1

THERMAL AND AIRFLOW NETWORK SIMULATION PROGRAM NETS

Hiroyasu OkuyamaInstitute of Technology, Shimizu Corporation

Tokyo+(135-8530)-Japan4-17, Etchujima 3-Chome, Koto-ku, Tokyo, Japan

phone:+81-3-3820-5538;fax:+81-3-3820-5959;e-mail:okuyama@sit.shimz.co.jp

ABSTRACTBased on the thermal and airflow network modelwith simple but perfect generic formulations andstable solving methods, a computer program NETSfor the practical simulation of coupled building heat,gas and air transfer system has been developed.NETS can simulate the feedback or the schedulecontrol on models' structural changes and variousdriving condition changes. A pre-processing systemcalled NETSGEN and a post-processing systemcalled NETSOUT have been also developed.NETSGEN enables designers to freely construct thethermal and airflow network model on energy savingnew ideas with an ease of simply drawing a picture.NETSOUT graphically displays the computed results.NETS is versatile and especially suitable for use inresearch, development and design of passive and lowenergy architecture.

INTRODUCTIONA simulation program for thermal and airflowsystems in buildings using thermal and airflownetwork models called NETS is being developed.The program has high degrees of freedom andgenerality, and provides a tool for designers anddevelopers of building facilities and designs toinvestigate new concepts by flexible simulations. Themain part of the program named NETS, which hasbeen developed using Fortran language for over 10years, originally aimed at simulating passive solarhouses. In some passive solar houses, heat flow iscontrolled by varying airflow paths and opening ofheat insulating panels according to the time zones,seasons, and ambient temperature. This means thatthe model structure varies with scheduling andfeedback controls, and NETS is suited for simulatingsuch variation. Preprocessing and postprocessingprograms, which are named NETGEN and NETOUTrespectively, are also being developed in these twoyears, and the total system is called the NETS system.This paper describes features of the simulationmodels, outline of the calculation theory, outline ofthe preprocessing and postprocessing programs, andsome applications of this simulation program thatmake use of the characteristics of this simulationprogram.

FEATURES OF THE THERMALNETWORK SIMULATION MODELThe mathematical model of the thermalnetwork[1]relates to what is called the heat capacitynodal system that is obtained by the spatiallydiscretizing method, and all heat transfer formsbetween node i and node j by conduction, radiation,convection, and mass flows are expressed by a singlekind of parameter cij called generalized thermalconductance. The heat balance at a node is definedby what is called a nodal equation of perfectlyconnected system assuming that each node isthermally connected with all other nodes as shown inthe equation below. In this equation, xi is thetemperature of node i, mij is the heat capacity of nodei, cij is the generalized thermal conductance fromnode j to node i, gj is the jth heat source of the totalnumber ng, and rij is the ratio of heat that flows fromgj to the ith node; no is the total number of the nodesthat have known temperature values such as theoutside air temperature, and n is the total number ofnodes having unknown temperature values.From this nodal equation of perfectly connectedsystem that holds generally regardless of the spatialdimension or shape of the calculation objects, thefollowing ordinary differential equation of vector

Figure1. Concept of thermal network

gj j(ng)

i mii

cij=0

cji

j

rijij

i

ij

x(n)

xo

cij

cji

(no)

j

ng

j

jiij

non

j

jij

n

j

ji grxxcxm ⋅+−⋅=⋅ ∑∑∑=

+

== 1

,

1

,

1

, )(�

2

matrix is derived for the system of total capacitynodes. This equation is called a state equation afterthe terminology of applied mathematics of the systemtheory.

gRxCoxCxM o ⋅+⋅+⋅=⋅ �

Only system parameters cij, mij, rij , and the modelsizes n, no, and ng change with the objects ofcalculation. If the system parameters that are not zeroare given, those system parameters that are not givenautomatically become zero. These are the reasonswhy the computing programs for constructing theunified equation and solving the ordinary differentialequation have complete generality. While spacediscretization is usually done by the finite volumemethod, even when the finite element method ispartially applied, a scheme has been devised to makeit possible to calculate the total system as a wholeusing the above-mentioned equation model bycombining the partial models constructed by thesedifferent methods. This scheme involves theimprovement of formulation relating to the boundaryconditions of the conventional finite element methodand the definition of subscripts for the systemparameter[1].Simulating the variation of state values such astemperature with time leads to time integration of theordinary differential equation. While all of thevarieties of conventional time integration methodsgive only approximate solutions, the author hasproposed a strict solution, which is called analyticaltime integration method by projectivedecomposition[1]. However, this strict solutionrequires the eigenvalue analysis of system matrix,and it is usually difficult to quickly obtain exacteigenvalues of large system matrices. Therefore,approximate time integration has to be used from apractical point of view, and the stability ofcalculation is the most important factor for thisapproximation. This is because conditions imposed

