AIVC 11085 4155

Advanced Feedback Control of Indoor Air Quality Using Real-Time Computational Fluid Dynamics

Edward Ratnam Thomas Campbell, Ph.D.

ABSTRACT

This paper describes the partial implementation of a novel method of controlling indoor air quality (IAQ) for critical applications. The proposed method uses a numerical modeling technique known as computational fluid dynamics ( CFD) for modeling the effect of variable ventilation rates for intelligent and rapid control of air contamination in space. This paper describes how a CFD model is made to run in real time linked to a feedback control loop. The technique was simulated in a graphical programming language. The simulation results indicate that a quasi-transient potential flow CFD model is a viable technique for feedback control of/AQ, anti it is currently being implemented in an experimental validation.

INTRODUCTION

A rapid and intelligent way of controlling indoor air qual­ity (lAQ) can help operators of buildings, HV AC equipment, climate chambers, and clean rooms to more easily achieve their objective of improving human productivity, reducing product failure, and minimizing energy consumption.

The ac~uracy of a control system is dependent on a knowledge of the model of the process on which it acts. The model of the process can be obtained by many modeling approaches . The current trends for estimating a model of envi­ronmental processes are increasingly moving toward statisti­cal and other artificial intelligence techniques, such as time­series, fuzzy logic, neural networks, and genetic algorithms. These modeling techniques act like "black-boxes," i.e., they avoid the more traditional method of building models from the laws of physics. Moreover, these new techniques, similar to traditional mOdeling methods based on physics, assume a lumped parameter system; an assumption in which an envi­ronme.ntal variable such as velocity, temperature, contaminant concentration. etc., is assumed uniform ovedhe whole region of influence. Thus, the spatial variation ofthe controlled vari"

Roy Bradley, Ph.D.

able is ignored and the control system acts on the feedback signal of a single-point measurement in space. Such an assumption can be highly unrealistic in applications where the controlled variable can vary considerably over distances.

An alternative method is to use a distributed parameter approach. Such an approach results in dynamic equations that are partial differential equations in space and time.

Although few environmental processes can be strictly modeled as a lumped-parameter system, the main hindrance in implementing a distributed-parameter control system is the great complexity in expressing the process model in terms of partial differential equations and obtaining realistic solutions for it with reasonable computing power. Thus, control system designers settle for the lumped-parameter approach based on some mean or maximum/minimum value of the controlled process variable. However, examples do exist in literature for distributed-parameter-based temperature control of heat exchangers (Leigh 1988) and furnaces (Smith and Corripio 1985), but they are restricted to one.dimensional distribution. Examples currently are not available for the distributed­parameter control of internal environmental processes in the built environment.

The environmental transport processes within confined boundaries, as in buildings, is governed mainly by the laws of fluid dynamics, and, hence, the technique of computational fluid dynamics is an appropriate choice for implementing distributed-parameter control.

For computational fluid dynamics (CFD).based feedback control to be successful, the time- taken by the computer running the CFO model to generate converged results at each time-step must be equal to·the sampling time of the feedback controller. But CFO simulations are usually computationally intensive. In simple terms, this means that the time taken by the computer to complete one time-step is several times more than the actual time interval of the physical process .. This was the 'mairi challenge faced at the beginning of this research

Edward Ratnam is a doctoral student, Thomas Campbell is professor and head.of the Depanment of pnergy and Environmental Technology, and Roy Bradley is professor and head of the Depanment of Mathematics at Glasgow Caledonian University, Glasgow, Scotland, UK.

THIS PREPRINT IS FOR DISCUSSION PURPOSES ONLY, FOFI INCLUSION IN ASHRAE TRANSACTIONS 1998. V. 104, Pt. 1. Not to be reprinted in whole or in part without written permission of tne American Society ol Heating, Refrigerating and Air-Conditioning Engineers, Inc., 1191 Tullie Circle. NE, Atlanta. GA 30329.

· Opinions. findings, conclusions. or recommendations expressed in this paper are those ol the au1nor(s) and do not necessarily reflect the views of ASHRAE. Written questions and comments regarding this paper sl'loulcl be received at ASHRA!: no later than Ftbl'Liary 6, 1na.

• Manipulated

System boundary I --~ ~ .... . ~

,-.. •-,""' , ... .. ~- ~ .... IAQ variables to be controlled: Velocity, Temperature & Contaminant ·

..... _ ... ,. ____ .-"'r.'"'-,, .... ~

variables at Inlet

1 _ . Heat Source

Air temperature · ·, Ca11tammant ~ 1

1

Flow rate • · · ···source , / .-...__ I : ----,.... ... _. ___ ('_

Figure I ConcepiUal problem deftf i.1.ion.

\ ·'

t .... :~ .< .,

Outlet

I

·, ~

Figure 3 ·· Inside ·of the climaie. chamber showing the air inl~t grilles and the neat simulator assemblv

project. This paper demonstrates the·· use df a potential flow 1 (cover removed). . equation that is conven.ed into a "quas'i_-tr.ansient" CFD mod~! . .• · .. . . . t.? overcome .Lhe. timeliismatch barrier and implement a r~~.\ 7 . . A' heals. unul~t~r and a c?.n1:1,?1'.mi.nt simulator were _design~d ume CFD fe~~p~k~, li . 'ii'·.~ ... . .and 1mplerrletl_ftd. mle-~e!f~~tor assembly consists of six

.. .x-.,1t ~ , - · tub:ular'heaters~ each with 360 W capacity.

PROBLEM DEFINITION

The conceptual problem shown in .. fag.ure 1 · was·ton·sid­ered.

INVESTl"GATION·PROGRAM · - ,, · 1; )~" ry·, '. 1 ·1 • ., , !)1

;, General Description :and Experimental Strate!Jyi '·. .. -"'< . G! ;;. :· . ,..

For particulate contamination,:eon.u:oHnvestigations, a laminar flow clean room i~ Pt.eferable when studying the inter­actions between airflow; temperature, and contaminant behavior and distributi~~- Construction of a laminar. flow clean roorn··w ith HEPA filtersTs Vf!r/ e~j:x!n~i.ve -~nd .J*_not considered es5entlal for lhe present' invi!~iiMau'hn: I~~tead , the con·srruction of a climate chamber was 1apptoveC1, ba.S~cf on the CrOSS-flO;;.._, TdisplacefuehC type df ventilaOOD lt'i ·i a iabo?~tOry adjacent to ihe CFO reseill'ch facility (set 'Fig&es 2:1j, afid.4). ·~.. 'r'JI.,~ .. · ·~ .. ' ~; ~ ''' .•. ,, ... ·~

t'l ,,. ' •

Fi~~re l·) The,: ,f{inµit~j c~amb(!r 1for. frivesJig;afin&. CFD "_,, ,._ ff{edqac_,}(,, rqf!Jf9[ of in,dOQJ11:air qJUJ,[j~ ,;O,(ld

contamif!_ati01;i,. , .;. · :i. : , ;) <''.: 1 :: ·; " .':.

