Srinivas Paper
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Computationally efficient model for refrigeration
compressor gas dynamics
M.N. Srinivasa, Chandramouli Padmanabhanb,*aDepartment of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, IndiabDepartment of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
Received 22 February 2001; received in revised form 22 November 2001; accepted 30 November 2001
Abstract
In this paper a computationally efficient steady state model for a typical refrigeration reciprocating compressor is
proposed. The plenum cavity is modelled using the acoustic plane wave theory, while the compression process is
modelled as a one-dimensional gas dynamics equation. Valve dynamic models, based on a single vibration mode
approximation, are coupled with the gas dynamics equation and acoustic plenum models. The steady-state solution of
the resultant coupled non-linear equations are posed as a boundary value problem and solved using Warner’s algo-
rithm. The Warner’s algorithm applied to compressor simulation is shown to be computationally more efficient as
compared to conventional techniques such as shooting methods. Comparisons are based on the number of iterations
and time taken for convergence. Effect of operating conditions on the overall compressor performance is also investi-
gated.# 2002 Elsevier Science Ltd and IIR. All rights reserved.
Keywords: Refrigerant; Gas; Compression; Reciprocating compressor a ` ; Modelling; Design
Compresseur frigorifique : mode ` le efficace pour e ´ tudier la
dynamique des gaz
Mots cle s : Frigorige ´ ne ; Gaz ; Compression ; Compresseur a ` piston ; Mode ´ lisation ; Conception
1. Introduction
Reciprocating compressors are widely used in food
processing, chemical and air conditioning/refrigeration
industries. They are favored for variable-speed operations
in refrigeration industries as compared to rotary vane and
semi-hermetic compressors [1]. Modelling of the recipro-
cating system and its simulation is of immense impor-
tance as it provides an insight into the energy used
during the compression process, compressor efficiency
and influence of various design parameters on the com-
pressor performance. The steady-state simulations are
used in fault diagnosis [2] wherein the simulated pres-
sure profile is compared with the experimental one.
Discrepancies reveal problems such as leakage and slug-
ging. Steady state indicator diagram has been used to
analyze the importance of phenomena such as valve lift,
valve stiffness and leakage on compressor performance [3].
The mass flow rate that occurs through the valves into
the suction and discharge plenums leads to gas pulsa-
0140-7007/01/$20.00 # 2002 Elsevier Science Ltd and IIR. All rights reserved.
P I I : S 0 1 4 0 - 7 0 0 7 ( 0 1 ) 0 0 1 0 9 - 8
International Journal of Refrigeration 25 (2002) 1083–1092
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* Corresponding author. Tel./fax: +44-235-0509.
E-mail address: [email protected] (C. Padmanabhan).
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tions due to the finite volume associated with the ple-
nums. These pulsations have been identified as a majorsource of noise radiation from reciprocating com-
pressors. In order to predict and hence reduce the noise
generated, a good understanding of the parameters that
control the source of pressure pulsations is required [4].
Soedel et al. have done extensive work in the modelling
of the plenum gas pulsations in the case of single and
multi-cylinder compressors [5,6]. Their formulation
couples the compressor gas dynamics with that of the
plenum by using an impedance approach. Benson and
Ucer [7] modelled the compressor-pipe interactions
using a modified homentropic theory by the method of
characteristics. Dufour et al. [8] have used experimental
steady-state pressure profile in the simulation of the
transient(start-up and shut-down) and steady-state
dynamics of compressor housing and analyzed the
vibration of the whole unit.
Related modelling efforts include those of Popovic et
al. [9] who modelled the positive displacement recipro-
cating compressor using a semi-empirical method whichis based on thermodynamic principles and a large data
base. It needs data on pressure, temperature, mass flow
rates, at the compressor inlet and the outlet and power
input. The model took into account the energy transac-
tions that occur between compressor and its surround-
ings. McGovern et al. [10] analyzed the compressor
performance using exergy method where an energy
approach is undertaken. The non-idealities are char-
acterized as exergy destruction rates as losses to friction,
irreversible heat transfer, fluid throttling and irreversible
fluid mixing.
