doctorate Thesis, Waseda University, Tokyo, December, 1987. 2 H. Okuyama, Network numerical analysis method for heat transfer and airflow in buildings, Proc. 17th Symposium by the Committee of Building Heat Transfer in Building Environment, Committees of Architectural Institute of Japan, Aug. 1987. 3 H. Okuyama, A computer modelling method of building airflow network and the solution of nonlinear simultaneous equations, Proc. o f Annual Meeting Society of Heating Air-Conditioning and Sanitary Engineers of Japan, Oct. 1989, p. 729, (in Japanese)

Model number Author

10 S. A. Dominguez, Dpto. de Ingeneria, Energetica y Fluidomecanica, Escuela Tecnica Superior de Ingenieros Industriales, Avda. Reina Mercedes, E-4101 Sevilla, Spain

References Model numbers Author

ii, 12 R. Mounter, Centre Scientifique et Technique du Batiment, Station de Recherche, 84, Avenue Jean Jaures, F-77420 Marne la Vallde Decex 2, France

References Model number

13

Author

J. KronvaU, Department of Building Science, Lurid University, P,O. Box 118, S-221 00 Lund, Sweden

Reference

1 J. Kronvall, A i r Flow in Building Components, Report TV'BH-IO02, Division of Building Technology, Land Institute of Technology, Lurid, Sweden, 1980.

Model number Author References

14 T. Tsuchiya, Department of Architecture, Faculty of Engineering, Toyo University, 2100 K~irai, Kawagoe-Shi, Saltama, Japan

94 Model number Author

15 K. Nitta, Department of Architecture, Faculty of Technical Art, Kyoto Kogei Sen-i University, Kaidomachi, Gosho, Matsugasaki, Sakyo-ku, Kyoto-shi, 606, Japan

References Model number Author

16 M. Liddament, Air Infiltration and Ventilation Centre, University of Warwick, Science Park, Barclays Venture Centre, Sir William Lyons Road, Coventry CV4 7EZ, UK

References

Model number Author References

Model number Author Reference

Model number Author References

17 T. Sasaki, Department of Architecture, Hokkaido University, Nishi 8-chome, Kita 13-jou, Kitaku, Sapporo 006, Japan 1 T. Sasaki, M. Hayashi and N. Aratani, On the ventilating characteristics of the space under the fluctuating wind pressure, Proc. Int. Conf. Roomvent 1987, Stockholm, Session 4a, pp. 1-12. 2 T. Sasaki and N. Aratani, Study on change from summer-oriented houses to winter-oriented ones and their ventilation, Bull. Faculty of Engineering, Hokkaido University, (145) (Dec.) (1988) 125-151, 3 T. Saski et al., Der Liiftungszustand v o n d e r Luftschicht durch die Wind-Unruhe, Trans. A / J (Archit. Inst. Japan), (372) (Feb.) (1987).

18 H. Matsumoto, Toyohashi University of Technology, Department of Regional Planning, Tempakucho, Toyohashi-shi 440, Japan 1 H. Matsumoto, M. Nagatomo and H. Yoshino, A calculating method for predicting air pollution in multi-celled buildings, Proc. Meeting of Tohoku Branch of AIJ, 1988, pp. 33-36 (in Japanese).

19 G. Walton, National Institute of Standards and Technology, BR/A 313, Washington, DC 20234, USA 1 AIRNET - a Computer-Program f o r Building Airflow Network Modeling, Rep. NISIR 89-4072, National Institute of Standards Interagency, 1989. 2 G. N. Walton, Airflow network models for element-based building airflow modeling, ASHRAE Trans., 2 (1989).

Model number Author Reference

20 M. Herrlin, Lawrence Berkeley Laboratory, Bldg. 90, Rm. 3074, Berkeley, CA 94720, USA 1 M. K. Herrlin, MOVECOMP: a multizone infiltration and ventilation simulation program, A i r Infiltration Rev., 9 (3) (1988).

Model number Author

21 Y. Utsumi, Miyagi National College of Technology, 48 Nodayama, Shiote, Medeshima, Natori 98112, Japan

References

Model number Author References

22 W. de Gids, TNO Division of Technology for Society, P.O. Box 217, 2600 AE Delft, Netherlands

Model number Author

23 B. Spruit, ISSO-Netherlands, Institute for Study and Promotion of Research in the Field of Building Services, Postbus 20740, 3001 JA Rotterdam, Netherlands 1 "ISSO-4" (to be published) 2 M. Liddament, A i r Ir~iltration Calculation Techniques -- A n Application Guide, Air Infiltration and Ventilation Centre, June 1986.