2

The choice of a contaminant simulator was more compli­;,_ 'i;ated because ~he type of contaminant chosen influences the

overall design of the climate chamber. Choosing aerosol or

sma~l, p~iTI,~~ a~ .~e cori11~n inant v~f!~l~~~al.\s: ~?~~,~~~ns_ive ., ~~d' c_~_qiple~. p~1c~]ati: .. ~oun~e~~ 't'/ tl1:~ ~sro~1at~p f~qu1re­

' mei'lt of expensive ~PA filters in the inlet air and perfect . sealing of. tHe climate chamber· to keep · out foreign particu-

, lates.' Pafticle sizes less than 0.1 µm b~have similarly ' to gas ·:, 'moleculef traveling with ·Brownfan movement (ASHRAE ' 1993') . . With · this ration~le~ it was· de~ided to , ~~e ·. C01. gas · €oricen1.r"ation a~ ine 'i ariable for ~i>ntarriiriant~ ~bnl,.01. U-se of

· . . · . • l' , •, : · . · , f'"J 41 .... • l .t . I 3 .

·. C02 als.o help,s W ~1im.pel) the inOuen~e of dust and other

'., c~~!tamjniml$ in the cjiffiat~ · c~~~und th, us _he,lp,,s avoifi the { use.,ofr ~,xpe_psive <µ\cl come~~~ p;rrti1=u)~e co~nters ;and, filtra-

tion equipment. Moreover, the use of C02 ,i!Jso broadens the results of the study to offices a_nd other open plan .buildings. A contaminant simu~4tor was ·designed :~d : implemented as shown in Figure 4: Both the Heat 311d coq~aminant simulators are controlled·bi'actuatbrs a,S 'show-h in Figure, 4 .

. r ; :A,relative gain ;.matrix (:Bristol ·l966)1ana!Ysis ·c6ttfinned i l the intuitive pairing' of the C'orittolled and R'lanipU:f~ted Van­, ·:·ables:! Thus, cc>ntah'tinant eoncentratioh 'is vaned by varying

• ' • • ' ' . f ' ' .. : .. .. • • ' '. : -~ • • ,; ...., ' .~ •

· ·•me m1er ano ·exnaust ran speeos s1mu1taneous1y as1n·g· van-• ' ' - .r . r· · · '.-

.· · able~fre(thencY'Hl'~erters·. and the spa:ce t~ro~rature is varied : by' varying .the rieac"inr)~l rate~ LO the irilit ~ir d~ci h~at~i using · · ' • ~ · • · r' * •. , .. , '' · .. r · ~ -~, · · - ~ ·· ' , ·

.· :~ th rist~t'cis sh~~n iii 'fi ure '4: :~ " {;' ' . ;· ' . . , ,, l ::.· ·11·:: :••,- . ...-~JI .t l ' . j· )il ~.:~J r'. J.1,: ): .:· i

1;- ;•L,atent heat:exchangesfare,.ignoredi and;·he-nce, moi'sture

. ·disu-/bution is neglected for the i;;urr.ent investigation, although . · humidity sensors are: used for1experimenui purposes and· for . :Jumped-parameter mooelirtg ofrelative'huniidity dynamics in ··the·cliinate 'chamber. · "; ; :; : ~!·<

4155

~ - · 2,·;

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· IJ I ,_,.

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-~

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• ~·· ~1r-.

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··~ ":, .. ~I•,•

2A.,j

(\ . I

'- .l ·'-

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:, s.mSorSignals:'' - · · - · · - · I:_ . - A~1or Signals · - · - · - · - -.r{ / .1.lfl ,'J"U't•

.,, ' i I . I !

~~---~-~..,.-J ,@11fti1aa I 2.7m '

l ~ · -·--- · -·- · - · - · - · - · --- · ~ ::- :c·, I t . I' -.

,.-Figure 4 . Geometr.ico.1:configuration of the .. expehrriental setup. and computational domain of the real-time CFD .controller. model., · '. .~1 .

• , ,. • . · . 1 . , . ~ · ! .. · ·:, ~ · r : ~ • · ' . .1 2. . . · ·:.~ . · .1 . ·. .1 ; • •

Simulation "Modeling of the IAQ Process in the . Climate Chambe'r'using Comm~rCia1 1cFD Soft.Ware

. . . ' -~ .. , _, . 'i ": . • :

,- .. ,The ;equations that describe th!': JJµid flow, heat,:;i.and concentr,ation withjn <\n;enclosure iri:e all based.on. the conser-

• vatiQn of mass. mpmentp,m. thel"t!lfll energy, aqd concentra­tion .. ~pecie~ wit~in th~ .~nclos:~~~i . The b~i<; equat~ons for three-dimensional incompressible turbulent flow of a Newto·

, . t"' '' •• ' ; ··• '. ,. •.• ',I . t · • '

nian fluTd 'are ·oased "cin the solu'tion of Navier-Stokes .equa-tion'S, the fuass. terhpe~ature and ~co'rlcenci-ation equ~iioris. and

): th'e·tfanspon"eqoa:t ions 'fcfrturbulent velo'City ahd its scafo: All elide equai.iohs, except' the m~s cdn~ervation -:equatl6n, 'have

,,. the .gen~ral f6nn: ' ···• '. . • , ,,.,- l'l '"''·1 1 •

,, : ... a '·., .. ,, .... a ;· · · ... a .. :··. • ·' "·a· ·.: c ·~·;.,,. , ' . .. ""1""') +··"'"1'P""'·) +.a'---(.p,v"')·+ ;:;'"(nw°')!.= ·~ ' • 'al\t<'r. .... ciX~ .n"t' -·· y· · 'I' · uz tr · 'I' · · '

• ! I ,,, :.-:!(~*~~y+·:yo~~~~F~(~~~~s~~~~: (l)

Ii'. where.w is L~e i:iependent variable and S~ is!lhe source tenn for

1 •• eaoJ:l:gep~.nEle,JH v!l{iable :J;q,u~tiQn l als0 rl!presents the conti­.;: flU)~Y equ.at~on wh~n .$ 'E . l~nd ~0!:=ri P·i~~1\Ce .~lte \ietaile<;i: Q~ri­

vatiq11,{l,nd .e.xp.~!i<?».-Rf tqt~ ~~ualio~ c~, be f,9,und in m~ny u P?oks o~. Quid : 9~~wiic~.!i it \~ 09IY .. b.rie~r 1cited ,her~; A

co~file_rcial dp pa:ck"lge was enmloyeg, to .soJ ve, the system of equatiohs rep'reseii~ing t~e, a.~o·~f eq

1

uaifo,~. Th~· \I/all~ were treated as adiabatic, and C02 cdntenWJtion"in the inlet air was

.,assumed equal to the1aYe,I'age .~ient value ·of 400.ppm. . :-1 . . Open-.~oop step testing .is: sti·Jt the· widely; used 'process ide·ntification te..dlnique-. ip <he industry;, and .Table J: lists the inpµt boundjl.I}', c()pditi.o~.s u~p :f<:i.r,dhe i;imulation ~. in. the commercial CFD package. These ar~. the., -s.~e bo);mdary

., 4155

conditions to be applied in. one"9f the· exp,c;rime,ntaJ lj!Jit cases of the climate chamber for the fonhcoming experimental vali­d~\9?: pro;rai:n- J,be. ,pr()~ess tr~i;1.sfer fu~iztio~ . obta,ipe4, from a step test usually is expressed in the fonn of a first order plus dead time (FOPDT) model;"

... , · ! ·.:.: ·. ;i K e':Tos '~ !'J;