Almost all of the prior investigators of reciprocatingcompressor gas dynamics have carried out their simula-
tions using numerical integration of the non-linear cou-
pled structural gas dynamics equations [4–7,11]. They
viewed the problem as an initial value problem, and per-
formed simulations which always included the transient
solutions. This had the following disadvantages:
these simulations need to be performed until
steady state conditions are attained and is a time
consuming process;
the initial conditions for the compressor para-
meters were chosen such that the solution con-
verges to steady-state [6]. The problem of
choosing initial conditions becomes a major issue
as the number of model parameters increase. For
instance, this approach will not work well for
the case of multi-cylinder simulations. In such
cases, convergence is achieved only with rea-
sonable guesses of steady-state values.
Recently, Srinivas and Padmanabhan [12] demon-
strated the computational effectiveness of Warner’s
algorithm [13] in compressor plenum acoustics simula-
tions. In the present work, the focus is on developing a
computationally efficient tool for modelling the dynam-ics of the compression process in a single cylinder com-
pressor with one suction and discharge valve.
Temperature effects are not incorporated in the present
model. However, other non-idealities, as identified by
Woollatt [3], have been introduced in the present model.
This leads to a non-linear boundary value problem, and
Warner’s algorithm [13] is incorporated to obtain the
steady-state solution directly. Since this procedure cir-
cumvents the need to calculate the transient solutions it
is computationally superior. The computational effi-
ciency of this approach is demonstrated by comparing
the time for convergence and number of iterations with
Nomenclature
Ad, As Cross sectional area of the valve, m2
Asv, Adv Suction flow area, m2
c Velocity of sound, m/s
C ds, C dd Coefficient to account for non-ide-ality
F pd, F ps Spring pre-loads, N
kd, ks Valve spring constants, N/mm
l Length of the plenum, mm
mc Cylinder gas mass, kg
md, ms Valve mass, kg
n Polytropic gas constant
m:in Mass flow in the cylinder, kg/s
m:out Mass flow out the cylinder, kg/s
Pc Cylinder pressure, Pa
Psuc, Pdis Plenum pressures, Pa
P1 Plenum pressure just outside thevalves, Pa
Q1 Mass flow rate, kg/s
S 1 Cross sectional area of the plenum,
m2
S 2 Cross sectional of the anechoic ter-
mination pipelines, m2
t Time, s
V c Cylinder volume, m3
V str Volume swept by the piston, m3
V cle Clearance volume, m3
xd, xs Valve displacement, m
xmaxd , xmaxs Maximum valve displacement, m
x:d, x: s Valve velocity, m/sZ (!) Impedance, Pas/m
Greek letters
c Cylinder gas density, kg/m3
s, d Density of plenum gas, kg/m3
Time period (2/!c), s
!c Compressor running frequency, rad/s
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traditional techniques. Important parameters affecting
the compression process are studied for a variety of
operating conditions.
2. The mathematical model
As shown in Fig. 1, the system that is considered is
the reciprocating air compressor cylinder, with spring
type suction and discharge valves. The plenums are of
finite volume. We consider a very long coiled tube being
connected to the plenums (not shown in Fig. 1), so that
we can assume that this arrangement approximates an
anechoic or non-reflecting termination. The piston has
reciprocating action through the crank shaft arrange-
ment and no leakage is assumed. A clearance volume of
10% of the stroke volume is assumed.
We are not interested in capturing the pressure varia-
tion of the compressor cylinder spatially, rather, onlythe average pressure as the reciprocation takes place.
This facilitates the use of the overall mass balance
equation in the contracting volume of the system as a
whole.
mc ¼ cV c ð1Þ
dmc
dt¼ m
:in À m
:out ð2Þ
V c ¼ V cle þV str
21 À cos !ctð Þ
È Éð3Þ
Assuming the gas to be polytropic one gets:
Pc
nc
¼ constant ð4Þ
Eqs. (1) and (4) in Eq. (2) yields:
dPc
dt¼ À
nPc
V c
dV c
dtþ
nPc
cV cm:in À m
:outð Þ ð5Þ
where m:in, and m
:out, the mass flow rates through the
suction and the discharge valves, are functions of cylin-
der pressure Pc, valve motions xs and xd , and plenum
pressures Pdis and Psuc. Due to the non-ideality of thevalve, it does not shut down instantaneously as soon as
an unfavorable pressure difference is created. It takes
some time for it to get decelerated from its original
motion, turn the direction and shut the opening. We
need to account for this leakage of gas and its effect on
cylinder pressure Pc for a real simulation. Including
these effects makes the mass flows in the valves take the
following forms based on the flow past orifices [14]:
m:in ¼
C dssAsv
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 PsucÀPcð Þ
s
q for Psuc>Pc and xs>0
ÀC dscAsv ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 PcÀPsucð Þ
cq for Pc>Psuc and xs>0
8<
:ð6Þ
m:out ¼
C ddcAdv
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 PcÀPdisð Þ
c
q for Pc>Pdis and xd>0
ÀC dddAdv
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 PdisÀPcð Þ
d
q for Pdis>Pc and xd>0
8<:
ð7Þ
Here Asv and Adv are the flow areas through which
the suction and the discharge take place from the cylin-
der respectively, and are given by 2xsrv and 2xdrv,
where xs and xd are the suction and discharge valve
displacements from the closed position.