References

95 Model number Authors References

Model number Authors References

Model number Authors References

Model number Author References

Model number Author References

Model number Author

24 F. AUard, J. J. Roux and D. Caccavelli, Laboratoire Equipement de l'Habitat, Centre de ThermiqueURA CNRS 1372, INSA de Lyon, Bgtiment 307, F-69621 Villeurbanne C~dex, France 1 D. CaccaveUi, J. J. Roux and A. Roldan, Proc. Infi/trat/on, A i r Flow Distribution and MieroComputation Roomvent 87, Air Distribution in Ventilated Spaces, Stockholm, 1987, Session 4a. 2 D. CaccaveUi, J. J. Roux and F. AUard, Transferts a6rauliques dans les b~timents; pr6sentation de deux niveaux d'approche, Journde d'Etude de la Socidtd Frangaise des Thermiciens, dtat des connaissances sur la ventilation~ Paris, Nov. 26, 1987. 3 D. Caccavelli, J. J. Roux and F. Allard, A simplified approach of air infiltration in multizone buildings, Proc. Pth AIVC Conference, Gent, Belgium, Vol. 2, Sept. 1988. 4 D. Caccavelli, J. J. Roux and F. Allard, Mod61isation du comportement thermique des b~timents multizones. Adaptation ~ un processus de conception, Tb2se de Doctorat, INSA de Lyon, Nov. 1988, 473 p. 25 F. Allard, G. Achard and A. Roldan, Laboratoire Equipement de l'Habitat Centre de Thermique-URA CNRS 1372, INSA de Lyon, B~timent 307, F-69621 Villeurbanne C6dex, France 1 A. Roldan, G. Achard and F. Allard, Influence des infiltrations et des transferts a6rauliques entre pi~ces sur la charge thermique d'un b~timent multizone, Proc. Third Int. Congress on Building Energy Management, ICBEM 87, Lausanne, Sept. 1987, pp. 178-185. 2 A. Roldan, Etude thermique et a6raulique des enveloppes de b~timent. Influence des couplages int6rieurs et du multizonage, Th~se de Doctorat, INSA de Lyon, Dec. 1985, 310 p. 26 H. Esdorn, H. E. Feustel and J. Guo, Hermann-Rietschel-Institut, Technische Universitaet Berlin, Marchstrasse 4, D-1000 Berlin 10, FRG 1 H. Feustel, Beitrag zur theoretischen Beschreibung der Druck- und Luftmassenstromverteilung in natilrlichen und maschinell geltifteten Geb~uden, Dissertation, Technische Universitiit Berlin, 1983, VDI-Fortschrittsberichte, Reihe 6, Nr. 151, VDI-Verlag, Duesseldorf. 2 J. Guo, Weiterentwicklung des Programms gem~ss 1) und 2) mit dem Ergebnis einer Berficksichtigung thermisctmr Druckdifferenzen auch innerhalb eines Geschosses und einer spi2rbaren Verringerung des Rechenzeiten, Interner Institutsbericht, 1988. 27 P. J. Jackman, Building Services Research and Information Association, Old Bracknell Lane West, Bracknell, Berkshire RG12 4AH, UK 1 P. J. Jackman, Heat loss in buildings as a result of infiltration, BSE, 42 (1974) 6-15. 2 P. J. Jackman, A study of the natural ventilation of tall office buildings, JIHVE, 38 (1970) 103--118, 28 C. Melo, Departmento de Engenharia Mecanica, Universidade Federal de Santa Catarina, CX. Postal 476, 88.049 Florianopolis-SC, Brazil 1 C. Allen, Wind Pressure Data Requirements f o r Air Infiltration Calculation, Tech. Note 13, Air Infiltration and Ventilation Centre, Bracknell, UK, 1984. 2 A. J. Bowen, A Wind Tunnel Investigation using Simple Building Models to Obtain Mean Surface Wind Pressure Coefficient f o r Air Infiltration Estimates, Rep. LTR LA 209, National Aeronautical Establishment, NRCC, Canada, 1976. 29 D. M. Sander, National Research Council Canada, Institute for Research in Construction, Building M 24, Montreal Road, Ottawa, Ontario K1AOR6, Canada