GP(s)<=~ 1, . , .. ".(2) "•. \ 1\ •I,. ~ f ~ ( I • I ) fr I ,., •

.. T~.!5.1.n~ 1the bPJ.to.ro)ef,t,corne.r as the coordinatf( (0,0.0), the

beh~v.ior of all wi:~s: JAQ va.i;iables was monitored at fiX~ ·g_rid " po'irits, as \l<;>te,d fo. Table. 2. dut of.these. ,the first .threir, grid

_ ' ') ~ ! •' ,..,, \ f1") -.• I I • ~ ,,... - ~

... P;?,int~i:~ere ~tio~~n v,t;ry close to the o!>.s.t~cle : '.Jbe z location · \\'.a.s varie(.19 im,..~s~i~ate the thre~-dimeQSion, i,I behayi'!L of

the variables.' Since it is not feasible to site the sensors so Close

to .1~b,~t-Auo.a"lQ. ;$~~ .~~.ll~-~~, · 1· · ~klions :"':tt ,. . , .. •.. ~ . ~ ~ ut... . ' ,. 1 • lf

~e~e monitored'$ · ~~·1p; ~qjJ~~·-· ... : e . ~b ·~ .f ·~ .co2 .~atte~Jw~-Test Cas~ .. k~cr ~e1=ond$ after applyjngfo1i~ step

· ~v: • .r l~"'- .. .:.. ~~ • ~.. , .• - ._ '!!'t~.1: -i. ... 1..,,u.l , . "'"";r """""~)· ·-' '"!"' .. ,,.VP'-~ r- . .;..,".~. l:~l)~· J -~ I"! ..... ..... ,. .. , ;- .. J ' {_

~ ~ . ~-... \• -· f, ~ ..... ~ ._!\. . . • 1' ,.~~~:")·~~ . '

~a~Si!i of_~mulation ·Reaul~ if \ '· l~· .;-c-~ . ,

.·~ Wh~n ~-: bou~~ 901nditions~f. ~i1~~ ·f\~~£ ;~1~ to

}~~ · S:Y.S .tep%. · e-Jl! "f~UlfeC!1;'yi ~m. o .. ~t. nel~~ 1.bl~ . ~~.an· !· e· , ~p ~~~\C02 ;P.~i~~m~h. d:~on~e~fi;a~~n ·~~n'~jc~tiri~~-at ,a .• ~~~i inlet air

·i.~1,0pe!~~1tt~!.1 .~ ~eg11rm_ti; · j!fip. pn~~~~~~~·- ' r~p~rt ·l:i~h.avroP." .. , A s1mtl'!: -tit;(r~~~-~o~:eds~ 1.t) ~1· ~~~cuy ~~em,~.~.m,ag~iludes. Ho'tW~e'~~~p~r~\~fr\ ·•· _ i~~w a 'clear!Q.ri'S~rtf cflange for all gnd ldcitidrrs: Fd°r 1e&Se B .

·"it w<IS observed that all tl'iree "IAQ'·vmables show transient . chan'ieS>·af all grid 16eations,"indicating the stronger depen­dence of IAQ on inlet air velocit}"chang~s. ·

3

I

~

TABLE 1 Initial and Boundary Conditions tor Meeting Open-Loop Dynamic

Testing Requirements for Feedback Controller Design

Case A: Step Increase in In!et Air Temp:

Time-Step, Inle~Air Inlet Air Sec Temp., °C .Velocity, mis Simulation Criteria

0 16 0.05 Heat and contaminant simulator operating conditions : C02 emission rate= 4 .33 x 10-' m3/s from time t=O until end of simulation run. Heat simulator surface temp. = 80°C from time t=O .. .. until end of simulation run. First. the initial steady-state velocity distribution is obtained for an ~ . . i . (. ,, -·. ! input of 0.05 mis . To get the initial temp."and C02 com;entrat10n, both the heat and contaminant . " ...

. :.;~· simulators are activated as above and _the simulation is run until steady-state conditions prevail,

-' before stepping-up the inlet air temp. :

1 Step increase Constant at . -~ .....o'

to 20 0.05 .. ; ::l ·~ • • • ~

- ~ . . Continue Until ·. Steady Stale

Case B: Step Increase in Inlet Air Velocity: .l ~ ,...

Time-Step, Inlet Air Inlet Air - ""!>''< ','"ti ' !/.\. i . -~ ~tf~- . '- ~,l!.'~ l _, ..

Sec Temp., °C Velocity, mis , ...... -.. Sim}:l41!~~ittel'1t.I(' ?nJ.~~ . ;.. · . ... • ' __ ,; :!Ii' j

0 16 0.05 ·Heahnifcontamjr:ifili1 simulacor operating c 0rid~1i b'ns!.c'&~~'l:i-ll'irs~ton rate= 4.33 x 10-" m3/s .. . fr~;; ti~~ ·t~ until end ,of simulation run. He~Csimu\ator ~urla~Memp = 80°C from time t=O until end of.simulation run; First, the initial steady-state yelocily distribution is obtained for an input of 0.05 rrils:·To get the initial temp. li~d C02 concentration . both the heat and cont~minant

-I

simu1lators are activ<1l~d l\~_,abo:'<e and th.e simu.lation is run until ·steady-state coriditioris prevail,

'•: before stepping-up the inlet air velocity.

I Constant at 16 Step increase ; •' ' r to0. 11• ; : : ' ' ~ • . *I I- \ I I -

'i - . ... '· : r· ., · l~I r;1 ).l. ·..: · '

, -Continue u,,n1 Steady · · • Stille ; -. -

._.· ... , •• C! I\_,, ,,."' ... \}I

, ! ... JJfJ:. I' i: :, ',,

' -;;: L; .•. ' i( I I

~I ~. I

"!~ I ~ t .' I • • : !

, , . 1!

,,; )i" -.·1 v ,,:fl ,., ,, ' 'I •o

- ,'J°',f): .. !j ~ ;: ; .. i·.•.-; • •• t 'l .... .,

:, f - i:.;LJ ·· · " ' J-:< '" ·.. TABLE 2 <t . : ;:;-" ,,;, , ~ · - ·~, ~ ' ·C.·~c;r ;.- ·!.i

Monitored Cells in CFO Simulation of the Boundary Conditions of Table 1 ':''I

- Monitored Cb&dinates,' (x,y,Z)~ n( · ·Reqrks :. .. -·, :i! : · h~·:n ,'.J

1 1(1)'~~ ~ o.2.~5 ,_?-~fsr~ . .., .' 1 <;:lo~e to heat and contaminant source and waJl;' ZI .= 0.075 correspontls to· average-depth cif · °'

· .l'!~~~!iory _of~cl)sensorfrom !he ~ll, ,- v !·; L·. ' .. >r ·- · :' . ,, H - ' ., '

(, I. qs1;0. ~2~, . 0(3~5,l "'~::,-] .1 :• : ' .;;: I Close to heat and contaminant source and away frorn\~alf i = <P25 faces· the cer:il~~.of an' i.nleL

( l. ! 25i '0.22S-, U-:575) 1 '.' 1" ;. ~ ·..; Crd~e to \igat a:id contaminant sour~~ and awi y' fro1~w~I; z~· 0, ~7.5 fa~es the, '.:g;;p_s:~;.between

L ' :.~ . ~.-.-( (.> , ~ J i; ~ <.: ... _ ... • . : .. }./' • -Jo i'ni~Fs . .i , . . )""" ~ • • ,..r ~ , , i :, • . • ' . . ·' . , . • • ' : l ... I

rt :;;..,:~' '\ ;~~" ,r;.,:;;:;- :1 . ,, \ l • V'-.J • J. . V.l...l t V oVl .J/

•":

" ! . • • r'it'}.''

