temperature- and pressure-feedback control laws, and to evaluate the adequacy of these ... specific heat capacity of gas at constant pressure, J/kg-K ... From the ideal gas law, the pressure ... matrix terms, variation of the LN2 injection-valve area', the drive-fan speed,. 7 ..... Such a decrease in AT is shown, for example, in.
NASA. Technical Paper :1695
I
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1695
1 :
c.1
:.
LOAN
AWL TECHNIC KlRTL.AND AFB
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Development and Validation of a' Hybrid-Computer Simulator .for. a
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r-
.
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:Transonic, Cryogenic Wind. Tunnel
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~
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,
-
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"Jerry J. Thibodeaux. and S. Balakrishna
,
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SEPTEMBER
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NASA Technical Paper 1695
DevelopmentandValidation of a Hybrid-Computer Simulator for a TransonicCryogenic Wind Tunnel
Jerry J. Thibodeaux Latlgley Research Center Humnpto~r, Virgitria
S. Balakrishna Old Domiuion U)?iversity Norfolk, Virginia
National Aeronautics and Space Administration Scientific and Technical Information Branch
1980
SUMMARY E x p e r i e n c e d u r i n g t h e past 6 y e a r s o f o p e r a t i o n o f t h e L a n g l e y 0.3-Meter Transonic Cryogenic Tunnel has shown t h a t t h e r e are problems associated w i t h theoperationandcontrol of s u c h t u n n e l s . One problem h a s been a n i n a b i l i t y to p r o v i d el o n g - t e r ma c c u r a t ec o n t r o l of t e s t parameters. A d d i t i o n a l l y , t h e time r e q u i r e d f o r t r a n s i t i o n from one test c o n d i t i o n to another has proven to be e x c e s s i v e l yl o n g . Due t o t h e h i g h d e g r e e of process cross-couplingbetween the independent control variables, man-in-the-loop operation has proven to be much less e f f i c i e n t t h a n desirable i n terms of l i q u i d - n i t r o g e n a n d electricalpower usage.Forthesereasons,studieshavebeenundertaken a t theLangley Research Center to model the cryogenic-wind-tunnel process, t o validate t h e model by t h e u s e of e x p e r i m e n t a l data, and to c o n s t r u c t a n i n t e r a c t i v e t u n n e l s i m u l a t o r w i t h the v a l i d a t e d model. A d d i t i o n a l l y , t h i s model has beenused to d e s i g n closed-loop f e e d b a c k c o n t r o l laws f o r r e g u l a t i o n o f t h e temperature and pressureparameters. The g l o b a l mathematical model t h a t h a s b e e n d e v e l o p e d c o n s i s t s of coupled, nonlinear differential governing equations based on an energy-state concept of t h e p h y s i c a lc r y o g e n i c phenomena. Although t h e fundamentalprocess is q u i t e stable, t h e tendency for c o n t i n u o u s d r i f t i n g from b a l a n c e d e q u i l i b r i u m e n e r g y c o n d i t i o n s is p r e v a l e n t . The p r o c e s se q u a t i o n s , t h e simulationresponses,and t h ee x p e r i m e n t a l data are p r o v i d e dh e r e for f u t u r er e f e r e n c e . Also i n c l u d e d are t h e c o n t r o l laws andsimulatorresponsesusing these closed-loop feedback schemes. INTRODUCTION
H i s t o r i c a l l y , c a p i t a l a n d o p e r a t i n g costs havetended t o keep t r a n s o n i c wind t u n n e l s small, and the many problems encountered a t h i g h p r e s s u r e s h a v e tended to keep o p e r a t i n g p r e s s u r e s l o w . The n e t r e s u l t has been t h a t e x i s t i n g ( a m b i e n tt e m p e r a t u r e )t u n n e l s operate a t Reynoldsnumberswhich are f a r too l o w t o i n s u r ep r o p e rs i m u l a t i o no f the f l o w e x p e r i e n c e d i n f l i g h t , p a r t i c u l a r l y w i t h r e g a r d t o shock-kmundary-layer i n t e r a c t i o n s e n c o u n t e r e d o n modern high-subsonic and t r a n s o n i c a i r c r a f t . O f t h e v a r i o u s ways of i n c r e a s i n g R e y n o l d s number t h a t havebeen t r i e d or proposed f o r t r a n s o n i c t u n n e l s , c o o l i n g t h e t e s t g a s t o c r y o g e n i ct e m p e r a t u r e s (150 K or lower) appears to be t h e b e s t s o l u t i o n i n terms of model, b a l a n c e , as well as c a p i t a l a n do p e r a t i n g costs (ref. 7 ) . Personnel and s t i n gl o a d s , a t t h e NASA LangleyResearchCenter (LaRC) havebeenstudying the application ofthecryogenic-tunnelconcept to v a r i o u s t y p e s of high Reynolds number t r a n s o n i ct u n n e l ss i n c e t h e autumn of 1971 a n d , t h r o u g h e x t e n s i v e t h e o r e t i c a l a n d experimentalstudies,havesuccessfullydemonstratedboththevalidityand p r a c t i c a l i t y o f t h e concept. As a r e s u l t of t h i s w o r k , t h e f i r s t major t r a n sonic tunnel especially designed to t a k e f u l l a d v a n t a g e of c r y o g e n i c o p e r a t i o n is now u n d e rc o n s t r u c t i o n a t LaRC. T h i st u n n e l ,t h eN a t i o n a lT r a n s o n i c
Facility (NTF), w i l l provide an order ofmagnitude increase i n Reynolds number capability over existing tunnels i n the United States when it becomes operational i n 1 982. It can beshown
that for equal test
Reynolds numbersand for any arbitrary l e s s t o t a l energy, and therefore costs less to operate, than an ambient temperature tunnel doing the same amount of testing. Even so, t h e operation of large cryogenic t u n n e l s w i l l be veryexpensive i n absolute terms. For example, the NTF, when operating a t i t s maximum Reynolds numberof 120 x l o 6 a t transonic speeds, w i l l use liquid Although nitrogen ( W 2 ) a t the rate of approximately 454 kg/sec (1 000 lb/sec) the average IN2 usage rate i n the NTE' w i l l bemuch l e s s than 454 kg/sec, it is s t i l l highly desirable, if not essential, that the tunnel be operated i n an e f f i c i e n t automatic manner i n order to minimize W2 consumption.
maximum operating pressure, a cryogenic tunnel uses
.
Experience w i t h the Langley0.3-Meter Transonic Cryogenic Tunnel (0.3-m (ref. 2 ) demonstrated the need forautomaticcontrol systems i f the f u l l potential of thecryogenictunnel is to be realized. Although thebasic cryogenicprocess is stable, there is astrong tendency for drifting from preset by imperfect tuntest conditions because of the heat-transfer effects created nelinsulation.Additionally, due tothe highdegree of processcross-coupling between independent controlvariables(temperature,pressure, and drive-fan speed) and the desired test conditions (Machnumber, Reynoldsnumber,and dynamic pressure), man-in-the-loop operation has proven to bemuch less efficient than desired i n terms of LN2 and electrical-power usage. ET)
I n order to meet the specific control needsof the 0.3-m E T as well as of cryogenic tunnels i n general, a study has to s t u d y the control requirements been undertaken a t LaRC t o develop and validate a mathematical model of 0.3-m E T process, t o u t i l i z e t h e model i n a hybrid-computer simulation t o design temperature- and pressure-feedback control laws, and to evaluate the adequacy of these control schemes by analysis of closed-loop data. The results of this s t u d y are reported herein. SYMBOLS
A
area, m2 or percent
b
pressure-loss coefficient
cm
specific heat capacity
of metal, J/kg-K
cP
specific heat capacity
of gas a t constant pressure, J/kg-K
CV
specific heat capacity
of gas a t constant volume,J/kg-K
D
dimensionality constant
E
t o t a l energy, J
h
specific enthalpy,
2
J/kg
K
gain
KM
= 597(1
M
Mach number
m
m a s s flaw rate, kg/sec
N
f a ns p e e d ,
P
t o t a l pressure, atm (1 atm = 101.3kPa)
b
heat flaw, J/sec
r
pressure r a t i o
S
Laplace v a r i a b l e
T
t o t a l temperature, K
t
time, sec
U
i n t e r n a le n e r g y ,
U
s p e c i f i ci n t e r n a le n e r g y ,J / k g
V
volume, m3
W
m a s s , kg
Y
h e a t - t r a n s f er c o e f f i c i e n t , J/sec-K
a
c o o l i n gc a p a c i t yo fg a s e o u sn i t r o g e n ,J / k g
B
coolingcapacityofliquidnitrogen,
Y
r a t i o of s p e c i f i c h e a t s
rl
fanefficiency
0
thermal mass, J/kg
T
t r a n s p o r t time l a g , sec
-
O.~M)P-O*O~~
rpn
J
J/kg
Subscripts:
a
acoustic
C
t u n n e l circuit
e
exit 3
" .
.. .
F
fan
G
gas
i
inlet
L
liquid
m
metal
P
plenum
set
set pvoai n l ut e
The use of a d o t o v e r with respect t o time.
a quantitydenotesthederivative
of t h e q u a n t i t y
MATHEMATICAL MODEL OF THE LANGLEY 0.3-METER TRANSONIC
CRYOGENIC TUNNEL
The developnentof a c o n t r o l - c o m p a t i b l e model of t h e 0.3-m TCT (shown s c h e m a t i c a l l yi nf i g . 1 ) h a sb e e nd i s c u s s e di n d e t a i l i nr e f e r e n c e3 . The f u n d a m e n t a lp r i n c i p l e s ,a s s u m p t i o n s ,a n de q u a t i o n so ft h i sm o d e l i n ge f f o r t are p r e s e n t e d i n t h e a p p e n d i x o f t h i s paper. Thesegoverningequations prov i d e a simple, s i n g l el u m p e d - p a r a m e t e rm u l t i v a r i a b l e process model of t h e 0.3-m TCT. C o n t r o la n a l y s i so ft h em a s s - e n e r g yi n t e r a c t i o ne x i s t i n gb e t w e e n t h e mass o f g a s i n t h e t u n n e l a n d t h e c o n t r o l i n p u t parameters was used t o developthedynamic model from which t h e real-time i n t e r a c t i v e s i m u l a t o r was a s s e m b l e d .T h i sr e s u l t e di n a concept of e n e r g yc o n t r o lo ft h et u n n e l by states, m a n i p u l a t i o no ft h ep r o c e s s The b a s i c t h e r m o d y n a m i c e q u a t i o n f o r d e t e r m i n i n g t h e time r a t e of change of t h e t o t a l e n e r g yo ft h eg a s( i g n o r i n gp o t e n t i a la n dk i n e t i ce n e r g y ) is
&
= Heat f r a n t h e t u n n e l
+
metal
Heat f r o m i n j e c t i o n o f
+
LN2
Heat of compression from the fan
+
of g a s e o u s n i t r o g e n
Heat f r a n e x h a u s t
or
.