References Model number Author

30 K. Klobut, Helsinki University of Technology, Faculty of Mechanical Engineering, Otakaari 4, SF02150 Espoo, Finland

References Model number Author References

31 P. Dalicieux, Ddpartement Applications de l'Electricitd, 77250 Moret sur Loing, France

96 Model n u m b e r Author Reference

Model n u m b e r Author References

Model n u m b e r Author Reference

Model n u m b e r Author References

32 P. Warren, Building Research Establishment, Bucknalls Lane, Garston, Watford WD2 7JR, UK 1 E. Evers and A. Waterhouse, A Computer Model f o r Analysing Smoke Movement in Buildings, CP 59/78, Building Research Establishment 1978. 33 V. Dorer, EMPA ABT 176, CH-8600 Duebendorf, Switzerland

34 J. Gabrielsson, Ekono Association for Power a n d Fuel Economy, P.O. Box 27, 00131 Helsinki 13, Finland 1 J. Gabrielsson and P. Porra, Calculation of infiltration and transmission heat loss in residential buildings by digital computers, JIHVE, 35 ( 1 9 6 8 ) 3 5 7 - 3 6 8 .

35 C. Y. Shaw~ Institute for Research in Construction, National Research Council, Bldg M-24, IRC, NRC, Montreal Road, Ottawa K1A OR6, Canada 1 D. M. Sander and G. T. Tamura, FORTRAN IV Program to Simulate Air Movements in MultiStorey Buildings, DBR Computer Program No. 35, National Research Council of Canada, 1974. 2 D. M. Sander, FORTRAN IV Program to Calculate Air Ir~filtration in Buildings, DBR Computer Program No. 37, National Research Council of Canada, 1974. 3 C. Y. Shaw, D. M. Sander and G. T. Tamura, A FORTRAN IV Program to Simulate Stair-Shqft Pressurization Systems in Multi-Storey Buildings, DBR Computer Program No. 38, National Research Council of Canada, 1974.

Model n u m b e r Author Reference

36 G. Walton, National Bureau of Standards, BR/B 114, Washington, DC 20234, USA 1 G. N. Walton, Thermal Analysis Research Program, Reference Manual NBSIR 83-2655, US D e p a r t m e n t of Commerce, 1983.

Model n u m b e r Author

37 S. Irving, Oscar Faber Consulting Engineers, Marlborough House, Upper Marlborough Road, St. Albans, Hefts. ALl 3UT, UK 1 S. J. Irving and A. P. Wilson, Validation of a smoke m o v e m e n t program, Build. Eng. Res. Technol., 2 (4) (1984) 1 5 1 - 1 5 9 . 2 S. J. Irving, The c o m p u t e r simulation of s m o k e m o v e m e n t during building fires, Fire Prey. Sci. Technol., (22) ( 1 9 7 9 ) 3 - 8 .

References

Model n u m b e r Author References

38 M. Holmes, Arup Research & Development, 13 Fitzroy Street, London W l P 6BO, UK 1 M. J. Holmes, Design for Ventilation, Proc. AIVC 5th Conference, September 16-19, 1985,

Netherlands. 2 M. J. Holmes and T. Salnsbury, Ventilation design for a bus station, Proc. Pth AIVC Covtference,

Gent, Belgium, Sept. 12-15, 1988.

Model n u m b e r Author Reference

39 W. de Gids, TNO Division of Technology for Society, P.O. Box 217, 2600 AE Delft, Netherlands 1 W. F. de Gids, Calculation Method f o r the Natural Ventilation of Buildings, Publication No. 632, TNO Research Institute for Environmental Hygiene, Delft, 1977.

Model n u m b e r Author Reference

40 W. Brinkmann, Bundesbaudirektion Berlin, Fasanenstraase 87, D-1000 Berlin 12, FRG 1 W. Brinkmann, Zur Bestimmung des L i i f t u n ~ e b e d a r f s h o h e r Gebiiude, D i s s e r t a t i ( m , Teehnische Universit~t Berlin, 1980.

97 Model number Author Reference

41 H. E. Feustel, Lawrence Berkeley Laboratory, Building 90, Room 3074, 1 Cyclotron Rd, Berkeley, California 94720, USA 1 H. E. Feustel and M. Sherman, A simplified model for predicting air flow in multizone structures, Energy Build., 13 (1989) 217-230.