(:':091_5, 0.9,:? •_.~:~?~. ,c. :._ 'i I

t ••

Downstream of heat. ancJ i.:ontaminant·sources ;.z = 0.07!5 c6rresponds t0 average' dei)tl\ ·of piojection of each.sensor from the .wall.. :. ::·. ·: ·" i,.:• ' . ' , ' ·.;: ·, ·

·:~:·, n .. -.. .' ··,, :-.. .'! • ., .. , .... cr·i, '"'r ,l.o' 1 f [. ' • ~ ' . Tjf " . 7 ~ ·

1.1. 11 '""• I !<', ~ ~ !i ~ {J~,q • ·; 'JI ! .({ \·~f ~. , r •

··' ' .. '• t.f ,i';.•

' .. l ~.: : •: . 1 ~· I "',1( •:

. ' ~-r · ,., -.· ,. .. ':1-·1 ·:111 ,1 <.J . '. ~ i" .... ~

.,. .. ,,,_ ~ l -~ ~~· .q,: '!' •• :.11'

:...: , .... , .. :" .. : ·· ·: ' . ; ·: ·: .. 1 ! ~ .. · . .. l -. I •t.. .11 'f • · ~ ·

4 4155

J'l

~:~:···· =:·-··

: .•• i . .:,~ ....

3-D CFD ·ofTr..roJent Flow: Heat Transfer and Contamination in Climate Chamber Initial c:ondition:. . . • .ifllel 16 deg C, 0.05 iri/s, with heater and ~02

Transient flow, ini,ei 20 deg _C, 501 . iterations"S~ sec:onds . ·. r , · ·'< ,, ' -· , . • .

28-MayT.97 M , ,.

SC l-C02 I

TIME = 51.000d LOCAL MX· 0.S769E-01 LOCALMN• 0.5970E-03'

0 9769E-01 0.9076E-01 0.8382E-01 0 7689E-01 0.6995E-01 0.6302E-Ol 0.5606E-01 0.491 SE-01 04221E-01 0 3527E-Ol .. 0 2834E-01 0.2140E-Ol 0.1447E-01 :. 0.7533E-02 0.5970E-03

y ·- Lx

Figure 5 C11ntaminant pattern corresponding to bburidaty~onditions a/Table J, Case A. (Key: 0.597 x 10-3 = 400 ppm.) ' ;., ,. . ..

A program was written using a graphical programming language (GPL) for deriving Cl FOPPT.model from process input::output data. :Tue response data were analyzed using __ thif•" . program, and lhe "results in tenns of process gain, KP, time constant, 't, and dead time T0 are plotted in Figures 6-11 . For Test Case A. the gain and time constant were plotted only for the temperature variable, since only this variable exhibits significant dynamic behavior.

implement linear controller, design. The contaminant gain exhibits·pesitive·gain at two grid locations, as snc»wn in Figure 10, The gains ar.e, however, negative -at the two sensor-loca­tions, indicating a decrease in contaminant concentration at increased inlet airflow rate.

Discussion of Simulation Results

The dead times for all variables in both Cases A and B were below one second, which is below the controller time step and, hence, can be ignored. Therefore, the speed of the

., . . . ; . IAQ process variables is dictated by their respective time · ·· .. , , C<;>.Q~~nts.~ " ' " +: ' .1;

1( •;:~·r ; '.) :. ~ ,.J'.· 'J. 'v· ,.!.:i;t·

_For boundary conditions .corresponding~\o · Tesl Case A, - ·· Figure 11 shows th~_ comp~i~9n·o9ilije cBn.stants/ofall .~~ tewpe@~l!r!! gain.is .hig~r neiµ- t.b~ Ji~at~ource.~.rnd lower : _ three IAQ variables at the five 'grid ·1ocafioris:·1t showS'that cfownstrearri: ~f iiie : h~al ··source, as shown in Figure 6. temperature response generally is very slow followed by However, the time constant plotted in Figure 7 exhibits ~n · . contaffiinant c9~centration at .each grid . location. · However;,

-.. 9PPb~1t~- b:tf?~~vi9r,)~: . -it .js ~~all, oefil . the- h~ai. sourc~ -~d :___ " velocit~ dynamics is m~ch faster~ es~cialfr near t~eheat and . mucti lug-heF downstre~. ·Tius 1s as· expectelfsmce the po)nts contammant so~rce. However, at the two sensor locin1ons, downstream of' .th'e 'hear source experience ~slow dynamics velocity dynarnic.s slows down and its time constant is iri QCS:~UJiLOf .the effects..oLthe wall. For -boundary conditions··· excess of one' minu.te because 'Of wan effc#s··an·d ·th-e flow corresp0n.ding to•Tesr. CaseiB;·the velocicy ·gaill'is higher riear . phenomena in that 'region. . '

, the heat and contarni_!!an1. ~9urces, as_,sb.own in figure 8. This ·: · . The above analysis, in conjunction with Fiat.ire 6, ~· 1 .......... ,.... .. .- - · • e ts as CXJ?CR~ed Sil}lfC a fiµid ~xperiences.. acceleration while confirms that the environmental process in the climate cham" going past an obstacle. The temperature gain is negati_v~ ! ·a~• . l;:ler is a inultivariable distributed-parameter problem sincethe showtrin Figure 9, ·indkatfrig tne"coollng effe.ct of increased velocity affects both temperature and contaminant levels and inlet airflow. the IAQ variables and their individual dynamics spatially vary

The dynamic parameters of the contaminant were computed after linearizing the nonlinear response of the contaminant. This linearization normally is done in order to

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in three dimensions.

The grid location ( 1.625, 1.625, 0.075) is preferable for siting the temperature and contaminant sensors. as the dynam-

5

6

1 ~~~~~~--4.-.---.-1..--.....---==-~· ~· ~~~~~~~~~~~

~ 0 9 l ~ o:a ~

B..-'Jt:. 0.7 -.5 0.6 ..'.. "' ~ 0.5 -GI

!5 0.4 ' ~ 0.3 + ~ 0.2 -

~ O .~ -- ~_j_~~l_~~~_L~~l._~~~1-~--1~~~.-L~~~-=-~~~-=-==--:-:::--1.125. 0.225, 0.075 1.125, 0.225, 0.325 1. 125. 0.225. 0.575 1.625, 1.625, 0.075 1.975, 0.975, 0.075

Grid Co-ordinates, (x,y,z), m

Figure 6 Temperature gain at various grid.locations from simulation· resulH1f Test Uase A: " -~" ·,

' ~ i:} •.. ' 11ib :· ,.i ~ ..

'l~.\ ,·:· ·.~!

140 u .

~ 120 t !:-- 100 "'.'"

'E' -ao .l. • I - 60 + en c I 0 40 + (.)