E =
a (WGC~T) = at
with heat energy added
4
-J
Surface
&, + b~ +
to t h e g a s b e i n g p o s i t i v e .
hLhL
-
&cpT
(GN2)
After mathematical manipulation, adding the transport delays involved in WmCmTS the measurements, and using the definitions = , c1 = (cp - cv)T, and 1 + tmS f3 e hL - cpT from reference3 , the temperature dynamics of the tunnelcan be wr it ten
&,
where
8 = W G C ~+ WmCma
From the ideal gas law, the pressure of a confinedgas is proportional to the mass of the gas and its temperature,= pK~WGT. After taking the appropriate derivatives and making substitutions, the time rate of ofchange pressure may be expressedas
ap
- = "
at
p aT T at
+ -p -
~WG at
wG
After substitutions and manipulation, the pressure dynamics for the tunnel can be wr itten
-
' aP P -TLs P=-" mLe at W,
where b = 0.197(l
-
P
-rGs
"
%e
WG
7PM y). Equations
aM + -P . T + DbMp T
at
(2) and ( 4 ) permit the description of the
of the gas in the tunnel due temperature and pressure response characteristics to the tunnel control inputs.
Other important relationships necessary for modeling the 0.3-m TCT are given as follows. The form of the equations used here reflects the specific physical characteristics of the 0.3-m TCT and the various elements used for measurement and control of the test conditions.
where
KM
= 597(1
-
0,3~)p-'*'35
tP
plenum time c o n s t a n t
Ta
a c o u s t i c time l a g
Tunnel circuit time:
tc =
0.01 49V
3
A M E
LN2 flow rate:
(0 6 AL 6 100%) (7) GN2 flow rate:
(Since KG is a f u n c t i o no f c a b l e for GN2 flow r a t e . )
p, two r e l a t i o n s h i p s are appli-
p > 1 . 5 atm 0 6 AG 6 100%
Mass of g a s i n t u n n e l :
WG = 341 . 4
"(-
T
Fan pressure ratio:
6
1
+
250
E2) -
(1
-
0 .033M1
s5)
Metal enthalpy: h = 2.75T2
-
0.0026T3
Fandynamics:
N
1
-
"
Nset
0 . 2 + ~ 0.56s ~
+
1
Cooling capacities:
f3 = -(l21
+
2p
66
+-T
391p T
Fan h e a t :
where
These equations describe the lumped-parameter mathematical model o f t h e 0.3-m TCT shown i nt h es k e t c hi nf i g u r e 1 a n dt h ep h o t o g r a p hi nf i g u r e2 . The some o ft h e l o c a t i o no ft h et h r e ec o n t r o li n p u t s ,t h es e n s o rl o c a t i o n s ,a n d p h y s i c a lc h a r a c t e r i s t i c so ft h et u n n e la r e shown i n f i g u r e 1 . The m u l t i v a r i a b l e modelused f o rd e v e l o p i n gt h es i m u l a t o r is p r e s e n t e d i n f i g u r e 3 i nm a t r i x form. The model o u t p u t s( t e m p e r a t u r e rate, Mach number,and p r e s s u r e rate)are r e l a t e d to t h ei n p u t s (LN2 i n j e c t i o n - v a l v e area, fanspeed, and GN2 exhaustv a l v e area) t h r o u g ht h e complexdynamics of thesystem.Examination of t h e modelshows it to b eh i g h l yc o u p l e d and n o n l i n e a ri nn a t u r e .I fc o u p l i n g were n o t p r e s e n t , t h a t is, i f t h e r e were no o f f - d i a g o n a l b e t w e e nt h ev a r i a b l e s LN2 i n j e c t i o n - v a l v e area', t h ed r i v e - f a ns p e e d , m a t r i x terms, v a r i a t i o n o f t h e 7
or t h e GN2 exhaust-valve area would result i n i n d e p e n d e n t c h a n g e s i n t h e total temperature, t e s t - s e c t i o n Mach number,and t o t a l pressure, r e s p e c t i v e l y . mass flow r a t e s o f l i q u i d The v a l v e - a r e a o p e n i n g s i n t h e m a t r i x c o n t r o l t h e and gaseousnitrogenthroughtheprocessdynamics to a f f e c t rates ofchange i n temperatureand pressure. First-order c h a n g e si n Mach number are c o n t r o l l e d by An i m p o r t a n tf e a t u r eo ft h i s model is t h e changingthe speed o ft h ed r i v ef a n . l a r g e c o n t r i b u t i o n to t h e p r o c e s s d y n a m i c s made by t h e e n e r g y stored i n t h e metal of t h e t u n n e l and by t h e GN2 h e a t - t r a n s f e r time c o n s t a n t (which v a r i e s s i g n i f i c a n t l y as a f u n c t i o n of t e s t - s e c t i o n Mach number, p r e s s u r e , andtempera t u r e ) . The importance of these f a c t o r s w i l l become e v i d e n td u r i n gt h e examdata i n a s u b s e q u e n t s e c t i o n of t h i s p a p e r . i n a t i o no ft u n n e lr e s p o n s e T r a n s p o r t time d e l a y s havebeenincludedinthe model to account for t h e mean time between i n i t i a t i n g t h e v a r i o u s c o n t r o l i n p u t s andmeasuringthe t e s t c o n d i t i o n s .F o re x a m p l e ,t h et r a n s p o r t time d e l a y r e s u l t a n tc h a n g e si nt h e associated w i t h t h e i n p u t o f LN2 is t h e l a g c o r r e s p o n d i n g to t h e t r a n s i t time from t h e LN2 i n j e c t i o n v a l v e s to j u s t ahead of t h e s c r e e n s e c t i o n where temperature is measuredby a thermocouple. S i m u l a t i o n of t h e 0.3-m TCT A t t h eb e g i n n i n go ft h i ss t u d y , it was decided to d e v e l o p a computer simulator of t h e 0.3-m TCT t o g i v e hands-on i n t e r a c t i v e c a p a b i l i t y f o r t h e p r o c e s s it was a n t i c i p a t e d t h a t a s i m u l a t o r of t h i s and c o n t r o ls t u d i e s .F u r t h e r m o r e , type would be v a l u a b l e for e v a l u a t i n g v a r i o u s o p e r a t i n g t e c h n i q u e s a s well a s of tunneloperatorpersonnel.Consequently,thecomputer f o rt h et r a i n i n g selected f o r t h e m o d e l i n g a n d s i m u l a t i o n e f f o r t was a h y b r i d computer system which p e r m i t s m a n u a l i n t e r a c t i o n a l o n g w i t h high-speeddigitalcomputation.
S o l u t i o no ft h es y s t e mp r o c e s se q u a t i o n s was undertakenon t h e hybridcomputersystem shown i n f i g u r e 4 . B a s i c a l l y ,t h ec o m p u t e rc o n s i s t so f a central digitalprocessorunit andan analogcomputer e l e c t r i c a l l y i n t e r f a c e d for data exchange. The r a t e ofupdatebetween t h e d i g i t a l and analogcomputersystems is 25 Hz.
Because o f t h e n o n l i n e a r i t y and t h e time dependency of t h e model, comput a t i o n s were s e g r e g a t e di n t o two p a r t s . A l l nonlinearcomputations were performed d i g i t a l l y b u t i n t e g r a t i o n of p r o c e s s e q u a t i o n s took p l a c e c o n t i n u o u s l y s i d e of t h e computer system. Shown i n f i g u r e 5 is a f u n c t i o n a l i nt h ea n a l o g b l o c k diagramofthehybrid-computersimulation. Ten i n p u t s from t h ea n a l o g computer u n i t ( a f t e r a n a l o g - t o - d i g i t a lc o n v e r s i o n ) a r e used i n t h e d i g i t a l computer to compute t h e e q u a t i o n s shown i nf i g u r e 5. The c o m p u t a t i o ni nt h e d i g i t a l computer results i n 11 o u t p u t s a p p r o p r i a t e l y scaled and c o n v e r t e d t o a n a l o gs i g n a l sf o ri n p u t t o t h ei n t e g r a t i n ga n a l o g s i d e of thehybridsystem. The loop diagrams of t h e model dynamics and simulation control along with the d i g i t a l l y c o n t r o l l e d a t t e n u a t o r s which allow t h e n o n l i n e a r d i g i t a l c a l c u l a t i o n s t o be i n t r o d u c e di n t o t h e analogcomputer are p r e s e n t e di nf i g u r e 6. Tunnel temperature dynamics ( f i g . 6 (a)) are o b t a i n e d f r o m i n t e g r a t i o n of thetemperature rate whereastunnelgastemperature T is used to d e r i v et h e metal temperature by u s i n gt h ei n v e r s e of t h e metal time c o n s t a n t l/b. The metal-
-
t o - g a sh e a tf l o ws i g n a l Tm T is used to d e r i v e -T i n a loopedmanner. Measured g a s t e m p e r a t u r e f o r d i s p l a y a n dc l o s e d - l o o pc o n t r o l l e r u s e is c r e a t e d by d i g i t a l d a t a p r o v i d e d t h r o u g h t h e d i g i t a l a t t e n u a t o r s . P r e s s u r e ,f a n , and Mach number dynamics ( f i g . 6 ( b ) ) are d e r i v e d by t h e i n t e g r a t i o no fs c a l e dp r e s s u r e rate l o b . A c o u p l i n g term fi hasbeenincluded to generatetheinfluenceoffanaccelerationonthe r a t e of change of pressure. is e f f e c t e d by a n a c c e l e r a t i o n - l i m i t e d s e c o n d - o r d e r t r a n s f e r Fan-speedmodeling f u n c t i o n . Fan revolutionsperminuteand Mach number d i s p l a yi n f o r m a t i o nf o r are a c q u i r e d a f t e r a p p r o p r i a t e s c a l i n g w i t h a n a l o g t h es i m u l a t o ro p e r a t o rp a n e l potentiometers. Figure 6 ( c ) shows d e t a i l s o f t h e p a t c h i n g n e c e s s a r y to create and c o n t r o l t h e 3-sec p u l s e i n p u t s u s e d to studythetunnel-modelbehaviorfrombalanced A l s o shown i n t h i s f i g u r e are t h ev a l v e c o n d i t i o n sa f t e rv a r i o u sd i s t u r b a n c e s . area d i s p l a y s i g n a l s f o r t h e o p e r a t o r c o n s o l e p a n e l , which w i l l b e d e s c r i b e d later. The l a s t analogdiagramused by thehybrid-computer simulator and shown i n f i g u r e 6 ( d ) is t h e c l o s e d - l o o p f e e d b a c k c o n t r o l law f o r t h e t e m p e r a t u r e a n d pressure l o o p s .P r o p o r t i o n a l and i n t e g r a l( P I )t y p ec o n t r o l l e r sa n dt h eg a i n s c h e d u l e sf o rt h er e s p e c t i v ev a r i a b l e s are d i s p l a y e d .V o l t a g ec l i p p i n g was necessary t o p r e v e n t n e g a t i v e v o l t a g e s s i n c e t h e v a l v e - o p e n i n g area c a n o n l y be p o s i t i v e . I t was r e c o g n i z e d e a r l y i n t h i s w o r k t h a t e x p e r i m e n t a l d a t a were r e q u i r e d to v a l i d a t e t h e p r o c e s s model. As a r e s u l t , t h e f i r s t phaseof work was to o b t a i nd a t af o r dynamicresponseoftemperature,pressure,and Mach number to changesof t h e i n p u t v a r i a b l e s t h r o u g h o u t t h e t u n n e l o p e r a t i o n a l e n v e l o p e . F i g u r e 7 is a p h o t o g r a p h o f t h e c o n t r o l p a n e l o f t h e 0.3-m K T a s it was a t t h e time of t h e s er e s p o n s e tests. P r i n c i p a lc o n t r o li n p u t s are IN2 i n j e c t e d r a t e , GN2 e x h a u s t r a t e , and fanspeed.Boththe LN2 and GN2 flow r a t e s a r e m a n u a l l yc o n t r o l l e d bycommands t o s p e c i a l l yd e s i g n e dd i g i t a lv a l v e s .T h e s e d i g i t a l v a l v e s are r e v o l u t i o n a r y a d v a n c e s i n t h e s t a t e of t h e a r t of f l u i d cont r o l andmeasurement.Multiple-ventingcontrolports,eachfittedwithan a c c u r a t e l yp r e c a l i b r a t e d ,b i n a r y - w e i g h t e dv e n t u r i , allow s e l e c t i o n of 256 or more d i s c r e t ef l o w r a t e s . Thus, f o rt h e8 - b i td i g i t a lv a l v e s used i nt h e 0.3-m K T , f l u i df l o w rate c a n be c o n t r o l l e d to w i t h i n 1 p a r t i n 256(28) with e x t r e m er e p e a t a b i l i t y , Because e a c hc o n t r o lp o r t is b i s t a b l e ( e i t h e r f u l l y open or f u l l y c l o s e d ) , t h e r e is no valvedeadband or overshoot which can be Also, each port canbe modue x p e r i e n c e dw i t hc o n v e n t i o n a la n a l o gv a l v e s , l a r l y r e p l a c e d or s e r v i c e d w i t h o u t removing t h e whole valvefrom i t s l o c a t i o n . F i g u r e 8 is a s c h e m a t i c o f t h e c o m m e r c i a l l y a v a i l a b l e d i g i t a l e x h a u s t v a l v e .