on spatial or time discretization to obtain stabilityincrease calculation time and the main memorycapacity, thereby often deteriorating practicality.NETS often uses the complete implicit method(backward difference). Further, to decrease thevolume of the inverse matrix calculation of thesystem matrix in this method, it is applicable toapproximately calculate the inverse matrix bydividing the rows, and it is also possible to improvethe computer economy by reducing the practicalnumber of nodes making use of the condensationtheory of the state equation[1]. In the future, thiscondensation method may solve the problem ofexcessive increase in the number of nodes when thespatial automatic mesh division is applied.

FEATURES OF THE AIRFLOWNETWORK SIMULATION MODELThe airflow network[1] basically consists of twomodels elements, zones and flow paths. Even when abranched duct system exists, the model elements arereduced to these two by assuming zones at the branchpoints. This generalization, however, requires themodeling concept that the static pressure at thebottom of a zone is assumed as the total pressureincluding dynamic pressure. So the author call this

Finite Volume Method

Figure 2�Unification of different spatialdiscretization models

Renumbering in global node numbers

Total system state equation

Finite Element Method

mij ,cij ,rij in localnode numbers

mij ,cij ,rij in localnode numbers

j

ng

jij

non

jijijj

n

jij grxxcxm ⋅+−⋅=⋅ ∑∑∑

=

+

== 111

)(�

gRxoCoxCxM ⋅+⋅+⋅=⋅ �

Figure3. Thermal network model

Figure4. Airflow network model

3

model a total pressure nodal system[1]. Themathematical model may as well be a linearsimultaneous equation system that is constructed ateach step in the process of repeated calculationapplying the pressure assumption method. This is asimultaneous equation system by the vectors of thetotal pressure and the Jacobian matrix relating tothese vectors. NETS defines an array of the totalpressure node (zone) numbers in the up stream sideof the flow path and those in the down stream side inorder to construct the equation system using simplealgorithm and data structure. In the calculation ofairflow balance, the algorithm[1] is made simple byindirect addressing appropriate total pressure node(zone) numbers by this array of numbers. The authorhas also elucidated the mechanism of vibrationgenerated in the normal Newton-Raphson methodand proposed a modified Newton-Raphson method.

DRIVING CONDITIONSDriving conditions refer to the conditions that drivethe model, and include meteorological conditionssuch as outside air temperature and solar radiation,artificial conditions such as temperature, calorificvalue, gas concentration, gas generation, as well asstructural and parametric variations of the model

itself. These driving conditions are executed byschedule and also by feedback control. The structuraland parametric variation of the model itself is calledmode change[1]. For example, it refers todisconnection or change in value of generalizedthermal conductance in the thermal network, andchanges in opening area, pressure loss coefficient,and blower speed in the airflow network. The modechange is defined individually and independentlyafter several subsets are defined in the universal setof the model elements, and is controlled specifically

Figure6. Pre-processor NETSGEN outline

173174

8

5051

6813 45

130

143

14675

121

53

12

147 64

6982

162

160

161 80

81

9

3

61

62

15

14111,112115,116117

89

88

176

175

111

100

99

141142

52

Subsystems

Coupled total system

Thermal Network ModelAirflow Network Model Gas Flow Network ModelSub-processCharacteristics ofmaterialsConductivity,Dischargecoefficient,etc.

Model elements

MethodFinite Element Partial model

(ex.)Heat exchanger

ModelCondensation

(ex.)One floor of bldg. (ex.)Wall

Driving conditions

Mode change

Feedback control

Daily schedule

Periodic schedule

173174

8

5051

6813 45

130

143

14675

121

53

12

147 64

6982

162

160

161 80

81

9

3

61

62

15

14111,112115,116117

89

88

176

175

111

100

99

141142

52

Nodal relation among subsystems

Total set of model elements

Subset2(Parts2)

Subset1 (Parts1)

Subset3 (Parts3)