;1 ,' I

D ' E 20 .:. j::

0 1.125, 0.225, 0.075 1.125, 0.225, 0.325 1.125, 0.225, 0.575 1.625, 1.625, O.Q75 1.975, 0.975, 0.075

Grid Co-ordinates, (x,y,z), m

Figure 7· Time constant.at various grid locations from simulation result of Test Case A. ·-:

- '("· 1\.I

~ •it .,,. Et'' 't :~

en .5. ·0.9 "'···" · , "-f< • - • - - - -- --- -·----- - --- n .. ~ ... '<! -;, Ml ~~

0.7 I ~ ii: .5. 0.6 1 'Jt:.B.. 0.5 T

c .. o.4 T ."2 ·i:J;l,'3 T "' I. ' . I CJ Q.2.> -~ VQi~t -_g ~ -i~1 n = :-·

·~ ... ); ;•·

h :

~ ~ :

.: . ~ I - · - . ~ l - .. ,. 1?<; •:.. .. ~ 1 - 1 25 ., • 12~ _.f • 625 . ,-1? ' " 1 ,.,-~ - .. -w, ~ '*-~ ' · ' ' \ _ • l • ..,, ~- J';_ ·i I . I • - ~" -~'"·

1', .. ~ .. • ... ~jfl'-.. . ' - \ "! .. ¥ ... - • Vi. d • Q.225, , ··~. 0.225, ' ' 0.225, ,!.,:.: 1:625, ~· .}1 0:975,

.. . ~ .... 1t~ ' . .>r- - ' • 'V.t:t- . ________ ?. .. ~~--.: _,. 0.325 --~;575_ -" . •j 0.075 11-t_9, 0.075

.. ,. QrJd;C;o-ordlnates, (x.,y;z); m:: J

;, : ~·\(·l'i .iig.'.tf';·: i! 1(1· ·:J ;.,~ ,~

..,

]... "' .. ·

l i·

t. . t ..

•.li ~

Figur~ 8 . ):' eloc!~ ?_4/{l:, f.C.,v.,ari<1,~~ grf(i lo~atio,n~ J;r.p~si""'¥!~ti(Jn {e~ult q[T ~s!1 9~e:l1· .i<·. 1 ,,,:, ·.\ ·. > i,, ~;'\ .

:1 I

9 I I

4166

Grid Co-ordinates, (x,y,z), m-

1.125. 0 .225. 0 .075 1.125, 0.225, 0.325 1.125, 0.225, 0.575 1.625, 1.625. 0.075 1.975, 0.975. 0.075

0 iii E -10 .:.

1- 1 ~ -20 .'..

Q.

-30 l ::.:: c;

I n; -40 + " GI I

~ I

iii -50 t ...

-60 l GI ~

E ' GI -70 1 ~

-so I

... •:o c· ~ ·w·.

Figure 9 Temperature gain at vo,~ious.grid locations from simulation resiiltxJfTest'Case B.

Grid Co-ordinates, (x,y,z), m

1.125, 0.225. 0.075 1.125. 0.225. 0.325 1.125, 0.225, 0.575 1.625, 1.625, 0.075 1.975, 0.975, 0.075 -Ill· E 29760 e ~ 9760 l ~

Q. ::.:: -10240 t I I I ,

. c

-30240 .l. c "

I

I E -50240 + Ill c; I e -70240 ~ s c; -90240 ~ ·~ - ., .'I ~· . ' ,. 0 (J I

-1 10240 l . 1":.

-130240 f· ~ '._ f ''. f , , : 1 • \ I ~ ., • • 1 > i •

""l "

Figure JO Contaminant gain at various grid locations from simulation result of Test Case B.

[JVeklcity

a Contarri1ant Concentration

250 __ _ •Te"l>fll'•!Jre.

u 200 : ~ .: 150

I 148.1 150.6· 143,.5 ..:

c; .! • c;

100 0 (J

• E j:: 50

0

1.125, 0.225, 0.075 1.125, 0.225, :Ol825 1.125, 0225, 0,575 1.625, 1.625, 0.075 1.975, 0.975, 0.075

Grid CCM>rdln••. (x,y,z), m

Figure 11 Comparison of time constant arvariouS'grid lOcalioriSfortill 'ihree IA(fvdrlhbies from si~ulation r~suft " , of Test Case B.

4155 7

ics of both variables match at that location as can be confinned by observing Figure 11.· Such matching makes the control design task easier.

• ' 1)

SOLUTION FORMULATION

Evolution of a Real-Time CFO Feedback Controller

The analysis presented in Figures f 0 a~d 11 and the over-:r all behavior of the contaminant as observed from Test Cases A and B suggest that contaminationrrs a difficult variable to control mainly hecause its time. constant is vory long, which is further worsened by the fact that the sensor measuring its , concentration adds another time lag. For example; the C02 sensor has a time constant of 45 seconds. The dynamics are also slightly nonlinear. This led to the application of the "cascade" control technique from classical sontro.1· t~ory. It consists of closing a feedback loop inside the primary control loop by measuring an intennediate·proeess variable. Cascade control is·indicated-when (Smith and Corripio 1985)::'· ~~

.• • "'I "··" • . . -'

the r<l°1ponse._ o( ~ . ~!ow 'ouwr' lq~p can be speeded up by a · faster:accing inner loop. ;· "l·

"! ·c •'\ F• , • •• ,

any distufb'a.hces that a'ffect th~ slave variable 'are, d,etected ~d compensated fo'r· ~y the sl~ve ~ontrolfer bef~re .they have Lime to affect the primary c'ontrol variable, and

• ·.:. J 1• .... ~ • ,_ • >' I . ••

.. ,ponline~ties of t,he process in the inner-loop·are handl~d by thalJ9pp and remo,ved from the more important outer loop. , ... , .. -. ,,

:~ .) •L • ..

'.lf. ,'.:

•

· : Thus. incthe case of the climate chamber sy~i~m. the veloc­-ity can be used •a\; the slave variable whose dynamics are about four times faster than those of th~L contaminant near the contam­inant sd~rce .' However, it is not feasible to site a hot-wire sensor

. ,. .. , . ·: . .. . so close to a· source of heat and contarmnant. If the hot-wire sensor is 'Siteq at either of the last two grid locations, then the advantages ar~ diminished becaus~- due to wall effects and flow

" phe~omen~ in . th~t region its dynamics are much slower at those

__ locations~ ~; ca}l,.~ s~en in Figure 11 . If somehow the velocity ' close to the sources of heat a,nd contaminant can be '.'inferred,"

· · then a co~~iderable advantage can be obtained becaU.Se the

. velocity dynam\cs at th~t location ait: auout 13 Lim~s faster than ,.r~e con~i~ant dyqamics at the contaminant sensor location.

,. · The GPL softwaie wa~" graphi;ally prograriimed with a

.. ,, ~ x 2 multivari~1~/cr. 1~l\g ~~.~tr~per,.as shown•lin· Figure 12. · ''The cascade.~911troJ ·19..<m.·(inqicated by he~vy. daslred lines in

Figure 12) also was .... program!:l'le~ in the ?PL software. The chain lines indicate . the ' intera~lion loops. The transfer func­

, ti on G 12 is made equal to zero si~ci; .~he .i{llet air temperature change haS negligible effect on the 'conWninant concentra­tion. Hence, no decoupler is required between M2 and Cl. Based on the FOPDT par~~ters indicated in Figures 6-11, a multivariable controller with decoupler can be designed and impleme~ted •without ~he ~lave , co~troll,er. tt11.wever, the incorporation of the slav~, loop in the above system necessi­tates a knowledge of the slave variable, air velocity, near the contaminant source.