I n p u t s to t h e i n j e c t i o n or exhaustsystems were r e a l i z e d by p u l s i n g a s e l e c t e de l e m e n to ft h ea p p r o p r i a t ed i g i t a lv a l v e . For t h e s e tests, t h e 6 . 2 5 p e r c e n to ff u l l - f l o we l e m e n t was c y c l e d . Mach number dynamics were determined by means of a 100-rpm s t e p c h a n g e i n s p e e d of t h e d r i v e - f a n motor. Total temperature, t o t a l pressure,and Mach number as well as t h e t h r e e i n p u t for t h e t u n n e l concommands were recorded a t a r a t e of 40 samplespersecond d i t i o n s( g i v e ni nt a b l e I ) , w h i c hs p a nt h ee n t i r eo p e r a t i o n a lr a n g e of t h e 0.3-m E T . The p h o t o g r a p ho ft h et u n n e l( f i g . 2 ) shows t h e LN2 i n j e c t i o n 9
valves (upper right), the fan section (lower right), and the piping leading to the digital exhaust valve (center left)
.
Operator Control and Display Panel
In addition to studies of the process dynamic behavior, an important reason for the simulation was to achieve man-in-the-loop interaction so that 0.3-m E T operational techniques couldbe investigated. Also, with such a simulator operator training could be accomplished at an insignificant cost compared with training in the tunnel. After appropriate scaling and electrical hookup to the analog patchboard, an operator display and control panel (shown in fig.9 ) was made available for the hybrid-computer simulation. Operator inputs are made through potentiometers which control the simulated liquid- and gaseous-nitrogen valve openings and the fan speed. The temperature, pressure, and Mach number digital displays permit realistic simulation of tunnel operation including operator imposition of constraints such as maxi mum cool-down rateor metal-to-gas temperature difference. Displays not provided on the simulator control panel but present on the tunnel control panel include liquid-nitrogen pump pressure, drive-fan motor power, and digitalvalve status indicator lights. Recording Instrumentation
The technique used to record the experimental data acquired from the 0.3-m TCT was straightforward and consisted of simply patching analog parameter outputs to a remotely located recording system. Data were directly digitized at a rate of 40 samples per second, converted into engineering u and placed on computer files so that computer plots could be generated and analyzed relative to the simulator results.
The procedure for obtaining the simulator data was not quite as straigh forward. Instead of direct digitization, the simulation data had to be first recorded on anFM wide-band recording tape. The recorder is shown in figure 10. The data were then put through a 40-sampler-per-second digitizing process for conversion to engineering-unit tapes which were used to create the computer file data base for simulator validation. Validation
of
the
0.3-m TCT Tunnel
Simulator
In order to validate the analytical model of the TCT 0.3-m used to develop the real-time cryogenic-tunnel simulator, a number of tests were performed b on the tunnel and the simulator. The results of these separate tests are compared and discussed. Details of the experimental-response tests are presented and the features of the data are correlated with the mathematical terms for validation of the simulator model. It is well known that linear time-invariant dynamic systems yield transient character istic responses to deterministic inputs (i .e., sine-wave, step, 10
ramp, impulse, or doublet inputs). These time-dependent responses can be directly compared with simulated responses. The cryogenic process is obviously time invariant, and though it is nonlinear, the tunnel characteristics can be easily analyzed by assuming linear behavior for small perturbations around an equilibrium point. Because the cryogenic-tunnel process has open-loop integrating temperature and pressure dynamics, stepinput disturbances from equilibrium were deemed unsatisfactory since saturation of responses would result. Also, for the actual tunnel, sinusoidal disturbances are difficult to realize except for fan-speed inputs. Consequently, easily generated mass impulse inputs were selected for creation of transient responses for both the TCT 0.3-m and the simulator. An additional argument for impulse inputs is that responses can be analyzed with regression analysis techniques for-parameter identification even when the responses are corrupted by measurement noise. During the response tests, both the 0.3-m TCT and the 0.3-mTCT simulator were established at specified equilibrium conditions by open-loop adjustment of the three control inputs and then subjected to impulse disturbances of LN2 mass injection, GN2 mass exhaust, and drive-fan speed. The disturbances were applied serially with sufficient time allowed between impulses to allow transients to decay and equilibrium to be reestablished.
The amplitudes and duration of the perturbations were selected so that changes in the tunnel conditions would be in excess of system noise. Thus, a 6.25-percent increment in the LN2 valve full-open area, a 6.25-percent increment in theGN2 valve full-open area, and a 100-rpm decrease in drive-fan speed were chosen as the input perturbation amplitudes. Each of these inputs was imposed for a periodof approximately 3 sec. This pulse duration corresponds to 3/4 to 4 tunnel-circuit time periods, depending on test conditions. Typically, these pulse inputs create changes in temperature of K to0.5 6.0 K, changes in pressureof 0.017 to 0.102 atm, and changes in Mach number of 0.006 to 0.030. The dynamic responsesof the experimental data and the simulation data are compared in figures1 1 to 37 for the various test conditions selected to cover thefull range of operation of the 0.3-m TCT. Inspection of the data shows that the records €or the simulator responses are practically noise free whereas the tunnel data exhibit some measurement and recording noise. The Mach number traces show a larger level of noise because Mach number is calculated from two pressure records, each of which has its own noise component. One particular problem encountered in obtaining the experimental data from the 0.3-m TCT was a 10- to 20-percent random drift from the nominal value in the LN2 pump pressure. This prevented accurate measurement of the mass flow of the LN2 injected into the tunnel. Once equilibrium was established, perturbation of the 6.25-percent element of theLN2 valve admitted an additional mass IN2 of into the tunnel circuit, typically between 0.5 and 1.5 kg per pulse. Perturbation of the 6.25-percent element of the GN2 valve exhausted an additional mass GN2 of to the atmosphere, typically between 0.2 and 1.0 kg per pulse.
11
ANALYSIS OF m Transient
L AND SIMULATOR Responses
Figures 11, 28, and 29 are providedas typical impulse responses alphabetically subdividedso that various features and characteristics of the temperature, pressure, and Mach number trajectories can be identified and explained. Prior to any intentional system disturbance the equilibrium conditions for the cases studied were established. The segment ABCD defines the portion of the response influenced by the perturbation to the LN2 valve The segmentEFG defines the portion of the response influenced by the perturbation to theGN2 valve area. The segmentHJK defines the portion of the response influenced by the perturbation of the drive-fan speed. Correlation of these dynamic records with the model mathematics was performed to prov better comprehension and insight into why specific results are obtained. This is done in the following sections for the three control inputs. LN2 Pulse Input
Temperature response.- Refer to the temperature trace of figure 11. Prior to A the tunnel was placed in a balanced mass and energy condition such th (b =zero T = 01, the the rates of change of pressure and temperature were liquid-mass inflow was equal to the gaseous-exhaust outflow (iL = k),and temperature, pressure, and Mach number were constant. During segment AC, LN2 mass flow rateis increased by AiL due to the increase in valve area of 6.25 percent of the full-open valye area during the perturbation, This create a negative temperature gradient(T < 0) due to the negative B term in equation (2). As the temperatureof the gas in the tunnel rapidly drops, the temperature of the metal in the tunnel shell lags behind and begins releasing stored heat energy to the gas, Eventually the amplitude of the temperature gradient is dynamically reduced as dictated by the lead/lag term of equation (2). Gas temperature (at the measuring station) continues to drop beyond point C. The value AiL returns to zero due to removal of the perturbation and closure of the 6.25-percent element of the LN2 injection valve. Recovery from the perturbation takes place in the segment CD due to continued heat fer from the walls to the gas. At point D, most of this heat transfer is completed. It may be noted that there exists an obvious temperature transport delay relative to the commanded input position. This corresponds to porthat tion of the circuit time constant (see (6)) eq. consistent with the circuit length between the LN2 injection station and the temperature-measurement station. All temperature data (figs. l l to 37) display this delay characteristic.
The temperature differential established between C and D by first a negative gradient (dueto liquid input) and then a positive gradient (due to wall heat release) can be predicted by reexamination of equation ( 2 ) . For zero change in exhaust flow and no added heat contribution from a ste?dily runni fan, only LN2 influences the differential temperature AT (or T). If AT 1 1 + tms is andrepresented by transiently is ( 1 + t;s) 8 1 + tGS
-(
12
)
approximated by
1 -
(since the energy of the Wmcm term in 8 = WGC,
wGcv
( BiLe-TLS
+
iL)
+ Wmcm
.