Figure5. State of mode in each parts

4

Figure7. Solar parameters for glass windows

Figure8. Transmittance and reflectance of glass

Figure9. Wall parts by one dimensional FEM

Figure10. Parts by two dimensional FEM

Figure11. Fan P-Q characteristics curve

Figure12. Nodal relation thermal and airflow network model

5

by parts and mode number of each part. These partsrefer to the aforementioned subsets and do notnecessarily mean spatial parts. The driving conditionsare controlled by schedule with a concept of dailypatterns. For example, the daily pattern of ordinarydays differs from that of holidays. The daily patterndefines changes in modes and system parameters,artificial conditions, and feedback control. Severalpatterns of these conditions in a day are prepared asdaily patterns, and a table that sets the sequence ofthese daily patterns is defined as the sequencedefinition table. The feedback control rule is definedas a procedure from detection quantities tooperational quantities. The above-mentioned modenumbers are included in these operational quantities.The daily pattern for implementing the feedback ruleis also defined, and PID control is possible as ameans of feedback control. The PID control iseffective for solving the problem of the delay in timeintegration between the measurement of detectionquantities and control operation in this simulation,which is not so in the actual phenomena. It is alsoeffective for handling the situation where thefunctional relationship between the operational

quantities and control quantities is unknown. Thetime integration interval is taken from the minimumof one minute to the maximum of one hour. Since themeteorological data are taken at the intervals of onehour, the gap is linearly interpolated. NETS also cancalculate air conditioning situations under the roomtemperature constraint in the same way as the usualthermal load calculation. In this case, changes in thenode numbers and the size of the state equation areautomatically executed since nodes treated asunknown temperature nodes change to those ofknown temperature.

PRE-PROCESSING AND POST-PROCESSING SYSTEMSThe model structure of NETSGEN can be designedbased on a CAD diagram. Stereotyped parts that arefrequently used can be registered in the library so thatthe model design efficiency is improved. Because themathematical models of this thermal network arecompatible with the finite element models, modelsfor walls etc. can be made by the linear finite elementmethod and stored as parts. Two-dimensional finiteelement model can be also made and incorporated

Figure13. Post-processor NETSOUT outline

Thermal Network Model Airflow Network Model Gas Flow Network Model

� � � � � � �

� � � � � � �

Parts numberMode number

ON/OFF

1 2 3 4 5 6 7

OFF OFF ON ON OFF OFF ON

Control rule number

State of mode in each parts

State of operation in each control rule

Spatialdistribution ofstate variables

Timesequence of

state variables

Temperatures or PMV distribution

Temperature contour map

Airflow distribution, Static pressureAirflow rate,direction

Pressure

Gas concentration distribution

Contour map

time

Statevalue

Temperature

Thermal load

Heat generation

Airflow rate

Static pressure

Blower flow rate

Gas concentration

Gas removal

Gas generation

time

Statevalue

time

Statevalue

Parts means not only partial modelbut also subset of model elements

Control rule means calculation process from sensor node to manipulator node

6

into the total model prepared by other finite volumemethod. The parts library function is also availablefor the airflow network. For the blower, both fixedair quantity and variable air quantity that variesaccording to the cubic curve of P-Q characteristic canbe applied, and the blower can be installed in anarbitrary flow path. After the model structures ofthermal and airflow networks are designed, modelelements such as node, generalized thermalconductance, zone, and flow path are clicked to openthe dialog, and values are defined. Mode changes aredefined by partially modifying the diagram of thebasic model. NETS stores the parameters of thesechange differences. The correspondence of nodenumbers among the thermal, airflow, and gas flownetwork models can be related intuitively bycomparing two of the diagrams for these models.Driving conditions can be flexibly defined byclicking the elements in the model diagram withoutany consideration to model element numbers such asnode number.NETSOUT displays simulation results in two generaltypes: one is spatial distribution displays relating tostate values such as temperature, gas concentration,room pressure, air quantity, PMV, and thermal load;

Figure14. Results of airflows and space pressures distribution

Figure15. Results of airflow rate time sequence

and the other is time series displays of these statevalues. The situation of mode changes and feedbackcontrol can also be confirmed. Spatial distribution ofstate values is displayed, in principle, by numericalvalues in the neighborhood of model elements.Change of state values with time is displayed on agraph with the abscissa showing time sequence, andvalues at a desired time is obtained by scrolling theabscissa.