Model number Author References

42 G. Hausladen, Schiedel GmbH & Co, Lerchenstr. 9, Postfach 50 05 65, D-Munich 50, FRG 1 G. Hausladen, Wohnungslilftung, Untersuchung der verschiedenen Ltiftungsarten bzw. Liiftungspraktiken unter hygienischen, bauphysikalischen und energetischen Gesichtspunkten, Dissertation, Technische Universit~t Milnchen, 1980, Fortschrittsberichte der VDI Zeitschriflen, Reihe 5, Nr. 73. 2 G. Hansladen, Luftwechsel in Wohnungen, Heizung, Liiftung Haustechnik, (1) (1978) 21-28. 3 W. Krueger and G. Hausladen, Ei~fluss van Wind- und thermischen K r ~ t e n a u f das betriebsverhalten yon mechanisch betriebenen Entlf~ftungsanlagen in mehergeschossigen Wohngebduden, Forschungsbericht ffir Haustechnik, Technische Universit~t Miinchen, 1979.

Model number Author

43 J. P. Cockroft, Building Services Research Unit, University of Glasgow, 3 Lillybank Gardens, Glasgow G12 8RZ, UK 1 J. P. Cockroft, Air flows in buildings, Proc. Environment Inside Buildings Symposium, Southend on Sea~ 1979. 2 J. P. Cockroft, Validation of buildings and systems energy prediction using real measurements, Computer Aided Design, 14 (1) (1982) 39-43.

References

Model number Author References

44 R. E. BiUsborrow, Department of Building Science, Faculty of the Architectural Studies, University of Sheffield, Sheffield S10 2TN, UK 1 R. E. Bilsborrow, Digital Analogue f o r Natural Ventilation Calculations, Report No. 6, Department of Buildings Science, University of Sheffield, 1973. 2 A. C. Pitts and I. C. Wards, A Review of the Prediction and Investigation of Air Movement in Buildings, Report No. B S 59, Department of Buildings Science, University of Sheffield, 1983.

Model number Author Reference

45 S. Swetiov, Soviet Union 1 K. S. Swetlov, Calculations of air infiltration in multi-story buildings using electronic computers, Vodosnabize i Sanitarna Tekhinika, 11 (1966) HVRA-Translation 122.

Model numbers Author References

46, 47 D. W. Etheridge, British Gas PLC, Watson House, Peterborough Road, London SW6 3HN, UK 1 D. W. Etheridge and D. K. Alexander, The British Gas multi cell model for calculating ventilation, ASHRAE Trans., 85 (Part II) (1980) 808-821. 2 D. W. Etheridge, Crack flow equations and scale effect, Build. Environ., 12 (1977) 181-189. 3 D. W. Etheridge and J. A. Nolan, Ventilation measurements at model scale in a turbulent flow, Build. E n r i c h . , 14 (1979) 53-64. 1 D. W. Etheridge and R. Gale, Theoretical and experimental techniques for ventilation research in buildings, Proc. Int. Gas Conf., London, June 1983, Paper C 18-33.

Reference for VENT 2

Model number Authors

48 F. Allard, Laboratoire Eqnipement de l'Habitat, Centre de Thermique, INSA de Lyon, B~timent 307, F-69621 Villeurbanne C~dex, France H. E. Feustel, Lawrence Berkeley Laboratory, Building 90, Room 3074, Berkeley, CA 94720, USA E. R. Garcia, Dpt. Ingenieria Energetica y, Fluido Mecanica, Escuela Superior de lngenieros Industriales, Avda. Reina Mercedes S/N, E-Sevilla, Spain Mario Grosso, Dipartimento di Seienze e Teehniche, Per i Processi di Insediamento, Polltecnico Di Torino, Viale Mattioli 39, 1-10125 Torino, Italy Magnus Herrlin, Division for Building Services Engineering, Royal Institute of Technology, S-10044 Stockholm, Sweden V. Dorer, EMPA ABT 175, CH-8600 Duebendorf, Switzerland L. Mingsheng, Mechanical Engineering Department, Texas A&M University, College Station, TX 77840, USA