By using wGcv this simplified analysis, the largest valueof AT should occur when 6 is largest and WG is smallest. Equation ( 9 ) shows WG is smallest when pressure is lowest and temperature is highest. For the tunnel conditions tested, WG is smallest at a pressure of 1 . 5 atm and a temperatureof 275 K. The experimental (tunnel) data presented in figures 11 and 29, for example, confirm that the maximum AT does, in fact, occur under conditionsof minimum WG. For the conditionof constant temperature,as the mass of the gas in the tunnel increases with increasing pressure, the amplitude ofAT should decrease correspondingly. Such a decrease in AT is shown, for example, in figures 29, 32, and 3 5 . Thus, the smallest AT occurs when B is smallest and WG is largest. For the conditions examined this occurs at 5.0 atm and 100 K. The tunnel data presented in figures 1 7 to 1 9 exhibited the smallest values of AT as predicted. The magnitude of recorded temperature differentials is somewhat smaller than predicted because of some filtering of the actual temperature measurements due to the response characteristics of the thermocouple used for the temperature sensor. is released
only after long a time period), then
Pressure response.- Refer again to figure1 1 . With attention now focused on the pressure trace, the following analysis will explain .the pressure behavio of the tunnel. Equation ( 4 ) is the tunnel state relationship for the rate of change of operating pressure. With constant values of gaseous exhaust and fan
P .
contributions in the pressure rate equation, only the cooling term - T and T P * -TLs - AmLe influence the pressure gradient. For segment AB the mass term WG of the pressure trace, p is negative because the cooling termis larger than the mass term. At point B the two terms are equal and opposite. As a result, = 0 and the minimum pressure is realized. For the segmentBC, the mass term becomes much-larger because of the additional liquid-mass input, and despite a negative T, a positive p ensues. Thus, the positive pressure gradient from B to C is due to the dominant heat transfer from the tunnel wall to the test gas. At point C, AinL is reduced to zero by reducing the valve incremental area to zero. Because the wall is warmer than the gas, the net heat flow to the gas causes of
b!
to become positive in the
P.
-
T
T
term.
As
a result,
increases until the heat transfer is complete and a new equilibrium value p is established.
This initial decrease in pressure due to the liquid input followed an by increase in pressureis characteristic of allconditions tested for the simulator and the tunnel. (See figs. 11 to 3 7 . ) The location of the minimum pressure (point B) varies as a function of the test conditions of the tunnel. For gas temperatures of 1 0 0 K, the minimum pressure consistently occurs very near the end of the liquid input (point C) (See figs. 11 to 1 9 . ) On the other
.
13
hand, a t a g a st e m p e r a t u r eo f 275 K, t h e minimum p r e s s u r e is v e r y n e a r t h e b e g i n n i n go ft h el i q u i di n p u t( p o i n t A). T h i s i n d i c a t e s t h a t a much more r a p i d amount o f e n e r g y r e l e a s e d p r e s s u r e r e c o v e r y is e s t a b l i s h e d b e c a u s e o f t h e l a r g e from t h e t u n n e l walls. T h i s is as e x p e c t e d s i n c e t h e metal e n t h a l p y (eq. (1 1 ) ) a t 275 K is e i g h t times t h e e n t h a l p y a t 100 K. A t t h ei n t e r m e d i a t eg a s tempera t u r e o f 200 K, t h e minimum p r e s s u r e v a r i e s i n l o c a t i o n b e t w e e n p o i n t s A and C. T h i s is due to t h e d i f f e r e n t v a l u e s o f t h e c o o l i n g e f f e c t e x p e r i e n c e d b e c a u s e wall h e a t release. I t s h o u l d be n o t e d t h a t minimum preso fv a r y i n gd e g r e e so f sure s h i f t s toward p o i n t C a s gas-weightincreases (i.e., i n c r e a s e i n p r e s s u r e ) . 26 i l l u s t r a t e t h i s f o r t h e 200 K case. The d a t a p r e s e n t e d i n f i g u r e s 20, 23,and An i n t e r e s t i n g p o i n t i n t h e s t u d y o f t h e r e s p o n s e of t u n n e l pressure to l i q u i d i n p u t is t h es y s t e mb e h a v i o r a t p o i n t D. When t h i s p o i n t is reached, most of t h e h e a t - t r a n s f e r e f f e c t s h a v e beencompletedandtunnelrecovery begins. A t temperatures of 200 K or 275 K ( f i g s . 20 to 371, t h e pressure l e v e l a t p o i n t D is much h i g h e r t h a n t h e s t a r t i n g or i n i t i a l e q u i l i b r i u m p r e s s u r e is almost t h e same a s t h e whereas a t 100 K ( f i g s . 11 t o 1 9 ) t h e f i n a l p r e s s u r e s t a r t i n g pressure. On t h e o t h e r hand, t h er e c o v e r y pressure g r a d i e n t is n o t as pronounced a t t h e lower temperature. The h i g h e rt e m p e r a t u r e data i n d i c a t et h a t t h e slope o f t h e r e c o v e r y g r a d i e n t i n c r e a s e s more n e g a t i v e l y as t h e Mach number (See f i g s , 20 to 22 and f i g s . 29 to 31 ) T h e s el a r g e rn e g a t i v e increases. g r a d i e n t sc a nb ee x p l a i n e dw i t ht h eh e l po fe q u a t i o n s ( 4 ) and ( 8 ) . The r a t e of is a functionofexhaust-massflow r a t e which i t s e l f is change of p r e s s u r e
.
r e l a t e d to
P
- k. fi
The e x h a u svt a l v e
area
a t t h he i g h e r
Mach numbers has
to b e l a r g e r t o m a i n t a i n e q u i l i b r i u m , a n d t h e r e f o r e when t h e i n c r e m e n t a l l i q u i d i n p u t is removed, more GN2 is b e i n ge x h a u s t e df r o mt h et u n n e l ,r e s u l t i n gi n fi. Note t h a t t h e r e e x i s t s e s s e n t i a l l y no d e l a yi n l a r g e rn e g a t i v ev a l u e so f t h e r e s p o n s e of t u n n e l p r e s s u r e to c h a n g e s i n IN2 flow r a t e . Mach number response.- The responseof Mach number to l i q u i d i n p u t c a n be e v a l u a t e d by u s i n ge q u a t i o n (51, which i n d i c a t e s t h a t Mach number is i n v e r s e l y N. p r o p o r t i o n a l to t h e square root o ft e m p e r a t u r ef o rc o n s t a n tf a ns p e e d Therefore, when t h e IN2 flow r a t e is i n c r e a s e d ,t e m p e r a t u r ef a l l s ,t h es p e e do f is c o n s t a n t , t h e Mach number i n c r e a s e s . s o u n dd e c r e a s e s ,a n ds i n c ef l o wv e l o c i t y T h i ss i t u a t i o n is i l l u s t r a t e d , forexample,infigure 1 1 i nt h ei n c r e a s ei n Mach Mach number is caused number f o r segment AC. Couplingbetweentemperatureand by t h ei n c r e a s ei nf a np r e s s u r e r a t i o due t o t h er e d u c e dt e m p e r a t u r e . (See eq. ( 1 0 ) . ) A t p o i n t C, t h e Mach number r e s p o n s eh a st h el a r g e s td e v i a t i o n , AM AT whichcanbe related t o t h eg a st e m p e r a t u r e - r e s p o n s ea m p l i t u d e by = - M 2T (derivedfrom eq. ( 5 ) ' ) .F i g u r e 11 shows t h a t f o r a Mach number of 0.3 and a temperatureof 1 0 0 K t h e p e r t u r b a t i o n i n l i q u i d flow r a t e causes a changein Mach number of 0 . 0 0 6 . (A computed valueof AT = - 4 K r e s u l t s . ) B e c a u s e of t h ep r e v i o u s l ym e n t i o n e df i r s t - o r d e rf i l t e r i n ge f f e c t so ft h et h e r m o c o u p l e ,t h e a AT o fo n l ya b o u t- 1 . 5 K. r e c o r d e de x p e r i m e n t a ld a t af r o mt h et u n n e li n d i c a t e All ofthetemperature-response d a t a from t h e t u n n e l p r e s e n t e d i n f i g u r e s 11
--
14
to 37 are s u b j e c t to t h i s type o f f i l t e r i n g . However, t h e r e is g e n e r a l l y good agreementbetweentunneland simulator responses. I n s m a r y , t e s t - s e c t i o n Mach number and pressure r e s p o n s e s of t h e t u n n e l to an LN2 i n p u t a g r e e q u i t e well with the mathematical model p r e d i c t i o n s d e s c r i b e d by t h e simulator r e s p o n s e s f o r t h e e n t i r e o p e r a t i o n a l e n v e l o p e . simulator p r e d i c t i o n s A c t u a lt u n n e l temperature r e s p o n s e s d i d n o t d u p l i c a t e q u i t e so well due to t h e dynamic c h a r a c t e r i s t i c s o f t h e t h e r m o c o u p l e u s e d f o r temperature measurements. GN2 Exhaust-PulseInpQt Once a g a i n i n r e f e r e n c e to f i g u r e 11, t h e t u n n e l andsimulatorresponses are examined f o r an e x h a u s t pulse o fa b o u t 3 sec. Theseresponses are marked EFG f o rs e l e c t e ds t u d y .E q u i l i b r i u mc o n d i t i o n s havebeen e s t a b l i s h e d prior t o p o i n t E (fi = = 0, hL = A s w i t ht h ep e r t u r b a t i o n t o t h e LN2 flow r a t e , t h e p e r t u r b a t i o n to theexhaust-gasflow rate is induced by i n c r e a s i n g t h e v a l v e area by a ni n c r e m e n t a l6 . 2 5p e r c e n to ft h ef u l l - o p e nv a l u e .T h i s was done physicallyforthetunnel and i n s i m u l a t i o n on t h e computer f o r a l l c o n d i t i o n s i n t a b l e I . I nt h ep e r t u r b a t i o np r o c e s sa ni n c r e a s ei nt h ee x h a u s t - g a s mass f l o w &IG is produced. A s d e s c r i b e di ne q u a t i o n ( 4 ) , t h i s r e s u l t s i n a neg-
I&$.
a t i v ep r e s s u r eg r a d i e n t
(-
p =
n e g a t i v et e m p e r a t u r eg r a d i e n t
--
Because t h ee x h a u s t i n g
A&e-TGs).
causes a
wG
(T) duringsegment
o r d e rn e g a t i v ep r e s s u r e - g r a d i e n tc o n t r i b u t i o nd u e
EF, t h e r e is a small secondto the
P -
-
T
term i n equa-
T
t i o n ( 4 ) . By and l a r g e however, t h ep u l s e causes a l i n e a rp r e s s u r ed r o pd u r i n g segment EF.The l i n e a rp r e s s u r ed r o pc o n s i s t e n t l yr e p e a t s for b o t ht h et u n n e l and simulator responses as shown i nf i g u r e s 11 t o 37. A t p o i n t F t h ei n c r e mentalvalve area is made z e r ot,h e r e b y making A& = 0 . Once A& is made is c h a r a c t e r i z e d by t h es t e a d y z e r o ,t h es l o p eo ft h ep r e s s u r eg r a d i e n t s t a t e gaseous-massflow r a t e &, which is a f u n c t i o no fp / E . Thus t h el a r g e s t p r e s s u r e g r a d i e n t s e x i s t when p r e s s u r e and temperature are maximum ( p = 5 . 0 atm and T = 275 K). Examinationofthedata shows t h i s to be t r u e . I nc o n t r a s t , t h e smallest p r e s s u r eg r a d i e n t so c c u r when p = 1 .5atmand T = 100 K . During is a d i r e c tf u n c t i o no ft h eg a s e o u s - v a l v e t h e i n t e r v a l FG, t h e p r e s s u r e g r a d i e n t area opening k . Duringsteady s t a t e , t h i sv a l v e - a r e ao p e n i n g is l a r g e s t a t h i g h Mach numbers i n o r d e r to m a i n t a i ne q u i l i b r i u mo p e r a t i o n . Because o ft h e l a r g eo p e n i n g a t high Mach numbers, more GN2 is beingexhausted. When t h e is removed, t h e r e d u c t i o n i n 6 . 2 5 - p e r c e n ti n c r e m e n t a lv a l v e - a r e ap e r t u r b a t i o n &G I is g r e a t e s t a t h i g h Mach numbers.For t h i sr e a s o n ,t h ep r e s s u r er e c o v e r y duringsegment FG is f a s t e s t a t M = 0.75 and M = 0.90 and slowest a t M = 0.30. ~
A s expected,ingeneraltheperturbationsoftheexhaust-massflow rate have more e f f e c t on pressure t h a n o n e i t h e t t e m p e r a t u r e or Mach number.During segment El?, however, a n e g a t i v e $, which is f i l t e r e d by t h el e a d / l a g term, is found. E q u a t i o n (2) is t h eg o v e r n i n ge q u a t i o nf o rt h i st e m p e r a t u r eg r a d i e n t .