:~ - Ml + . E3

"-OTI"P!!Sif !I -~ -~M3 " ' C3 .:rr- ~ 1 ~!~ .. +• I .. ·:· >'j

.' r· JD. ·11 d; . •,'f ;!•

f' ,,_ ,. j.. ' ~

'../

' '

';·~ ~ ;~?_f r~o· .... ' u,,, ••

;1c;-·, ,, l • I ' ... ,

:. l.! ~· .JJ\ ['. "l .• .ii !:....!-.. , :·11' r· , . ..

::'; 1 r .. ,, " . I

I I I

• ' - .. • J~-

l .. , . ,. J --- • r ·- . -· - · n1 -·~11~ ·-. - ·.1.~ ·;:.-:.-- __ ..J _ .. ; ·--.:--:~" ... I ,

r. . . I -·--~1 It---·-·-·-·-·-·-·-· I

:;ii) ,;··)·~-~-·

.1 'i'(,,'. '1 '

~ ......

" ·::®f ·····~ :~ d r,., i;. ,, .,! ' ·t- • . '.'.

'J• • "f • t j' • "'?• I f "" ;J'• - ·-. " £j

t f ';( •fl":' • " .;' .} . r,; -:-:. • ... -'l • ~ .~-, • "j • ,,. , .. ,

._

4'·) ,;• • ,#!:

..... ~!. .... '·-

' lU : Conum~t ~-Point: R2: T emJ1C?'lllll'e Set-Point; EI: Contaminant emir; £2: T~ error; • Mas!t:7 di11tb llc:r · ( 'eonwriinant ControllCr; Controller. 2: T cmoerwrure Cainrolla'.M I: Minipi&laltd VariablC buziiut

. fr\>111 .~ (OJXJ1mllct;0M2: Manipuliled V'arilblc Oulput from Tcmpcranuc Conlrollcr; E3: Slave variable error; S)avc CC!1"1rQ!\cr.Mr-Vcjociry Controller, Ml: Mmipullled Vuiablc Oulpllt from Slave Controller (Fan ouq1ul): Proccs.S 3: l]lc d)'lilri(ic pro=s d~bing tbc relalionship between the Slave Controllc:r Olltput M3 llJd the SIAvc

•· Controller .'l*'iable CJ: 0 : Sl.lvc Cooaullcd Variable (Air Velocity in~);~ 3: Feedback sasor for~ Slave

' f) •I•# , ~ controller loop: Pnxcss. I: The dynamic prv=s describing lhc n:lalio.Jh1p bCtw=i C3 ·mid il\c primary ~trolkd •

· ·l varllblc Cl ':' CI : Prim,vy controUc4 variable of Master loop, Cont.UhillanL conccnnnori;>~ t': FCCctbiflt sensor for ·' . lhc'PriiliT!y ~ntrollcd variable, Conwiiinani'$cruor; Process 2: The dynamic pn>ecss describing th.Q reWionsbi_p

. ~~·t-t~ C2; C2; Second l'fimlJ)' Conlrollcd Variable. Space TctnperlllUn:; Sc:asor 2: Feedbaclc sensor for the Second Pri~.!=<mtn>llcd Vapable,. Tcmr;nwrc,$Cllsor; Gl2: Tr.nsfcr Funttion ofth.c Interaction b«wecn Ml and

1- _;.,~1 ' ' t' Clr-02f:·~cr·Ftlnclion of the inler&eli~n. ~Ml and C2. •~' r.' ,'· hH:>r ' ·"' , ;. a. .. - 't ......

-~\:,

.: ... tl r· ,g;

""'. '~ :{'•

't l .... ,,

..... r: 1 I•

~· ... ~:.: · · .. .,, ,

. '

(~

F~gure 12 /ylµ(tivariablt'JAQ Mnttoller with .. CFD'Jleaback cascade controller in containment conrrohlcop. ,,, ·-h -.,,., .~ ~,. t.)I 'i.:ii i:.: 0 '"'1 .s.;... : .. ' '' le..,, • .._•:.:. . ','

8

.r.-

,f',' I

4155

•ii

I ~ :

For infen:\Qg .the air v~loc.ity. Process -3 in Figure 12 can Y~ (10) be' modeled 'by a "variety of numerical tech1.1iques. The most '' · accurate and current state of the art of these are based on either

·' Obstacle:

d'I' = 0 .ay

1 the finite volume or finite element method of solution of three­dimerlsional Navfor-Stokes equations as described by Equa-1ion' l. Since the velocity time constant is o~ the order of 13 to J.J seconds. the Nyquist criterion demands that the feedback. controller's sampling time be on the o~&~ of 1/\0th to I/20th pf··this value to avoid aliasing in a digiliti control system (Gol.ten and Yerwer 1991 )'. Probably only a powerful super­computer can provide modeling resulis within such a time frame. -' ·, '

.Thus, the search was~n for!a-mathematical model that is simple and robust, can produce quick results, and -~et be reasona~ly representative 9f the phy~ical p~qcess involved. -

I ~· }i - 11'1 ·' ., ._ ·-

Description of the Slave Controller and Its Process Model for Real-Time-ef:o F~dbacK Control '

If the flow is assu~~p1 irTotationaJ, inyiscid, and j ncom­pressible, it can be show'n that the flow dynarni~s can be expressed as ~ ~otential flow (l'.aber 1995) in te.rms of the ·stream function, \j/: • • .•

a2 , a2 , . , ...J!+J·=,0 2 .•• 2 • ax d)' • ~ I •

The velocity components are 'computed after obtaining the stream function distribution, ·

1 _

~ .· ti' (3)

The heat source. which forms a solid obstac;le, is modeled as

IV = 0 ' ~ ':~ ~ n<.J~.

(I l)

Controller Equation . Th~ generaL equation for the output of a PID control law

is. (Sm.ith ~nd Corripio 1985): :: I -. dE

, ., _, .Nf(r) = K, [E+r,fE -dt+!J.? -dt] (12)

where · ...•. ....

.. :• E = 8-C "'

• (13)

' Solution Method

l))e solution to. Eguation 3 is similar to the solution of a " transient two-dimensional diffusion problem and, hence, can

be marched out in time (Abbott and Basco 1989). Using the • . • 1

geometry and computational domain mentioned in _Figure 4, Equations 3 through 13 were graphrb:lly' prograrnmed in the GPL software. All the equ~tions are,solvq(,l: sj~ultaneously. A fihite~ difference method-of solution . known; ~ the Telenin 's

·· metnod (Holt 1'984) .,.;~ .grolirarnm~d ,t"or .solving the mode-I Equations 3 to I I . I~ this method, taking the closed boundary , ail) - .· . .

_,. '" u = ay ( 4

) _, as a reclal}gle, Cauchy data are prescribed on one sjde and used to \ntegrate Equation 3 step by step 'to the opposite srde. The iterations are continued until all the boundary values are satis­fied. However, for the.current work, these iterations continue indefinitely to keep track of changing boundary conditions in

aw v =-ax

-~-" .. j ~

(5) ·' ~-v

such that the continuity equation is automatically satisfied: -au+av-::,'6~ ~' -' : --.: • , ' •. : ' : ' : ~· (6) ' ax ay

Boundary Conditions ,

Inlet and Outlet:

7....,..,. ,_

The stream function must vary linearly to give;unifonn velocities at the inlet and outlet:

At inlet:

.-re~ time. 1 - " ~~

Th<( compuc~'tional time is strongly dependent on the mesh size. The computer used for this implementation in GPL is a PC486/DX2/66MHz with I 6Mb RAM. A time step of one second was used, and after some programming trial and error, it was found that a square mesh of 0.150 m is just enough to complete the iterations at each time step to closely match the transient of the velocity obtained previously from three-dimensional results from the commercial CFD software.