Valve dynamics have been modelled by many authors
[14–16]. The frame of reference is from the static equili-
brium position (closed position) such that, the valves do
not have any negative displacements. A maximum dis-
placement restriction is placed so as to make the equa-
tions emulate the real system. Considering the forces
acting on the valve(s), the modelling equation for the
Fig. 1. Schematic of single cylinder reciprocating compressor.
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discharge and suction valves become, on using a single
vibration mode approximation [5]:
md
d2xd
dt2þ kdxd ¼ C fdAd Pc À Pdisð Þ þ F pd; for xd
> 0 and xd < xmax
d
ð8Þ
ms
d2xs
dt2þ ksxs ¼ C fsAs Psuc À Pcð Þ þ F ps; for xs
> 0 and xs < xmaxs ð9Þ
where F pd and F ps are pre-loads acting on the valves.
Preload accounts for the compression of the spring
valves at its closed state so as to avoid any leaks. Since
the pre-loads have a negligible effect usually, they were
neglected in the calculations. The values of C fd and C fscan be obtained from [16]. These co-efficient account for
the loss of the energy due to the orifice flow.
3. Simulation
As one can observe, Eqs. (5), (8) and (9) form a cou-
pled system of non-linear equations which need to be
solved simultaneously over one cycle time of the crank-
shaft during which the piston completes one backward
and one forward stroke. Eqs. (8) and (9) being of second
order, makes the actual number of ordinary differential
equations, (ODEs) with the introduction of two vari-
ables (x:s and x
:d), to be solved as five. The aim of this
work is to obtain the steady-state variation of these
variables for a given mechanical configuration (the size
of the cylinder, operating frequency !, volume of the
plenums, mass, diameter of the valve openings, spring
constant of the suction and the discharge valves) of the
compressor, operating conditions and the properties of
the fluid used (Pconstsuc ; Pconstdis , s). This is achieved using
a computationally efficient technique (Warner’s algo-
rithm [13]) for solving boundary value problems (BVP).
In this method the initial value problem is converted to
a two-point BVP with periodic boundary conditions.
The steady state solution is characterized by the follow-
ing boundary conditions:
Pc t ¼ t0ð Þ ¼ Pc t ¼ t0 þ ð Þ
xs t ¼ t0ð Þ ¼ xs t ¼ t0 þ ð Þ
xd t ¼ t0ð Þ ¼ xd t ¼ t0 þ ð Þ
x:s t ¼ t0ð Þ ¼ x
:s t ¼ t0 þ ð Þ
x:d t ¼ t0ð Þ ¼ x
:d t ¼ t0 þ ð Þ
9>>>>=>>>>;
ð10Þ
where is the time period for one crankshaft rotation.
Calculations are triggered with some initial conditions
at t=0 for the five variables involved. The above system
of Eqs. (5), (8) and (9) are integrated for one period of
rotation of the crankshaft using the Runge–Kutta
method of order 7. After time t= we get a set of 5
values corresponding to the final state. If the initial
conditions correspond to the steady-state, all the five
variables involved will have the same value at t= as at
t=0. Usually this will not happen and the value
obtained at is taken as the initial conditions for the
next iteration. In the conventional method, the abovesteps are repeated until the steady state is reached.
The origin of time is when the piston is at the top
most position. Because we operate the compressor
between Psuc and Pdis, which may differ by a very high
magnitude, we can expect that both the suction and the
discharge valves not to be open simultaneously. We
assume that at the beginning of the cycle, xs(t=0)=0
and x:s(t=0)=0. This brings down the number of
steady-state initial unknown values to three. (xd (t=0),
x:d(t=0) and Pc(t=0)).