98

Reference Model numbers Author References

H. Yoshino, Dept. of Architecture, Faculty of Engineering, Tohoku University, Sendal 980, Japan H. C. Phaff, MT-TNO, POB 217, 2600 AE Delft, Netherlands Yasuo Utsumi, Department of Architecture, Miyagi National College of Technology, Medeshima, Natori, Miyagi, Japan 1 H. E. Feustel and A. Raynor-Hoosen (eds.), F u n d a m e n t a l s o f t h e M u l t i z o n e A i r F l o w M o d e l COMIS, Tech. N o t e T N 2P, A i r I n f i l t r a t i o n a n d V e n t i l a t i o n C e n t r e , May 1990, Coventry,'UK. 49, 50 J. Axley, Bldg. Technical Program, 3-437, Massachusetts Institute of Technoiogy, 77 Massachusetts Ave, Cambridge, MA 02139, USA 1 J. Axley and R. Grot, The coupled air flow and thermal analysis problem in building airflow system simulation, P r o c . A S H R A E S y m p o s i u m o n C a l c u l a t i o n o f l n t e r z o n a l H e a t a n d M a s s T r a n s p o r t i n B u i l d i n g s , A S H R A E T r a n s . , 95 (2) (1989). 2 J. Axley and R. Grot, Coupled airflow and thermal analysis for building system simulation by element assembly techniques, P r o c . R o o m V e n t '90, E n g i n e e r i n g A e r o - a n d T h e r m o d y n a m i c s o f V e n t i l a t e d R o o m s , 1990.

3 R. Grot, U s e r s M a n u a l -- N B S A V I S -- C O N T A M 8 8 , National Institute of Standards and Technology, 1990. 4 G. Walton, A I R N E T - A C o m p u t e r P r o g r a m f o r B u i l d i n g A i r f l o w N e t w o r k M o d e l i n g , N I S T R 80-4072, National Institute of Standards and Technology, 1988. TABLE 2. ( c o n t i n u e d )

A p p e n d i x C -- E q u a t i o n s u s e d i n t h e computer programs

Nomenclature is given in Table 14.

with n = 2 / 3

F=pDAP ~

(2J)

Q=K~

TABLE 1. Equations used for flow through cracks

(2k")

2 n

(1A)

Q =DAP n

(1B)

Q 3600

(1C)

FfDAP

D 3600 API/n

A P = a Q 2 + bQ

(1 D)

Q ~ CLAP'*

(1 E)

F = KAP ~

(IF)

Q = CAAP'*

(1 G)

F= 5 wCdO X (p[2g(pl - P2) -- bt])~/2~/ - Zn]3/2

TABLE 3. Equations used for flow through duct work

n

1/'2 m AP = 0.5LpQ 2

(1D

AP=aF + bF 2

(1J)

1/2

P - 2 v2(1 "{-~*)'{-APvE--PD= 0

~=~ F=pDA/m with nffi2/3

(1L)

Q =KAPn

(1M)

(2L)

ap=[K+ :L] ~j H_.~D_~D,p 0 Q~ (2AP) TM

QffiA

(3C)

(3D) +]~g

(3E)

TABLE 2. Equations used for flow through large openings 2pA F=DAP n

(2A)

Q •DAP n

(2B)

Q 3600

(2C)

D Aplm 3600 2 A p -1/2

F=

(2E)

Q =A(2Ap)lm(1/p)1/2 AP = SQ 2

(2F)

AP = oF+ bF 2

(2H)

(2 G)

AP "2Ap - ~

~ff~ F=KAP ~

(3F)

1

AP = CQ 2

2

Al 1 ~oj2

(3H)

(3J)

99

TABLE 6. ( c o n t i n u e d )

TABLE 4. Equations used for fan flow characteristics

Q = K , + K~AP + KsAP 2

(cA)

A P = K1 + K2Q + K3Q 2

(4B)

A P = AP o - K I Q - K2Q 2

(4C)

AP = Bn2D~. +

(4D)

AP. = Apgz

(60

(4E)

aP= (e,- p,g&)- (Pj- p~gh~)

( 6J)

Q2

A2D4

aP =f(QJ +K,F + K2F 2+ KaF a

(4F)

AP, = g I + K2Q + K3Q 2 + KaQ 3

(4G)

AP =

(4H)

~=Ko

c~ -

( C2Q2)

TABLE 5. Equations used for wind pressure

,~O= 2,/.)2

(5A)

tuD= C p0 v 2 2

(5B)

~=C~Vo~

(5C)