15
When A& is made zero a t p o i n t F, becomes p o s i t i v e d u e . to t h er e d u c e dg a s mass e x h a u s t i o n ,t h e r e b ye s t a b l i s h i n g a new temperature. The magnitude of AT
liquidflow (eq. ( 2 ) ) . be l a r g e s t w i t hf i g u r e
a &e -TGs
s i n c e t h e r e is zero change i n wGcv r a t e and no a d d e d h e a t c o n t r i b u t i o n from a s t e a d i l y r u n n i n g f a n Since is a f u n c t i oonf p/fi (eq. (811, AT is expected to a t h i g hp r e s s u r e s and low temperatures.Comparisonoffigure 11 29 i l l u s t r a t e s t h i s e f f e c t q u i t e well.
c a nb et r a n s i e n t l ya p p r o x i m a t e d
by
Fan-Speed P u l s e I n p u t The trajectories marked H J K i n f i g u r e s 1 1 , 28, and 29 correspond to t h e Mach number response of t o t a l - p r e s s u r e ,t o t a l - t e m p e r a t u r e ,a n dt e s t - s e c t i o n to a p e r t u b a t i o ni nf a ns p e e d . As w i t ht h e dynamicsofthecryogenictunnel o t h e r types o f p e r t u b a t i o n s , s y s t e m equilibrium is e s t a b l i s h e d a n d d u r i n g s e g ment H J t h e f a n speed is reduced by 1 0 0 rpxn. The f a n speed d e c e l e r a t e sa l m o s t l i n e a r l y as d e s c r i b e d by t h ef a n dynamics of e q u a t i o n ( 1 2 ) . Reduced f a ns p e e d results i n a pressure-ratio r e d u c t i o n which m a n i f e s t s i t s e l f a s a d e c r e a s e i n JK back t o t h e Mach number.Because t h ef a n is acceleratedduringsegment o r i g i n a ls p e e d ,t h e pressure r a t i o is i n c r e a s e dc a u s i n g Mach number to r e t u r n to its o r i g i n a l v a l u e , The maximum Mach number d e v i a t i o no c c u r s a t p o i n t J . AN T h i s is r e l a t e d to f a ns p e e d by AM = a s i n d i c a t e di ne q u a t i o n ( 5 ) . Since
fi
AN is made c o n s t a n t f o r a l l r u n s , t h e l a r g e s t Mach number d e v i a t i o n takes p l a c e a t t h e lower temperatures. Comparison of f i g u r e s 11 t o 1 9 w i t hf i g ures 29 to 37 c o n f i r m s t h i s phenomenon. A t 100 K, a t y p i c a l Mach number change is a b o u t 0.034compared w i t h a 0 . 0 2 0 change a t 275 K. Reduced fanheatproduca secondary influence on the Mach t i o n d u e to t h e s p e e d d e c r e a s e c o n t r i b u t e s number r e d u c t i o n . The i n c r e a s e i n Mach number caused by d e c r e a s e dh e a to f comp r e s s i o n is q u i t e small a n d c a n n o t b e e a s i l y s e p a r a t e d f r o m t h e p r i m a r y e f f e c t Total-temperature d a t a r e f l e c t t h i s by a s l i g h t of t h e decrease i nf a ns p e e d . temperature decrease during segment H J andanincreaseduringsegment JK, Equation ( 2 ) i n d i c a t e st h ei n f l u e n c eo ff a nh e a t QF o nt h e temperature graKpW3
(eq. ( 1 4 ) ) is a c o n t r i b u t o r to equa0.2~213 t i o n ( 2 1 , t h e maximum AT occurs when p, T, and M are maximum. A cornp a r i s o no ff i g u r e 37 ( 5 . 0 atm, 275 K, and M = 0 . 7 5 ) w i t hf i g u r e 1 1( 1 . 5 atm, 100 K, and M = 0 . 3 )d e m o n s t r a t e st h i sc l e a r l y . The t r a n s i t - t i m ed e l a yp r e v i temperature traces o ft h e s er e c o r d s . ouslymentioned is a l s o n o t i c e a b l e i n t h e
dient.
B e c a u s e hf ea an t
(1
+
E x c e p tf o rf i g u r e s 12,25, and 2 9 , t h et u n n e l and simulator r e s p o n s e s a g r e e q u i t e well. I nf i g u r e 12, t h eo s c i l l a t o r yp r e s s u r ea n d temperature r e s p o n s e sf o rt h et u n n e l are due t o a n i n a d v e r t e n t c y c l i n g o f o n e o f t h e smaller exhaust-gasvalveelements which is n o t shown i nt h ef i g u r e , Two fan-input commands were made which caused c u m u l a t i v e e f f e c t s i n t h e t u n n e l v a r i a b l e s shown i n f i g u r e 25. The secondinput,which was i n a d v e r t e n t l y made, is n o t shown i n t h e f i g u r e i n order to show o n l y t h e e f f e c t s o f t h e i n t e n 16
t i o n a li n p u t . The l a r g e pressure and temperature magnitudesexperiencedin pulse r a t h e r t h a n a 3-secinput. f i g u r e 29 are a r e s u l t o f a 5 - s e cl i q u i d Quasi-Steady-State Warm-up and Cool-Down T e s t s
tests oncool-downand I na d d i t i o n to t h et r a n s i e n t - r e s p o n s es t u d i e s , warm-up of the t u n n e l w i t h e x c e s s LN2 flow a n d e x c e s s f a n h e a t i n g , r e s p e c t i v e l y , were conducted to v a l i d a t e t h e q u a s i - s t e a d y - s t a t e h e a t - t r a n s f e r model. The basic energy equation of the cryogenic-tunnel
process is
where p Surface
3
.
WmCmTS
I n o r d e r to v a l i d a t e t h i s h e a t - t r a n s f e r model, time h i s t o r i e s of t h ea v e r a g e metal temperature Tm and gas temperature T were r e c o r d e df o o r r d e r e di n p u t energy terms. A matchbetween temperature, temperaturedifference,and time was s o u g h tf o rt h et u n n e l and simulator q u a s i - s t e a d y - s t a t er e s p o n s e s . Cool-down.- The a c t u a l cool-down process used for t h e 0.3-m TCT c o n s i s t s a t a c o n s t a n t r a t e and i n a s u f f i c i e n t q u a n t i t y o fi n j e c t i n gl i q u i dn i t r o g e n so t h a t t h e c o o l i n g c a p a c i t y o f t h e l i q u i d is g r e a t e r t h a n the heat conducted t h r o u g ht h et u n n e ls h e l l and t h eh e a tg e n e r a t e d by t h e f a n [mL(hL - cpT) >> QF]. T h i s c o n d i t i o n is e a s i l y r e a l i z e d by r u n n i n g t h e t u n n e l a t a v e r y l o w Mach LN2. I f w e n e g l e c tt h eh e a tc o n d u c t e dt h r o u g ht h e number w h i l ei n j e c t i n gt h e to t u n n e l walls, t h i s implies t h a t t h e e n e r g y e q u a t i o n c a n b e s i m p l i f i e d
at - S u r f ace & + "LB
wGcv dT =
Both t h e t u n n e l and t h e s i m u l a t o r were brought to a n e q u i l i b r i u m c o n d i t i o n o f 290 K and 1 . 5 atm w h i l em a i n t a i n i n g a c o n s t a n tf a ns p e e do f 1200 rpm. Liquidn i t r o g e n i n j e c t i o n p r e s s u r e was h e l d c o n s t a n t a t 6 atm t h r o u g h o u t t h e cooldown. S t a r t i n g from a c o n d i t i o no fe q u i l i b r i u m ,t h e actual cool-down process was s t a r t e d by i n c r e a s i n g t h e LN2 i n j e c t i o n - v a l v e area to 1 2 . 5p e r c e n t to achieve a 1.02-kg/secliquid-nitrogenflaw rate. Tunnel pressure was maintained constant during the cool-down process by m a n i p u l a t i o n o f t h e e x h a u s t 17
v a l v e area. The temperature o ft h eg a s ,t h ea v e r a g e temperature o ft h e metal of t h e t u n n e l s h e l l , a n d t h e t e s t - s e c t i o n Mach number were r e c o r d e d d u r i n g t h e cool-down. Both metal and gastemperatures were reducedand cool-down was cons i d e r e d complete when t h eg a sr e a c h e d a temperatureofabout105 K. The t o t a l amount of LN2 consumed was a l s o determinedandrecorded.Figure 38 shows t h e A s canbeseen,both cool-down p r o f i l ef o rb o t ht h et u n n e l and t h es i m u l a t o r . gasand metal temperature trajectories match q u i t e well. An i n i t i a l gas-tometal t e m p e r a t u r ed i f f e r e n c eo f6 5 K e x i s t s .T h i sd i f f e r e n c e decreases d u r i n g cool-down processofonly t h e cool-down, w i t h a d i f f e r e n c e a t t h e e n d o f t h e 1 5 K. The LN2 consumption to cool t h e t u n n e l from 290 K to 100 K was a b u t 1825kg,whereasthecomputersimulationforthe same cool-down p r e d i c t e d a n LN2 close a g r e e m e n tb e t w e e nt h es i m u l a t o rp r e d i c t i o na n d usageof1800kg.This t h et u n n e ld a t ag i v e sc o n f i d e n c et h a tt h eq u a s i - s t e a d y - s t a t eh e a t - t r a n s f e r model is accurate. Warm-up.- For a typical t u n n e l warm-up, t h e LN2 flow is reduced t o z e r o is o p e r a t e d a t c o n s t a n t Mach number and p r e s s u r e . For t h i s w h i l et h et u n n e l s t u d y , t h e warm-up was made a f t e r e s t a b l i s h i n g e q u i l i b r i u m c o n d i t i o n s w i t h b o t h metal and g a st e m p e r a t u r e s a t 1 0 0 K . S i n c e t h e LN2 flow r a t e is zeroand GN2 flaw r a t e i s v e r y n e a r l y so, t h eh e a tg e n e r a t e d by t h e d r i v e f a n i s thedominant f a c t o ri nt h e warm-up p r o c e s s .N e g l e c t i n ga n yh e a ta d d i t i o nt h r o u g ht h et u n n e l walls, t h i s . r e s u l t s i n t h e s i m p l i f i e d e n e r g y e q u a t i o n
dT
wGcv
;it a
&'
-
1
Surface
,
Qm
where
and
Bothtunneland simulator were s e t a t e q u i l i b r i u m c o n d i t i o n s o f 100 K and 0 . 6 , and 0 . 7 were u s e df o rt h e computersimulation 2 atm. Mach numbersof0.5, i n o r d e r t o show t h e e f f e c t o f Mach number o nt h e warm-up p r o f i l e . Once equilibrium was e s t a b l i s h e d , t h e LN2 flow was reduced t o z e r o by c l o s i n g t h e LN2 i n j e c t i o nv a l v e . Mach number and p r e s s u r e were m a i n t a i n e dc o n s t a n tt h r o u g h o u t eachwarnkup.Figure39 shows t h e warm-up p r o f i l e s p r e d i c t e d by t h e simulator 18