4. The Warner’s algorithm
This algorithm gives the initial values for the next
iteration using n+1 sets of guesses and the miss-dis-
tances where n is the number of variables, by solving a
matrix equation which reads as:
xT 0ð Þ ¼ bT
1; qT x1 0ð ÞÀ Á
1; qT x2 0ð ÞÀ Á
:
::
1; qT xn 0ð Þð Þ
26666664
37777775
À1x1 0ð Þ
È ÉT
x2 0ð ÞÈ ÉT
:
::
xnþ1 0ð ÞÈ ÉT
266
666664
377
777775ð11Þ
where xn(0) represents the nth guess of initial conditions
matrix for the next iteration, b is the n+1 dimensional
column vector, bT ={1,0, . . .,0}. q(xn(0)) is the miss-dis-
tances vector for the nth guess vector of the initial
values. Since the solution is periodic the vector q is given
by, q(xn(0))=xn( )-xn(0).
The number of variables being three, simulations are
carried out for four different sets of initial guess values
and the miss-distances are calculated. Through theWarner’s algorithm, the initial value vector for the next
iteration is calculated and the corresponding vector q is
obtained. The error for each set is:
ek ¼ qT xk 0ð ÞÀ Á
q xk 0ð ÞÀ Á
; k ¼ 1; 2; . . . ; n þ 1: ð12Þ
The set having the maximum error (ek) is replaced
with the new set found from the algorithm. The
iterations are carried out until the ek for the newly
guessed values becomes less the tolerance specified for
convergence.
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5. Effect of plenum volumes
The finiteness in the volume of the suction and dis-
charge plenums affects the Psuc and Pdis as seen by the
cylinder, due to non-linear mass flow. As the mass flow
occurs, the plenum pressure just above the valves fluc-
tuates. These variations are propagated to the other sideof the plenum at the speed of sound and are called the
acoustic back pressure effect. This problem has been
addressed adequately by workers on acoustics. The
pressures keep varying throughout the piston cycle time.
Therefore, steady-state also requires these variations in
the plenum pressures to repeat themselves after every
cycle. The variations depends on the mass flow rate
variations throughout the cycle time. These pulsations
can be modelled in two ways, using finite element ana-
lysis of the plenum volumes, or using the plane wave
acoustic theory [17] to obtain the impedance assuming
an anechoic termination. The latter method has beenapplied extensively by Soedel et al. [4,18]. Soedel and
Singh [18] characterized the coupling between com-
pressors in a multi-cylinder case by defining transfer
impedances in a distributed parameter model. Soedel
and his co-workers [19,6], used a lumped parameter
model to simulate the pulsations. Chen [20] developed a
graphical method for the calculations of the pressure
pulsations in the piping. From plane wave acoustic the-
ory the acoustic impedance at the discharge/suction
valve may be given as:
Z !ð Þ ¼P1
Q1
¼c
S 1 gc
S 1S 2coskl þ j sinkl
coskl þ j S 1S 2sinkl
ð13Þ
where P1 is the plenum pressure at the valve position
and Q1 is the volume velocity (or flow rate) exiting the
valve. A harmonic analysis of volume velocity (Q1)
yields,
Q1 ¼XM
n¼0
Bncos n À nð Þ ð14Þ
Substituting the above expression into Eq. (13), one
gets the plenum pressure at the valves (P1) as:
P1 ð Þ À Pfixed þXM
n¼1
BnZ n!cð Þcos n À n þ n!cð Þ½ �
ð15Þ
The above equations are applicable for both the suc-
tion and discharge plenums. The acoustic back pressure
is included in the simulation by assuming initially that
the plenum pressures do not change with time. The
steady-state initial conditions for the system variables
are calculated using Warner’s algorithm for a given ple-
num pressure variation. From the mass-flow rate varia-
tions at the calculated steady-state conditions, the
Fourier coefficients (Bn and n) are calculated. Using
these coefficients the plenum pressure (for both suction
and discharge) variations are calculated using Eq. (15).
Now, the new steady state condition is calculated withthe new plenum pressure variations. The above proce-
dure is repeated until the variations converge to the tol-
erance provided. The computational procedure followed
is shown in Fig. 2.