_ '1'1 =.HI AJ)I .. :;:-~-oil., -,~ .. .. . " . '" --· " .. .

At outlet: \f •:

IV 1 = ( Vour~>f -

-- tn --· - ··-· Although, theoreucally, the-outp~t -given by Equation 3 is ''quasi-transient," the controller interprets it in ten:ns of real time, which· enabled the achievement of real-time simulation of the CFD model for feedback cofttr0l-,purposes. The bottom left corner in the ·x-Y piane ·w~ us~d"as the grid reference (0,0) for m.i· tw0-dimensional simutation in GPL. Funner

(8) . __ ,.., ; • .• , ··:-•;::i "

where I and J are, respec.t,jyely ,, the::r:ow;and column numbers ' starting from zero. . . - - -;,:_ ~, . ~: : -, , \ .,, -,.,;,, '·'-· :'.:. -, ·• ' .. ·r

Walls: _ . . , . ',-. ; , -,: Since the flow is assu~ed t~ be invlscid, _only the _~ngen~, ·

tiai component of veloc.ftx. ~ilLC(iisi. ~i me-':walls~-~d the nonnal component will be zero; hem~e:~ _. , .. : : '" ~ ~·~'.:·~ - ' - '.

On horizontal walls:'. , \ ;:0:::;,.::":,~ :. ,, ; , .·: '" '..:~. - ~, ~> - ~ .,,

~~ = 0 (9)

On vertical wails: .. . 1 " ' •

•• · .1• :<1 j·,_I \'~ ':'l(\ • ' :-. r _; . -~~:·

4155 .... ...

.. details on t.l_le GPL 'imp,Je~e.ntatior(.of the real-time CFD controlJer mo.del ire shown in Figures.W-24.

The CFD controller e·guation (12) ,~as programmed using a parallel;l'!'lsremeni~l · ~f:b algonthm (Golten and Verwer

,1.. 199 I) after applying bilinear b'ans'fo'ftfl.s for digital implemen­. · talion !n the G.PL prcigraffir,The set Point can be chosen for any . . .... ,,-• ,. .. · · two-dimensional location provided the dynamics of the

, conu,oll~,d variable ·are · known at .that ·1oeatfo'n. The initial tuning estimates were obtained from Ziegler-Nichols open-

9

. . . .. ·. . .. 01 /

0 09 {

-~ _, (1 . 125, 0.225. 0.575)

~ :::: ,· / / I I ] 0.06 j I • • / •• ·-

:; " ,,--. I - 005 1 ; ~I

1-2-0 AeaJ·Tmi CfO Model Predicliofl , al Grid (1 .125. 0.225)

; . ...~ ;

3 i

; ~~~-~M~.-.-11-ll•H•IM•l•l•ll•ll•ll•:•~l•:•U•ll•ll•::•ll•U•ll•U•l•ll•ll•ll•M~H~ll~O-ll•ll•ll•ll•ll•H•l•ll~ll-ll•ll•ll~:~:.~:-.~:-.. ·ll•ll•l•ll•ll•ll•ll•H•ll•ll•H•l•ll•ll•M•ll•U•l•ll•ll~lll -,· r · ~·

0 • • - m ~ N ~ ~ M 0 • • - ~ ~ N ~ ~ ~ 0 • • ~ - ~ ~ N ~ • M - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ · ~ ~ ~ ~ ~ ~ ~ ~ ~; ~; ~

Time, 1

Figure 13 Prediction of ve/Ocity profile near contaminanFsource.

.r ~, . · ..:.•'.. :,.. : ~ ';". :.} loop fonnulas and als-o IAEand IT AE tuning formulae for set-' . point changes. The fii:ial tuning parameters were obtained with." K, = 25ms· 11ms·1,1'.1= Qd s, and T0 = 35 s. . · ·• -·

from 0.05 mis to 0.1 mis to 0.05 mis and als.o as step and ramp references for a longer duration. The perfotmance of the cm controller is shown in Frgures 17-19.

The IAE, ITAE. and Ziegler-Nichol's tuning formulae (Smith and Corripio 1985) also were programmed in the OPL program for quick and easy tuning of the PID controllers.

RESULTS

Discussion of Performance of the CFO Controller.

Referring to Figure 13, although there Is underprediction of steady-state velocity by the two-dimensional real-time cm model in the Z-plane, the time constant is well matched,

. . as indicated in Figure 15. The velocity gain is also reasonably Analysis of Perf_ormanc~. ~f t~~ ~.eal· T1~e CfD ··· · matched in at le~.it':"o of the grid locations. These character-Model Formulation .<·: : · ' ' : istics of the real~tiine ·cm model result in good control

To analyze the performance of the theoretically quasi~ ·" ':'" 'r~sponse, as can be confirmed from Figures 17 and 18. The transient but practically real-time cm feedback mode_!. . .o~~ryredic,tion q.f dea~. timC'.s, as .indicated in Figure 16,.-does formulation, the PID controller was put on "manual" mode, ' . . not affect the controller when it falls below the controller i.e., in open loup, and the boundary_c_onditio.ns of Table l, sampling time of one second. The steady-state accuracy is Case B, applied, F~ures 13-16,sho.w: the ~mparison. oftran- excellent, as zero error was achieved. The tracking of the sient and ~t~~dy-state characteristics !J.c?_tWeen .. the, two- velocity in response to ramp changes in set point is also very dimensional quasi-transi~rit CfD rrtddel ptedl'i:tio'fis in GPL - good, ·as indicated in Figure 18. ·· , and the thre~;d[~~!i~i9.11~l. truly transierlt, turbuient Navier- Howev~r;thfliliderprediction of velocity distribution by Stokes model predictions using the commercial cm soft- the real-time ;cm feedback model d~s. havt;~ a penalty: it ware package. results in higher inlet velocities from the fa~. as can be

Figure 13 shows that 'the two-dimensional model under- confirmed by ~omparing 'Figure 19 with Figure 13. predicts the velocity from 20% to 58% for the three grid loca- ·.. The real-time CFD program in GPL has been modified to tions close lO the heat and contaminant sourcir. Figure 1.4. . ··include actual velocity from a hot-wire sensor located at grid shows the comparison ofveloc;ity gain predictiorls by the two location (1.975, 0.975, 0.075). It is hoped it will help improve modeling techniques. Since gaif! is computed from steady- the accuracy cf the CFD model,~ it forms additional bound-state values, the pattern here is exactly the same as in Figure ary informatiob but located in the interior of the flow domain. 13. Figure 15 co~par~s .!~~oe £_OJ~§ian_l preqiciio'1s. Tne agree~ This·-is theoretically justified becalise of the elliptic nature of ment is very good beye.1 Fi,gure J.6.compares dead time preqic- ,, ·: the real-time CFIYmOdeL .: :; ·

tions and shows an overprediction of 0.3 lo ~.7 seco,n~s'. I Puring several runs of the real-time CFO model, no diver-. · ' .. ·· gence problems were encountered for various boundary

Analysis of Performance of the CFO Controller.