f o rt h et h r e ed i f f e r e n t Mach numbers. As e x p e c t e d ,t h ed a t ai n d i c a t e larger gas-to-metal temperature d i f f e r e n c e s as well as f a s t e r warm-up f o r h i g h e r Mach numbers.Figure 40 shows a comparison of an a c t u a l 0.3-m TCT warm-up p r o f i l e and a c o r r e s p o n d i n gs i m u l a t o r warm-up p r o f i l e a t 2 atm and M = 0 . 6 . As can be seen, t h e t u n n e l warms up s l i g h t l y slower t h a n p r e d i c t e d by t h e s i m u l a t o r , but the metal-to-gas temperature differences between the tunnel and simulator a g r e e to w i t h i n 2 K. These d i f f e r e n c e s between t h e warm-up p r o f i l e s are a t t r i b a t t h e b e g i n n i n g of t h e warm-up .uted t o s l i g h t v a r i a t i o n s i n t u n n e l p r e s s u r e process andperhaps a small error i n t h e c o n s t a n t KF. G e n e r a l l y ,t h eb e h a v i o r of t h e 0.3-m TCT and t h e b e h a v i o r p r e d i c t e d by t h e computersimulationofthetunnel show good a g r e e m e n t n o t o n l y i n t h e t r a n s i e n t cool-downand warm-up c h a r a c t e r responses, b u t also i n t h e q u a s i - s t e a d y - s t a t e istics, T h i sa g r e e m e n th a sb e e nf o u n do v e rt h ee n t i r eo p e r a t i o n a le n v e l o p e . Inviewofthisagreement,themathematicalmodeldeveloped to d e s c r i b e t h e t u n n e l is assumed to b e v a l i d a n d a c c e p t a b l e f o r t r a n s i e n t , q u a s i - s t e a d y - s t a t e , and s t e a d y - s t a t e p e r f o r m a n c e . Model .Closed-Loop Analysis S i n c et h eb e g i n n i n go fo p e r a t i o n of t h e 0.3-m E T , theneedforimproving the q u a l i t y o f d a t a o b t a i n e d d u r i n g t u n n e l tests has become i n c r e a s i n g l y appare n t . A major improvement i n t h e q u a l i t y o ft h ed a t ac a nb er e a l i z e di ft h e t e s t parameters c a n b e h e l d to closer t o l e r a n c e s f o r l o n g e r p e r i o d s o f time. I t is r e a s o n e d t h a t i f i n a c c u r a t e a n d i n e f f i c i e n t m a n u a l operator manipulation for holding and changing the t e s t parameters c a n b e e l i m i n a t e d b y t h e u s e of w i l l s i g n i f i c a n t l y improve,with a a d v a n c e dc o n t r o ls c h e m e s ,d a t aq u a l i t y s i m u l t a n e o u sr e d u c t i o ni no p e r a t i n g costs. As shown i nr e f e r e n c e 4 , byreductime, o n ec o u l dp r o p o r t i o n a t e l yr e d u c et h e cost o f t e s t i n g b e c a u s e i n gt h er u n ofdecreased electrical-power and LN2 consumption.Thesearguments a l l alluded to theimplementationofclosed-loopcontrolsystems,which are i n h e r e n t l y more r e l i a b l e ) t h a n t h e human operator. f a s t e r and more a c c u r a t e( a n dg e n e r a l l y C o n s e q u e n t l y ,p r o p o r t i o n a l - i n t e g r a l - d e r i v a t i v e (PID) p r e s s u r ea n dt e m p e r a t u r e c o n t r o l laws were d e v e l o p e da n dd e s i g n e df o ra n a l y t i c a le v a l u a t i o no ft h e hybrid-computer simulator o ft h e 0.3-m TCT. F i g u r e s 41 and 42 show schematic diagrams of t h e pressure and temperature loops, r e s p e c t i v e l y . Shown i nb o t h f i g u r e s are t h e e q u a t i o n s d e s c r i b i n g t h e d i g i t a l v a l v e s a n d t h e r e s p e c t i v e l a g s a s s o c i a t e dw i t ht h et e m p e r a t u r ea n dp r e s s u r es e n s o r s .C o n t r i b u t i o n so ft h e variousinput/outputelements are shown w i t h appropriate s i g n s c o n v e y i n g t h e process loop. influencetheyhaveonthe The closed-loop mathematical models of the 0.3-m TCT were o p e r a t i o n a l l y analyzedassuming local l i n e a r i t y andnocouplingbetweencontrols.For purposes o f i l l u s t r a t i o n , t h e p r e s s u r e loop c o n s i s t s o f f i r s t - o r d e r s e n s o r time c o n s t a n t t 2 , whichdeterminesfeedback measurementdynamicswith press e t - p o i n tv a l u e . The g e n e r a t e d error s u r e t h a t is c o m p a r e d w i t h t h e p r e s s u r e s i g n a l d r i v e s t h e P I D c o n t r o l l e r which, a f t e r appropriate gain selection, controls theoperationofthenitrogen-gas R o o t l o c u sa n a l y s i so f e x h a u s tv a l u e . the pressure performance.
loop i n d i c a t e s t h a t
a g a i n scheduleof
1
-
providesacceptable
P 6 19
A feedback loop similar to that used for pressure control is used for the temperature control with the applicable measurement sensor time constant a digital-valve dynamics. Included in the temperature control loop is a fan power feed-forward term necessary to account for the effect of fan-generated heat on the temperature loop. Root locus analysis of the temperature control -
ME -
loop indicates that a gain scheduling of T
would be satisfactory.
Figure 43 shows data from the hybrid-computer simulator for the closedloop performance for both low and high tunnel temperatures using only proportional and integral signals within the pressure and temperature controls. Closed-loop data from the simulator were acquired for temperature and pres sure set-point changes and finally for fan-speed changes. In figure43(a), the temperature set point is reduced by approximately 8 K. The temperature reaches82 K in about 10 sec and then slowly drifts downward over the next4 0 sec. This lag .is due to the heat transfer from the tunnel wall. The pressure control maintains pressure to within 0.03 atm and suppresses the fluctuations in pressure due to the temperature disturbance in 20about sec. It should be noted that Mach number increases because of the reduction in perature. Following stabilization of thegas temperature at 82 K, the temperature set point is returned to 90 K. The gas temperature reaches 90 K in 5 sec and, since the time spent at the lower temperature was too short the to reduce metal temperature much below 90 K, the gas temperature stabilizes quickly at 90 K. Again the pressure settling time is about 20 sec.
The next disturbance to be evaluated is a pressure set-point change fro 2.13 atm to 1.76 atm. An overshoot in the simulated tunnel-pressure process exists but stabilizes quite nicely. Closed-loop temperature oscillations caused by the pressure input settle in about 22 sec whereas Mach number follows the temperature oscillations in opposite fashion. After the pressure stabilizes at 1.76 atm, the pressure set point is returned to 2.13 atm. The relatively slow pressure buildup occurs because is itnecessary to increase the mass of gas in the tunnel. The rate of increaseis entirely dependent upon the mass flow rate ofLN2 into the tunnel. Closed-loop temperature control for the pressure disturbanceis maintained to within0.5 K and quickly returns to the temperature set-point value.
The last input for closed-loop study consists of a change in drive-fan speed to force a change in Mach number 0.75 fromto 0.65 quickly followed by a change in speed to force a change in Mach number0.65 fromto 0.85. Even with the large change in Mach number (0.65 to 0.85), very small temperature and pressure excursions occur, indicating acceptable performance of the temperatur and pressure control systems. Figure 43(b) illustrates the control-system performance for set-point changes at the high temperature 263 of K. Again the pressure and temperature loops perform well, with average settling times of 20 about sec.
20
Based on these simulator-generated results, the control laws derived on the basis of single-input, single-output analysis provide good closed-loop control of pressure and temperature. Coupling effects between process response and control input are evident, but converge very well using simple loop closure CONCLUDING REMARKS A hybrid-computer simulation of the Langley 0.3-Meter Transonic Cryogenic Tunnel has been developed and fully verified. Comparison of simulation and experimental transient response data exhibited very good agreement throughout the cryogenic-tunnel operational range. Additionally, quasi-steady-state cooldown and warm-up profiles have contributed significantly to the model validation by virtue of the small differences seen between actual and simulated operation. Therefore, it is felt that the single lumped-parameter nonlinear multivariable model has been proven to be globally accurate and reliable in duplicating tunnel temperature, pressure, and Mach number process dynamics. A plethoric compilation of data spanning the tunnel testing isrange provided as a data base for future reference.
Proportional-integral control laws designed using the validated mathematical model have been exercised using the hybrid-computer simulator and have been found to be quite satisfactory for control of both the temperature and pressure process responses. As a result, these control laws will be implemented in software for digital microprocessor controllers for temperature and pressure regulation of the Langley 0.3-Meter Transonic Cryogenic Tunnel. Langley Research Center National Aeronautics and Space Administration Hampton, VA 23665 June 23, 1980
21
APPENDIX !CHERMODYNAMIC MODEL OF THE LANGLEY 0.3-m TCT
In this appendix, a dynamic lumped-parameter model is developed for th 0.3-m TCT circuit. The need for a relatively simple model which can be nume ically simulated and rapidly executed to permit analytical design and inter active usage excludesan analysis basedon nonlinear partial differential equations of fluidflow, Lumped-parameter techniques are applied to produce a loworder model for the dynamics of the process variables at the test-section differential-delay/ordinary differential equations. location in the form of Temperature
Equation
The first law of thermodynamics applied to this analysis can be writ
This is an energy equation which states that the change in total system E is equal to the heat Q added to and the work w done by the selected system. The energy term consists of the sum of potential energy, kinetic energy, and internal energy. Because the change in elevation as the gas circu lates around the tunnel is small, potential-energy contributions were neglec For the tunnel testing conditions operationally used, the kinetic energy of the circulating gas was found to be a small percentage of the total system energy and was therefore ignored.