EXAMPLE OF APPLICATION TOHEAT STORAGE IN STRUCTURESNETS was applied for investigating a method to levelthe electricity load by reducing the cooling loadduring the daytime making use of the heat storage inbuilding structures at night. In this method, changeover dampers are installed in both suction side anddischarge side of the ceiling mounted air conditionerso that air is attracted not only from the room but alsofrom the ceiling plenum, and sent not only to theroom but also to the ceiling plenum. Since eachdamper has two modes of airflow, there are 2 by 2=4modes in total. These four modes are called the heataccumulation mode, the heat discharging mode, theradiation cooling/heating mode, and the normal air

Plaster board 12.5mm

Ceiling board 15mm

180mmPrecasted Wall

Carpet 6.5mm

GRC22mm

Insulation15mm

Pericounter450mm

Single glazing

15100

Floor121.5mm

Ceiling plenum1045mm

CH

=2

600

Seven Segmented

120

01

800

950

140

800

150

10mm

395

0

Outdoor

Room depth 6.4m

Figure16. Building structure thermal storage Office building section

����Accumulating mode�����Discharging mode�

����Storaging mode(normal airconditioning)������Radiative heating/cooling mode

��

� ��

Ceiling boardBlower

Coil

Air filter

Upper floor slab

Figure17. Air conditioner with four modes

7

conditioning mode respectively. In the radiationcooling/heating mode, air is blown into the ceilingplenum to cool or heat the ceiling boards aiming atan additional air conditioning effect by radiation.As an example of investigation, a plane of 6.4m by15.1m of a standard office building was simulated.

Figure 16 shows its sectional drawing. The roomspace together with the air layer between thewindows and blinds was divided in the verticaldirection based on the concept of zonal model. Floorslabs were divided into seven segments in the normaldirection. When the office is closed, the airflow iscaused by natural draft and varies depending on thetemperature difference between the inside andoutside of the building etc. Figures 19 and 18 showdiagrams for airflow network model and thermalnetwork model respectively. In the model, the box ofceiling mounted air conditioner was divided intothree portions, i.e. air inlet portion, coil portion, andair outlet portion. Zones were allocated also to thegaps in the ceiling boards. In the thermal networkmodel, slabs and outside walls were taken into thetotal model constitution after constructing parts bythe linear finite element method. Radiation heattransfer among the inside surfaces of the room wasmodeled being separated from the convectioncomponents. The standard meteorological data ofTokyo for the dynamic thermal load calculation wasused and nine days from July 25 to August 2 wasmade an approach run period. Figure 20 shows thevariation of room temperature, temperature in theceiling, mode change, and the change in internal heatgeneration on August 4 and 5. The numerical figuresin the figure show the time when the change in themode and internal heat generation took place. Duringthe one hour for pull down (from 8 to 9 o'clock),intake of outdoor air was suspended. However, heatremoval was not necessary during this period due tothe cool storage during night, and the heat loadoccurred only after the internal heat generationbecame large.Simulations were made for the cases in which theheat removal flow in the coil was PID controlledaiming at: 18degC and 23degC for the temperature inthe ceiling plenum, 26degC for the air temperature inthe zone 1.1m above the floor, and 0 PMV in thesame zones. The PID control was applied because ofthe fact that the control quantities and operationalquantities were separately located in the space, inaddition to the effect of PID control described in

Figure20. Mode change and internal heat generation

�

�

�

�

��

��

��

��

�

�

��

�� � �� �� �� �� ��� � �� ��� �� �� ��� � ��

Elapsed time

Tem

pera

ture

(deg

C)

Stop modeDischarge

Charging mode

Storage mode

Internal heat generation4.6kW

2.3kW

22:00

8:00

9:00

12:00

13:00

13:00

16:00 20:00

22:00

20:00

mode

FL+1.1m

Ceiling plenum

Mod

eIn

tern

al

hea

t gen

.

Figure18. Building structure thermal storage thermal network model

Figure19. Building structure thermal storage airflow network model

�Occupants 0.1 person/m2�Heat generation by occupants:70W/person�Heat generation by apparatus:17W/m2�Heat generation by lighting:23W/m2 to ceiling plenum 30%, to room 20%,to floor surface 50%

Where internal heat gen. is reduced to 50% 12:00-13:00�Outside air intake:5m3/h�m2 System operating schedule�Thermal accumulating period:22:00-8:00�Pull down period:8:00-9:00�Air-conditioning period9:00-20:00�Stopping period:20:00-22:00