Since the slave controller works under set-point changes dictated by the master contaminant control loop, it was subjected to set-point changes both as a simple step reference

10'

coi;i,djt.i9l)s,in the opeo11loop ~9de. This is because; it is an ellip­tic equation of the Laplace type and convergence is guaranteed for such equations. This feature is a considerable asset, as robustness is a very desirable feature for feedback control.

4155

-'0

§. ;::::. '0

§. c. .

:.:: c

Cii Cl ~ Cl ... 0 'ii >

o Turbulent, 3·0, Navier-Stoke's CFO lvbdel Prediction :

0.9 ..._ D 2-0, Real-Time CFO C.Ontrol M>del Prediction •

0.8 - . 0.86 0.7 0.6 0.5

0.4 0.3 0.2

0.46 0.398 0.398 0.4 0.398

o.1 I I ~--0.. , I. .:L I - ~ .. ~ · I I· · I , ..... I I . 1.125, 0.225, 0.075 1.125, 0.225, 0.325 1.125, 0.2.25, 0.575

Grid Co-Ordinates, (x,y,z), m

Figure 14 Prediction of\ielocity g'ain near coiita"1,inant s~·u·;~;_· , . .,,, .. ( ·"•~·.,.i: r,· 1w~•)4.--~<'··

J t"' ; \

'S''.~ ! : .• ;Jc·

. ~' .,. •.

"I

'I .or"'"'"~· a-o . ...,,,. ... """'"''" """' ,,_.,,, I 18 T"""----------- ---1: D 2·0, Real-Time CFO C.Ontrol M>del Prediction .

16 1 ' 14.1 " r17I . · . .I ·! ·u

.· ·8: 14

p 12

i 10 Ill . "' •" Klj c 8 ··;-. 6 GI E~ 4

... . ! •

~

13.2 13.3

.. ...

'~~. \;: . .. , .J, ; ~~

·1

13.3 • • I · I 13.3 • I

. ' .. .... 1

·r • •• I(,

.. I ' . ~ c

, ..

i=·1 •1; ·~t I ·.:r -'1 : I : i'·' I I L H \F.:li' Lt·-· Ir ·I '~'"1 I:.'·. . . .;rln< .., · "

1.125, 0.225, 0.075 1.125, 0.225, 0.325 1.125, 0.225, 0.575 .. ~ . ..., : .. J .:...···.·!· .. - Grid Co-ordinates, (lf,Y~),.in ,c ;:· ·

: . ' ~ .• ," :, . I '..L _' j, ·. .11'1 . · ··~ , : .... "'" . , ,):.. •• "":'1

.. Figare 1$_ :Fredictfori 'of time2consti:int''near' contamiiUih_t source;, ... ;. ~1 ~· · • .. ·i ·n·.t ·1 --

I ~·! .

If "f

• • 11\)t • ••

"11'.,,_ .") :-.!' ~ ~

,; ' {

I. ~I

, ··,

! ,· 1,L , :

':'1 ... , ,_,.,

... _. ... ; .... · . ~:

~ ... ::·; ;~ ... - :~ 5~ .

,.1t • . ";: '' !": .• . ~,''\, ,, ~) ..... ·"·n'!}

' • I '

n·.::. ~\ ;::.

n, ,. oTurbulent. 3'-0, Ns.vier-Stbke's cFo wooerf?l!ediction :'•:=,''

·1• t

" • <; . ,~,,,. ;:. ;;:11y •:;1:·, ,-. • :~~:- ;, ) .··~· ·.;": ..

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ffowever, tlw system can become µnstflble in the closed-loop mode bec1u,1se of the feedbi!,ck action. as was noticed when incorrect tuning parameters were fed to the PID controller.

CONCLUSIONS ANO FUTURE WORK

It is possible to control an indoor air quality variable, such as ventilation velocity. in two dimensions and in real time using computational fluid dynamics. A CFD model based on lt1e two-dimensional potential flow equation has been fonnu­lated as a quasi-transient model to achieve real-time operation. The model also reveals a detailed air velocity distribution for any given ventilation flow iate in real time. A scheme for cascade control of air contamination using the ventilation velocity as the slave variable has been designed and imple­mented in a GPL software using a CFD feedback PID control­ler.

A climate chamber based on cross-flow displacement ventilation has been designed and constructed for advanced indoor air quality control investigations.

The future work consists of experimentally validating this novel feedback control technique in the climate chamber and extrapolating the results for advanced ventilation control in clean rooms, offices, and other commercial building applica­tions .

ACKNOWLEDGMENTS

Financial suppon for this project through research grants from the Department of Energy and Environmental Technol­ogy. Glasgow Caledonian University, Scotland, United King· dom, is gratefully acknowledged. The construction of the computer-controlled climate chamber would not have been possible without the patient efforts of our technicians Mr. Tony Dynes, Mr. John Patton, and Mr. Graham Wylie . 111e computing assistanee of Mr. L. Yu with the commercial CFD software package is also gratefully acknowledged.

The first author would also like to especially thank ASHRAE te·chnical committee members for assistance in giliding the submission of this paper, in particular, Mr. James Gartner of TC 1.4, Control Theory and Applications, and Ms. Gemma Kerr of TC 2.3, Gaseous Air Contaminant Removal Equipment.

NOMENCLATURE AND DEFINITIONS

C = controlled (process) variable

E = error

FOPDT = first order plus dead time

G.p(s) = process transfer funytion .. (Laplace domain)

Gc(s) = controller transfer function (Laplace domain)

K,, = process gain

t = process time constant

T0 = ptocess dead time

R = reference signal or set point

s. :: Laplace operator. s·'

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::ri time

:::: controller sampling time

= controller gain

"' derivative time

= integral time

= manip1,1lated variable

:: main dependent variable. such as velocity, temperature. etc., in CFD simulation

= spatial coordinates, m

= x. y, and z components of velocity, m/s

= general diffusion coefficient of respective dependent variable. kg/(m/s)

= source term of respective dependent variable

= stream function in potential flow mechanics ~ = resullant velocity, .Ju-+ v·, mis

= computational fluid dynamics

= indoor air quality (temperature. contaminant concentration. air velocity, and relative humidity)

= parts per million

= high-efficiency particle arrestors

::: integral Of the absolute value of the error, r 1£( l )id I 0

=integral of the time-weighted absolute value of the

error, r tlE(t)ldt 0

= graphical programming language

= virtual instrument in GPL

REFERENCES

Abbott, M.B., and D.R. Basco. 1989. Computational fluid dynamics: An introduction for engineers. Essex. England: Longman Scientific & Technical.

ASHRAE. 1993. 1993 ASHRAE handbook-fundamentals, chapter 1 I, Air contaminants, p.11.2. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers.

Bristol, E.H. 1966. On a measure of interaction,for multi­variable process control. IEEE TransaeriOns on Auto­matic Control. V, AC~l l, pp. 133-134.

Faber. T.E. 1995. Fluid dynamics for physicists. Cambridge University Press, England.

Golten. J., and A. Verwer. 1991. Control system design and simulation. McGraw-Hill, England/

Holt, M. 1984. Numerical methods in fluid dynamics; 2d ed. New York: Springer-Verlag.

Leigh, J.R. 1988. Tempera'ture n\easurement and control. Peter Peregrinus Ltd nEE Press. UK.

Smith, C.A., and A.B. Corripio. 1985: Principles and prac­tice of automatic process control. New York: Wiley.

4155