Since no workis performed by the circulating cryogenic gas, this term o the general thermodynamic equation is zero. Therefore, it can be seen that h energy Q is the sole source for change in the level of internal energy of the gas. Mathematically this can be expressed in special form as
au
or
22
APPl3NDIX
where
U
i n teenrenragl y ,
U
s p e ciinf ti ecer n ae lr g y ,
WG
mass ot h fcei r c u l a t i nngi t r o g e n
J
J/kg t e s t gas, kg
is composed o f a number of i n d i v i d u a l The l e f t s i d e of t h e a b o v e e n e r g y e q u a t i o n s o u r c e s which c o l l e c t i v e l y c o n t r i b u t e to t h ei n t e r n a le n e r g yo ft h es y s t e m .F o r example, two-way h e a t t r a n s f e r e x i s t s between the ambient environment and the g a st h r o u g ht h ei m p e r f e c t l yi n s u l a t e dt u n n e l metal s t r u c t u r e . Heat of compress i o n from t h e t u n n e l f a n is o b t a i n e d as t h e t e s t medium is c i r c u l a t e d t h r o u g h Also, energy is added by i n j e c t i o n of LN2 andexhaustof GN2 d u r i n g t h et u n n e l . r e g u l a t i o n of t e m p e r a t u r ea n dp r e s s u r ec o n d i t i o n sw i t h i nt h et u n n e l . The s i g n c o n v e n t i o n s e l e c t e d is s u c h t h a t anyenergyadded t o t h e GN2 t u n n e l medium was consideredpositive. Expandingequation hand s i d e y i e l d s
Because
( A l ) by t a k i n g t h e f i r s t p a r t i a l d e v i a t i v e
of t h e r i g h t -
a u 6 cv aT, e q u a t i o n (A21 becomes
or
&
The term is r e a l l y t h e time r a t e of c h a n g eo ft h et u n n e lr e s i d e n tg a s can be expressed a s the difference between the injected- and exhausted-nitrogen masses, t h a t is, WG = mL
-
Substitutingthisalongwiththeappropriate energy terms f o r t h e l e f t s i d e o f e q u a t i o n
and
(A4 1
metal, f a n ,
LNz,
and GN2 h e a t
(A3) g i v e s
23
A f t e rt r a n s p o s i n ga n dc o l l e c t i n g
terms, t h i s e q u a t i o n
is
However, f o r a p e r f e c tg a s (whichcanbeassumedfornitrogen), T h e r e f o r e ,t h er e l a t i o n s h i p becomes hG = cpT.
u = c,T
and
Expressionswhich arf! f u n c t i o p o f local p r e s s u r e , t e m p e r a t u r e , andMach-number are now needed for Qm and QF i.n e q u a t i o n (A71 The development of QF is a c c o m p l i s h e di na n o t h e rs e c t i o no ft h i sa p p e n d i x . A d e t a i l e da n a l y s i so ft h e d e r i v a t i o n of t h em e t a l - t o - g a sh e a tt r a n s f e r Qm basedon a numerical estimationoftheheat-transfercoefficient by B a r t z is p r e s e n t e d i n r e f e r e n c e 3. R e s u l t s of that work i n d i c a t e t h a t
By u s i n ge q u a t i o n
(A8) t o g e t h e rw i t he q u a t i o n
By d e f i n i n g
e and
24
= WGC,
+
W,C,
( A T ) and r e a r r a n g i n g we g e t
APPENDIX
e q u a t i o n (A91 can be expressed a s
or
T h i s becomes
=
(")&
-
a + B
(i)& (a)& +
where tG
P
e
WGcvtm
and
WG
341.4
py(1 + >) T
250
(1
-
0. 033M1 05)
E q u a t i o n( A l l ) is thefundamental temperature r e l a t i o n s h i p f o r t h e model w i t h t h ee x c e p t i o no ft r a n s p o r td e l a y s needed f o r realism. Because t r a n s i t time is e x p e r i e n c e db e t w e e nc o n t r o li n p u t andmeasurement,puretransportdelays are i n c o r p o r a t e d . L i q u i d n i t r o g e n is i n j e c t e d downstream of t h e test s e c t i o n i n t h e 0.3-m TCT, and s i n c e t h i s e f f e c t is measured i n t h e s e t t l i n g chamber a time d e l a yo f e-TLs is used. The f a n h e a t of c o m p r e s s i o no c c u r sa f t e rt u r n number two i n t h e t u n n e l , a n d s i n c e it also is measured i n t h e s e t t l i n g chamber a delayof
e-TFs
is needed.
A smaller d e l a y ,
-
e TGS, is u s e df o rt h eg a s
25
APPENDIX effectssincegasventing is v e r y n e a r t h e p r e s s u r e measurementsensor in the s e t t l i n g chamber. By a p p l y i n gt h e s ed e l a y sa n dp e r f o r m i n g a b i t o fa l g e b r a , e q u a t i o n ( A l l ) is now
The onlyremaining unknown i n e q u a t i o n (A121 is t h e h e a t e n e r g y g e n e r a t e d test gasaround t h e t u n n e l . T h i s c o n t r i b u t i o n by t h e f a n w h i l e c i r c u l a t i n g t h e c a n be r e p r e s e n t e d by
I f w e assume t h a t t h e mass flow r a t e a t t h e t e s t s e c t i o n *; i s t h e same a s t h e mass flow r a t e a t t h e f a n i n l e t ( i . e . , i* = . h ~ , i ) ,t h e nt h ef a n - i n l e t mass flow rate can be expressed as
i ~ , =i 6965
P AM(1 +
fi
0.2M2)
-3
where p is p r e s s u r ei na t m o s p h e r e s , A is t e s t - s e c t i o n area i n square meters, and T is temperature i nk e l v i n s .T h i se x p r e s s i o nc a n be found i n anythermodynamic t e x t for t h e c a l c u l a t i o n of mass flow r a t e of an i d e a l gasthroughan isentropic nozzle. The t e m p e r a t u r ec h a n g ei ne q u a t i o n (A13) a t t h e f a n s e c t i o n is found by u s i n gt h ef a np r e s s u r e - r a t i oe q u a t i o nf o rs t e a d y ,i s e n t r o p i cc o m p r e s s i b l ef l o w , M a t h e m a t i c a l l yt h i s is
26
APPENDIX
where
Y
4
cP
-,
t h e r a t i o o fs p e c i f i ch e a t so ft h eg a s
under c o n s i d e r a t i o n .
By
CV
r e a r r a n g i n gt h i s ,e q u a t i o n
(A1 5) becomes
or
Working o n l y w i t h t h et e m p e r a t u r e
T~
'=( Because
AT
Te
+
)
T i , or
p~~ -
=
we can write
AT Y-1
Ti
-
term i nt h ea b o v e
which, a f t e ra d d i n gt h e
AT
-
+
T i = Te
-
AT, e q u a t i o n (A17) canbeexpressed
as
AT Y-l
)
AT
AT
terms becomes
27
APPENDIX
Solving equation (A18) for Al', we get
which, after assuming a fan efficiencyof
;I, becomes
or
As with any closed-circuit tunnel, the steady-state fan pressure ratio r can be expressed as a function of the integrated pressure-law coefficient and the normalized test-section Mach number. Mathematically,
r = 1 + bM2 Introducing this into equation (A19), we get
r AT
28
= 1 "
n
Y -11
-
(1
+
bM2)
APPENDIX
- -Y-1 T h ien n e r
term
yielding
1
+
(-
(1
+
bM2)
y ) b M 2 .
a f irst-order T a y l o r series
c a n be e x p a n d e idn
S u b s t i t u t i o ni n t oe q u a t i o n
(A20) gives
or
P l a c i n ge q u a t i o n s( A 1 4 )a n d
Because
Te = T
(A21 1 i n t oe q u a t i o n
(A131 r e s u l t s i n
( t h e t o t a l gas t e m p e r a t u r e ) , i f we l e t
69 65
KF
- Acpb 17
a ncda n c e l
l i k e terms, t h e above c a n be w r i t t e n a s
r$)
8
From a c o n t r o ls t a n d p o i n t ,e q u a t i o n (A221 s h o u l d be r e p r e s e n t e di n terms of a system i n p u t . From a c u r v e € i t of t u n n e le x p e r i m e n t a l d a t a , a r e l a t i o n s h i pb e t w e e nt h es y s t e mi n p u t of r e v o l u t i o n s per m i n u t ea n d Mach number is n e e d e d .T h i sf u n c t i o n was d e t e r m i n e d t o be
where KM = 5 9 7 ( 1 yields
-
0 . 3 ~ ) p - 0 - 0 3 5E . quation
(A231 c o m b i n e dw i t he q u a t i o n( A 2 2 )
29
APPENDIX
F i n a l l y ,t h e 6 s y s t e me q u a t i o n of t h e m a t r i x i n f i g u r e 3 c a n be o b t a i n e d mass flow rate e q u a t i o n s by s u b s t i t u t i n g e q u a t i o n (A241 andthefollowingvalve i n t o e q u a t i o n (A12) :
where
KL
4 3.47
where
KG
= [2
-
d F p
and
( y) ] 1.5 1 * 7
21.8
AL = I n j e c t i o nv a l v eo p e n i n gi np e r c e n t ,a n d
and
AG = E x h a u s tv a l v eo p e n i n gi np e r c e n t .
Mach Number Equation A s previouslymen,tioned,thefan speed and t h e t e s t - s e c t i o n are related by t h e empirical e x p r e s s i o n
Mach number
For any g i v e n Mach number, t h i s r e l a t i o n s h i p resulted i n a good f i t o f t h e surrounding t h e 0.3-m TCT data ( w i t h i n ? l o rpm). Because o f t h e plenumvolume test s e c t i o n ,t h e Mach number is d y n a m i c a l l yi n f l u e n c e d .P r e v i o u st e s t i n gi n d i cated t h a t t h i s i n f l u e n c e is of a f i r s t - o r d e r t y p e e f f e c t because of t h e n e t f l o w i n t o or o u t o ft h e plenum. Also, t h e r e is a s l i g h t d e l a y associated w i t h a f a n rpm c h a n g e t h a t is to be i n t e r p r e t e d a s a t e s t - s e c t i o n Mach number v a r i a (A25) becomes t i o n . From t h e s e two f a c t s ,e q u a t i o n
30
APPENDIX where
-
KM
= 597(1
O . 3 ~ ) p - ~ m ~ ~ ~
tP
plenum time c o n s t a n t
Ta
a c o u s t i c time lag
is p r e s e n t e d i n t h e t e x t as e q u a t i o n ( 5 ) , is t h es e c o n d Equation(A26),which e x p r e s s i o n of t h e model matrix i n f i g u r e 3 and relates t h e rpn i n p u t t o t h e Mach number o u t p u t . PressureEquations The l a s t dynamicmodelfunctionused to d e s c r i b e t h e c h a r a c t e r i s t i c s o f l a w (whichnitrogen t h e 0.3-m K T is t h e pressure e q u a t i o n . From t h e i d e a l g a s v e r yc l o s e l ya p p r o x i m a t e s ) pressure is r e l a t e d to temperature according to
where WG is t h e mass of t h eg a si nk i l o g r a m s .S i m p l yt a k i n gt h ef i r s t derivativeofthiswith respect t o time y i e l d s
where M.E.
P denotes manentum e f f e c t s .
But
WG =
P K1 T
and
T = K1wG
partial
w i l l cause
e q u a t i o n (A27) t o be
ap
p
- = - W,
at
Since
~WG
at
+E T
2 + M.E. at
. - w f equation - = mL awG
at
aP = -
at
P -(mL
wG
- iG) + E
T
(A28)becomes
2 + M.E. at 31
APPENDIX
or
-aP = - mP L - - ~ +P; T. + M .PE. .
at
wG
WG
Themmentum e f f e c t s are a t t r i b u t e d to t h e f a n p r e s s u r e - r a t i o c h a n g e s and press u r e losses and were found to be related to t h e t o t a l pressuredynamics according to
aP aM = DbMp at at
where b is t h e pressure-loss c o e f f i c i e n t and D is a d i m e n s i o n a l i t yc o n s t a n t . If we i n s e r t t h e l i q u i d t r a n s p o r t d e l a y , t h e g a s e o u s t r a n s p o r t d e l a y , a n d t h e (A29) becomes momentum e f f e c t s ,e q u a t i o n
aP
- = -
at
where
b = 0.1
P
wG
mLe
-TLS
,,(, - --).
