Parallel Operation of Turbo-Compressors in a Common System

60-GTHYD-8
PARALLEL OPERATION OF TURBO-COMPRESSORS
IN A COMMON SYSTEM
W.
T. Fu rgerson
Nuclear reactors which are des igned for power produc­
tion have their h eat remove d by some cooling fluid which
may be a liquid or a gas. Since the apparent success of
the British power reactors there has been a growth of
interest in gas-coo l ed reactors in thi s country.
Th e relatively low volumetric heat capacity of gases
requires that large volumes of coolan t be circulated.
Gas-cooled reactor designs whi ch are currently of interest
require coolan t circulation rates sufficiently large that
turbo-compre ssors, either axials or centrifugal s , are a
practical necessity . B ecause of th e coolant volume flow
rate and for reasons of safety most gas-cooled reactor
systems are being design ed with two or more compres sors
in parall e l .
It i s w e l l known that turbo-compres sors w i l l surge i f
coupled t o a circuit i n wh ich t h e resi stan ce i s too high .
It is not so well known tha t it is possibl e to have a
system which operates satisfactorily with a single com­
pressor but would be inoperable if the single compressor
were replaced with two or more compressors in parallel
having a combined characteristic equal to that of the
single n1achine.
STORAGE
VOWME
v,
assumed th at the head v s flow c haracteri stic s of th e com­
pre s so r and th e c ircuit resi stan c e s are straight lin e s . The
following dynami c e quation c an the n be written
d4 8
ao dt 4
where :
---
-
A
STORAGE
VOLUME
+
a3
d8
d;
==
0
( 1)
is a perturbation from the steady-state opera­
ting point
A2
Cro s s s ectional areas of
line s , resp ectivel y
R1
and
R2
connecting
R1
and
R2
Mas ses of fluid contained in
ne cti ng line s , respectively
b
Slope of compre ssor characteri stic c urve at
steady- state operating point
F i g ur e l
STORAGE
VOLUME
8
d 38
d2 8
a l dt 1 + a 2 dt 2
M 1 , M2
v,
COMPRESSOR
1,
+
Slope s o
c urves
P0
--
fR 1
and
R2
con­
circuit characteri stic
Steady- state reference pre s sure
Vo lumes of the respective storage volumes
v,
STORAGE
VOLUME
COMPRESSORS
v
-
1
F i g u re 2
It can b e se en that this e quation resembl es the case for
vibration s with linear damping and linear self-exci t ation.
The circuit resi stan c e s are anal ogous to vi scous friction ,
and they act t o dampen flo w perturb atio n s . T h e compre ssor
charac teri stic i s also a damping f ac tor if it has a n ega­
tive slope , but it can b ecome a self- excitation facto r if
its slop e is positive. The sy stem i s considered stabl e i f
a perturbation d amp s o u t with time either by d amped
o scill ation s or by critical damping. I f the system is un­
s tabl e it will go into a rel axation o scillation-the wel l­
known surge.
The first criterion of a stable sy stem is satisfied when
A compre s sor and it s circuit are repre sented s chemati­
cally in Fig. 1 . If the analys i s is confined to small p er­
t urbation s from the steady-state operating point it can be
(2)
27
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-
-
-
-
-
-""""'
----=---=-
__
--
-
-
that of the system curve. Such an a ssumption is an invi­
tation to trouble in the case of parallel compre s sor
installation s .
Generally , compre ssors having a h e ad v s flo w curve
with a steep n egative s lope will h ave greater stability in
a given system than machines with flatter curves. Some
sy stems are being design e d for variable speed com­
pres s or operation in order to obtain flo w control. In
designing such systems it must be kept in mind that com­
pres sor curves tend to become flatter at decreased speed.
It is possible to h ave a system which operates sati s­
factorily at design speed but becomes unstable at reduced
speed.
The design of the flow circuit can affect the stability
of the system by influencing the sys tem constants, b, [3 ,
and {3 2 , o r by affecting their coeffi ci ents in e quations
( 2) and ( 4). Th e slopes of th e circuit resi stance curv e s ,
{3, a n d f3 2 , are usually positive , b u t a diffuser placed in
the circuit c an produce the effect o f a n e gative slope and
bring about reduced stability. A multip l e compre s sor
in stallation is particularly sen sitive to diffusers placed
in the individual compres sor circuits since there i s no
compensating stabilizing effect from a reduction in flow
area elsewhere in th e system.
The above statements are applic able to liquid circu­
lating systems using turbo pumps provided two or more
fre e liquid surfaces exi st.
If the single compres sor i s replaced by two or more
identical compressors in parallel as in F ig. 2 the dynamic
equation i s
( 3)
In thi s case the criterion for stability i s
(4)
Th e difference between sys tems h aving single com­
pre ssors and those h aving more than on e can be s een by
comparing equations ( 2) and ( 4). In the former the entire
system resistance as repre sented by {3 I and f3 2 acts to
stabilize th e system, while in the latter th e only effective
resi stance for stability purp o s e s is that which is unique
to a given compressor in th e R 1 position.
A multi-compressor system is therefore inherently less
stable than a system with a s ingle compressor; all other
things being equal. Thi s margin of stability can be great
enough to mean the difference between a system which
is stable and one which is un stable. In th e case o f
single compre s sors i t i s common practice t o as sume that
a system is inherently stable if the slope of th e com­
pressor head vs flow curve is algebraically less than
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