Table1. Simulation conditions

8

"DRIVING CONDITONS". Figures 21 and 22 showthe results for the case in which PMV is controlled to0 instead of controlling the room temperature. It isshown that the room temperature becomes lower than26degC in this case.By totaling the heat removal flow, the ratio of theload that has been shifted from day to night (peakshift ratio) due to the storage in structures comparedwith the normal cooling load without heat storage,and the heat loss by the heat storage (heat storageloss ratio) were calculated. Table 2 summarizes theevaluation indices from August 3 to August 5. Theseresults show that the peak shift ratio is higher than

35% and the heat storage loss ratio is about 4% whenheat is stored with the target temperature in theceiling at 18degC. When heat is stored with the targettemperature of 23degC, the peak shift ratio is about15% and the heat storage loss ratio is about 2%. Forthe investigation of such new concepts as mentionedabove, creation of new simulation programs oraddition to or revision of existing programs has beenrequired. However, the NETS system has beenproved to be generally applicable because of itsgenerality of the models and driving conditions.

ACKNOWLEDGEMENTS:The preprocessing and postprocessing systems havebeen developed under the "Life Value CreationHouse Project" by the Ministry of International Tradeand Industry (abbreviated as House Japan). Theauthor also thanks colleagues of Institute ofTechnology, Shimizu Corporation, and people ofKimura Laboratory of Department of ArchitecturalEngineering, Waseda University for their cooperationin the development. The author will gratefully acceptthe applications for the trials of this NETS system.

CONCLUSIONAmong the many existing models for heat transferand airflow in buildings that apply spatialdiscretizing and formulation, the author's thermal andairflow network models can be proposed as general,universal and simple ones. For the time integrationmethod of the thermal network model, simple andunified numerical formula and a most accuratemethod have been proposed. For the airflow networkalso, simple and unified structure of model data and astable solution have been shown. Further, apreprocessing system that makes use of the generalityof the model is described. This model can be flexiblyapplied to the investigation of new heat transferstructures. A concept to handle the structure changeof model called the mode change has been introduced,and the results of investigation on the effect of heatstorage in building structures have been described asan example of application and verification of theconcept. The structures of the proposed thermal andairflow network models are compatible withconventional models making standardization andunification possible.

REFERENCES:[1] Hiroyasu Okuyama, Theoretical study on thethermal network model in buildings, Doctorate thesis,Dec. 1987.[2] Hiroyasu Okuyama, et. al., Development ofthermal and airflow network simulation program,NETS (part 2), Outline of preprocessing andpostprocessing systems, Proc. for Society of heatingAir-conditioning and Sanitary Engineers of JapanAnnual Conference, D-14, pp. 269~272, Aug. 1998.

Figure21. Temperatures and PMV

16

21

26

31

36

8/4 0:00 8/4 12:00 8/5 0:00 8/5 12:00 8/6 0:00Elapsed time

Tem

pera

ture �

degC

�

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

PM

V

Outdoor

PMV

Ceiling plenum

MRT

Figure22. Thermal loads

0.0

2.0

4.0

6.0

8.0

10.0

8/4 0:00 8/4 12:00 8/5 0:00 8/5 12:00 8/6 0:00Elapsed time

Hea

t rem

oval

by

cool

ing

coil(

kW)

Night charging load

Day time load

[MJ]Night timeload : A

Day timeload : B

Daily load: C

Reducingratio : D

Heat lossratio : F

Stored heatin slab : G

Controltarget

Plenum-chamberto 18�

PMV to 0

Aug. 3 113.1 153.4 266.6 0.401 0.041 73.8Aug. 4 116.8 183.8 296.9 0.357 0.038 74.1Aug. 5 116.8 183.4 300.2 0.362 0.044 73.6

Controltarget

Plenum-chamberto 23�

PMV to 0

Aug. 3 45.4 215.0 260.5 0.160 0.017 31.1Aug. 4 45.3 245.0 290.3 0.143 0.015 31.3Aug. 5 48.6 245.1 293.7 0.148 0.021 30.8

In case of using no storage (intermittent air-conditioning)Night timeload

Day timeload : E

Daily load: E

Controltarget

- PMV to 0

Aug. 3 0 256.0 256.0Aug. 4 0 286.1 286.1Aug. 5 0 287.7 287.7

1. On-peak load reducing ratio �D=(E-B)/E2. Storage heat loss ratio �F=(C-E)/E3. Stored heat in slab�G=sum(temperature decrease in slab×thermal capacity)4. Daily thermal load �C=A+B

In case of using night storage (control PMV to zero in occupied space)

Table2. Building structure thermal storage performance computed results