AP=po(T~- T°ITogH k T, T o /

(6G)

(6K)

= Apg~

TABLE 7. Equations used for outside pressure fluctuations

(~,2)0~=0.5(p~)0'

(7A)

Q~ = 1/ZANZT(0.00 lV= + 0.0035HAT+ 0.01) 1/2

(7B)

TABLE 8. Equations used for circulation flow on large openings

o..c,.(_:.)°-' Q = K A P °'~

(SA) (8B)

with AP = Apgh

(8c)

AF=Fo, z.-Fz~H (5D)

A P = 6~- v i i 2

2

kP=

P v2 ~

TABLE 9. Equations used for single-sided ventilation

with v =Vo2334[ 1 + 2.8 l o g ( H + 4.75)]

(5E)

~kP=Kv2cp

(5F)

with Cp as input

Pwi"d = CP 1 Pv 2

(SG)

AP=CpAP,~

(5H)

TABLE 6. Equations u s e d for thermal buoyancy

AP=pgAH A P = (Po- ~ ) g ( H - Ho) H 1 _ 1 AP= 3462(-Ho)(~ ° ~1

No equations were specified

TABLE 10. Equation used for cross ventilation

Q = KAP°'87

( 1 0A)

TABLE 11. Equations used for pressure coefficient

(6A)

%=0.75-1.05

(6B)

% = - 0 . 4 5 + 0 . 1 5 -~Q 9O

(6C)

~ 9O

if Q < 9 0 ° if Q > 9 0 °

1

(11/%)

=~kPwind= 2 P~P'v2 AP = (Po -- I~)gH

(6D)

A P = (po - p~)gH(X-- 0.5 - N /2 )b + c

(6E)

Q = ( C D A I n ) ( A O g ~ ) 1/2

(6F)

(continued)

c,= c,, = c, = cw = %,~

0.75 - 0.01667b + 1.25 - 0.02667b + 2.0 -0.4 =

1

if if if if

b =0-30 ° b = 30-75 ° b = 75-90 ° b=90-180 °

Cp, ~

=

-

0.3

(11B) (11C)

100 TABLE 12. Equations used for temperature gradient

Q

=yD~l~l o~>-~

TABLE 14.

(12A)

HI

dP dz Pffi

gPo273 2,+Tzo

(12B)

P~f

and dPffi - p g dH

R(Tr.f-&H)

(12C)

h

Tzfaz + T.,oand P,,ffigJ P(z) dz

(12D)

0

TABLE 13. Algorithm to solve the nonlinear set of equations

~CjAj]

(lSA)

Pj+I=P#- ZQ' ZV CR =

(13B)

ZDAPTM

(13C)

(continued)

Symbol

Description

Unit

C Cp

crack flow coefficient surface pressure coefficient flow coefficient diameter effective leakage area mass flow rate friction factor function of gravity height derivative o f f ( P ) constant crack length duct length flow exponent pressure volume flow rate gas constant resistance absolute temperature relative temperature velocity wind speed position of a neutral plane depth of crack

( m3/m h Pan) (-)

A

difference

F. O

summation absolute temperature friction factor temperature gradient air density fitting loss factor viscosity of air

(-) (-) (K) (-) (K/m) (kg/m a) (-) (m2/s)

D d E F f f(...) g H J K L l n P Q R . S T t v w Zn

z

~= o

03D)

P~+ 1= P~ - Correction

( 13 E)

Minimize over ~ ~/i2(P) ) N

03F)

p ~a

[A][AP] ffi [q]

(13G)

Subscripts .+, = r . -

(lSH)

j~

~Q, = 0

(13I)

d dyn f, i, r, s

i

TABLE 14. Nomenclature

Symbol

Description

Unit

A

area coefficient constant turbulent pressure gradient

(m 2) (-) (-) (Pa/m)

a, b, c

B bt

(continued)

(-) (m) (m) (-) (Pa) (m3/h) (J/kg K) (h Pa/m 3) (K) (°C) (m/s) (m/s) (m) (m)

Greek letters

A At

withfi(P)=J-l;t*J Y /.,.~

(m3/h Pan) (In) (kg/h) (kg/h) (-) (-) (m/s 2) (m)

i j j + 1 lee NET o ref s t wind

z 0

discharge dynamic locations in the duct system inside iteration step iteration step + 1 leeward side inside outside reference stack total windward side height above reference level reference