7PM
. P. aM - P- mGe -TGs + - T + DbMp WG T at
T h i s is e q u a t i o n ( 4 ) i n t h et e x t .
Of course, t h e
v a l v e mass flow r a t e e q u a t i o n s are t h e same, and upon s u b s t i t u t i o n for of f i g u r e 3 is d e r i v e d . arrangement t h e t h i r d m a t r i x e q u a t i o n
32
$ and
REFERENCES 1. Kilgore, Robert A.; Goodyer, Michael J.; Adcock, Jerry B.; and Davenport, Edwin E.: The Cryogenic Wind-Tunnel Concept for High Reynolds Number Testing. NASA TN D-7762, 1974.
2. Kilgore, Robert A , : Design Features and Operational Characteristics o€ the Langley 0.3-Meter Transonic Cryogenic Tunnel. NASA TN D-8304, 1976. 3. Balakrishna, S.: Synthesis of a Control Model for a Liquid Nitrogen Cooled, Closed Circuit, Cryogenic Nitrogen Wind Tunnel and Its Validation. NASA CR-162508, 1980. 4. Ray, Edward J.; Ladson, Charles L.; Adcock, Jerry B.; Lawing, Pierce L.; and Hall, Robert M.: Review o€ Design and Operational Characteristics of the 0.3-Meter Transonic Cryogenic Tunnel. First International Symposium on Cryogenic Wind Tunnels, Proceedings of the Symposium held in the Department of Aeronautics and Astronautics at the University of Southampton, England, Apr. 3-5, 1979, pp. 28.1 - 28.15.
33
TABLE I.- NOMINAL
Figure 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
34
VALUESOF TUNNEL AND SIMULATOR TEST CONDITIONS
Total temperature, K 1 00 100 1 00 1 00 100 1 00 1 00 100 100 200 200 200 200 200 200 200 200 20 0 275 275 275 275 27 4 275 275 27 5 275
Test-section Mach number 0.30 .60 .90 .30 .60 .95 .30 .60 9,0 -30 .60 .90 .30 .60 .90 .30 .60 .90 .30 .60 .75 .30 .60 .75 .30 .60 .80
.
Total
pressure, atm 1.57 1.57 1.57 3.00 3.00 3.07 5.00 5,00
4.93 1.57 1.50 1.57 2.65 3.00 3;00 5.00 5.00 5.00 1.57 1.57 1.57 3.00 3.00 3.00 5.00 5.00 5.00
TOTAL PRESSURESENSOR
3 VOLUME = 14.16 m WEIGHT OF METAL (AL-6061) = 3200 kg 2 TEST-SECTION AREA = 0.1239 m Figure 1
W VI
.- Schematic of Langley0.3-MeterTransonicCryogenicTunnel.
TUNNEL PROCESS MODEL
-
$[
pM2
e(1 t O.ZM'?
3 ('
1
"m') +
tGS
e-TFS -KG
(&)(-)
e-TGS
"laS
e KM.\Tfl+t
0
Figure
.- Lumped-parameter
3
P
s1
multivariable model of 0.3-m E T .
0
X
W
OD
679-1665.1/
Figure 4.-
Hybrid-computer simulation facility.
I
I DCA‘S
ADC’S
L;
1.
2.
TAPE INPUT
3.
LLl RECORDER
d.
t2
5.
6.
WGcv’rn
7. ANALOG COMPUTER
AG
-
U.
PL
-
9.
N i 1
-
D I.
11.
QV=
12.
,
40
=_ I T
c SIMULATOR CONTROL PAKL
13. 14. CONTROLS: ArAC.N DIGITAL COMPUTER
~~~
W
~
Figure 5.-
B l o c k diagram of hybrid-computer simulation.
~
P 0
- 10 v RECORDER
t
1
TRUE GAS TEMPERATURE
4-
I
I 0
Tm - T
-T
“
t
WGC$m
‘I1
I ’mCm wG %‘m
I
L
I
”
L
SIMULATOR D I SPLAY MRAL TEMPERATURE
(ADC- 8)
1 CONTROLLER 4
THERMOCOUPLE OUTPUT
-“--I\
- 1ov -T 5
Te
L
S I MU LATOR D l SPLAY GAS TEMPERATURE
(a) Temperature dynamics. Figure 6.-
m o p diagrams of model dynamics and simulation control.
MEASURED GAS TEMPERATURE ( RECORDER 1
- 10 V
SIMULATOR DISPLAY
cCONTROLLER
10;
-;
+ 1ov
)RECORDER P
I
ObMp
/.
-
fi KM COMPUTER PANEL
600
Nset
,SIMULATOR
rprn/sec LIMITER
- 1ov
D I SPLAY, rPm
FAN rpm ,RECORDER
- 1ov
-N
SIMULATOR PANEL
- 100 rp rn
(ADC-3)
SWITCH
-lov
-0-
"1
&RECORDER
+ 1ov
I MI
M1
-v
I DISPLAY
MACH NUMBER
(b) Pressure,fan,
and Mach number
Figure 6 . - Continued.
y10 v
dynamics.
SIMULATOR PANEL
Ip h)
- 1ov
@
I
COMPUTERPANEL
- 1ov
AREA
,LN2 VALVE (A DC-4)
- 1ov 6.25% A AL
SWITCH
SIMULATORPANEL I
- 1ov
I
- 1ov
1 6.25% A A G
4-
SWITCH
1ov
L,NZ (c) Simulator analog block diagram. Figure 6.-
Continued.
PRESSURE (A DC-6)
TEMPERATURELOOP
IN2 VALVE AREA
PROPORTIONAL
4R
10
(ADC- 4)
INTEGRAL
-T 30
QV G A I N SCHEDULE
SIMULATOR METER DISPLAY
4p-
- l0FEED lvFORWARD
GN2 VALVE AREA
PRESSURELOOP
7RECORDER h
GAIN SCHEDULE VOLTAGE
(d) Closed-loop controllers for
Figure 6.
D P
w
temperature and pressure.
- Concluded.
6 7 9 - 1 666.1
Figure 7.- Control panel 0.3-m 'ET.
Figure 8 . - D i g i t a lc o n t r o l
valve.
(1 atm = 1 4 . 7 Psi.)
45
I
Figure 9.- Control panel for hybrid-computer simulation.
679-4645.1
Figure 10.- Simulator instrumentation.
Y -.4
SIMULATOR'
LL
3
c
a
SIMULATOR'
" I V
2z
0.280
6
0.280
0-
c
G
-100 rprn to N
r
2
0
g
1
s24 o
I
18 6
1
12
I
I
I
30
I
48 36
I
42
I
1
1
I
I
I
54
60
66
72
78
TIME. Sec
Figure 11.-
Simulator and tunneltransientresponsedataat M = 0 . 3 , and p = 1 . 5 7 atm.
T = 100 K,
Q
I
1 .
w D:
3 x-
SIMULATOR 90
D: 0
w
+ 5
2
U
6 I-
"I
" -
" TUNNEL
90
6.25'kto AL
2z
L
-100 rpm to N
l"r
-I
0
a
s L)
I
I
I
I
1
I
I
I
I
I
I
I
0
6
12
18
24
33
36
42
40
54
60
66
I
72
TIME, Sec
Figure 12. - Simulator and tunneltransientresponsedata M = 0 . 6 , and p = 1 . 5 7 atm.
at
T = 100 K,
78
cn
0
6.25% to AG
6.25% to AL
2
5 6 a:
s u
L . "L I
I
0
6
I
12
-100 rpm to N
7
I
I
I
I
I
I
I
I
I
24
30
36
42
I
18
48
54
60
66
72
TIME,
SeC
Figure 1 3 . - Simulator and tunneltransientresponsedata M = 0 . 9 , and p = 1 . 5 7 atm.
at
T = 100 K,
I
18
I
SIMULATOR'
" TUNNEL
'
' -100 rpm to N
I
I
I
I
I
0
6
12
18
24
I
I
3 0 3 6
I
I
I
42
48
54
I
I
6 0 6 6
I
I
12
70
TIME, Sec
Figure 14.-
Simulator and tunneltransientresponsedata M = 0 . 3 , and p = 3 . 0 0 atm.
at
T = 100 K,
=
n I-
2
E
7 98
a -
0 X
u
2z
O0.580 . 7
0
I-
0.580
" -
E
'-' 7 Y
a: 3
v) v)
2.93
Y
-1
4
6
I-
SIMULATOR/
2.93
SIMULATOR'
TUNNELI
6.25% to AG
6.25% to AL
I-
n
n
3
a
z 24
I
I
I
0
18 6
12
I
I
-100 rDm to N
I
I
I
I
I
I
I
I
I
30
36
42
48
54
60
66
12
7a
TIME , Sec
Figure 1 5 . - Simulator and tunneltransientresponsedataat M = 0 . 6 , and p = 3 . 0 0 atm.
T = 100 K,
n
+ -I
a
E
" -
"I
TUNNEL
98
/
3-071 3-071
+
.
"
TUNNEL
--/"
SIMULATOR'
3.00
TUNNEL'
3. 00
-
25
-100 rprn to N
1
2
0
a
.z V
-
I
0
I
1
18 6
12
I
I
I
I
I
24
30
36
42
I
I
I
48
54
60
7 1
78 66
I
72
TIME ,Sec
Figure 16.- Simulator and tunneltransientresponsedata M = 0 . 9 5 , and p = 3.07 atm.
a t T = 100 K,
I
-
-"
X
u
3
o 0.280
7
z
0
vl
V
0.280
E
-
z
3 -.
fi a
5.M1 4.93J
SIMULATOR'
n
___L_c_. TUNEL'
4.965
5
n
TAL
-100 rprn to N
d
0 "1
a
s
V
I
0
I
6
I
12
I
18
I
24
I
30
I
I
36 42 TIME, Sec
I
48
1
54
Figure 17.- Simulator and tunneltransientresponsedataat M = 0 . 3 , and p = 5 . 0 0 atm.
I
60
I
66
I
12
T = 100 K,
I
78
-100 rpm to N
I-
3
Y
a
5 -1
0
z
0
u
I
I
I
I
0
6
12
18
I
24
I
1
I
I
I
I
I
I
I
30
36
42
48
54
60
66
12
78
TIME,
Figure 18.VI VI
SeC
Simulator and tunnel transient response data at T = 100 K, M = 0.6, and p = 5.00 atm.
6.25% lo AL
55 -
z OI
u
-100 rpm to N
-I 0
I
0
I
6
I
I
I
I
I
I
I
I
12
la
24
M
36
42
48
54
I
I
I
I
60
66
72
78
.
TIME. Sec
Figure19.-Simulator
and tunneltransientresponsedata M = 0 . 9 , and p = 4.93 atm.
at
T = 100 K,
I
1
I
i
-
... 0 c
TUNNEL'
198
:5
w VI
J
1.57
SIMULATOR4
VI
w
TUNNEL4
a
I-
-100 rpm to N