6. Results and discussions
6.1. System considered
The considered compressor system had the following
specifications:
!c ¼ 314 rad=s rs ¼ 10:75 mm
md ¼ ms ¼ 0:0162 kg n ¼ 1:12
ks ¼ kd ¼ 3:64754 N=mm stroke ¼ 45:97 mm
rd ¼ 15:75 mm
s ¼ 5:6 kg=m3
bore ¼ 66:68 mm
The suction and discharge plenums have the follow-
ing specifications: Anechoic pipe diameter=15 mm;
Plenum diameter=150 mm; Velocity of sound(c)=150
m/s; Length of the plenum (l)=70 mm.
The numerical simulation was performed with 500
time steps over one cycle of piston motion. Validation is
done by calculating independently the total mass flow
per cycle through the suction and discharge valve from
mass flow rate data. Excellent agreement is obtained as
shown in the Table 1.
6.2. Degree of convergence
The convergence of the given compressor calculations
using Warner’s algorithm is shown in Fig. 3. The error
involved with each new prediction is brought down expo-nentially which showcases the effectiveness in the use of
Warner’s algorithm in such boundary value problems.
Even with the worst guesses (amounting to an error of the
order of 108%), the algorithm assures convergence as
early as in the sixth iteration for a tolerance of 10À6.
Table 2 compares the number of iterations required by
the conventional ‘shooting methods’, and the ‘Warner’s
algorithm’ for various pressure ratios. Given in brackets
is the time taken (in seconds) for convergence of itera-
tions. For almost all the cases, Warner’s algorithm dis-
plays good convergence. It can be observed that the
number of iterations required increases as the pressure
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ratio decreases. The figures correspond to the number of
iterations to obtain the steady-state solutions, given the
suction and discharge plenum pulsations.
6.3. Parameter studies
In order to discuss the various phases that a com-
pressor undergoes during its steady-state, let us take the
case of an operating pressure ratio of 1:5. The steady-
state cylinder pressure variation is shown in the Fig. 4.
We note that the initial cylinder pressure is almost equal
to the discharge pressure. We can expect this, because
the volume variation is taken such that the slope of the
profile gradually approaches zero at the t= . Therefore,
there is not much compression that takes place in the
last part of t= . The compressed gas has enough time
to be vented out through the discharge valve.
As the piston moves from its top position, Pc follows
the perfect polytropic gas law as the mass content is
constant. One could note that Pc comes down with a
high slope, corresponding to the high rate of volume
variation. Once Pc<Psuc, the suction valve opens. With
the slope of Pc being high, the suction valve opens up
with a high velocity, thus making the compressor
experience a high mass flow rate (Fig. 5). The initial rate
of increase of xs in Fig. 5 indicates this. As Pc increases
the driving force for the suction flow reduces. Thus the
valve starts closing even though there is some driving
force for the flow to take place because of the potential
energy of the compressed spring. Consequently, this
decreases the flow into the cylinder. The valve does not
shut fully as can be clearly seen from the suction valve
velocity profile in Fig. 6. During this closing phase of
the valve, there exists no back flow. The volume of the
cylinder still increasing, the pressure of the cylinder falls.
Again the valve opens and allows the flow to take place.
This occurs when t is approximately 2. This time the
valve closure is accompanied with some leakage.
Table 1
Validation of mass flow calculations, integrated over one cycle,
from simulation (in kg)
Pressure ratio Suction flow Discharge flow % Error
1:2 23.3115 22.9669 1.478
1:4 11.2715 11.1632 0.961
1:5 16.1335 15.3992 4.55
1:6 11.7862 11.1897 5.06
1:7 8.9069 8.7477 1.786
1:9 4.6304 4.6438 0.289
Fig. 3. Convergence rate of iterations using proposed technique.
Fig. 2. The flowchart for the algorithm.
Table 2
Comparison of computational effort between conventional and
proposed simulation methods. Shown is the number of itera-
tions for convergence with time taken in seconds in parenthesis
Pressure ratio Conventional method Warner’s method
1:2 Diverges 12 (5)
1:4 54 (10) 10 (4)
1:5 30 (7) 7 (3)
1:6 20 (5) 5 (2)
1:8 12 (4) 5 (2)
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Then the system undergoes a pure compression phase.
The discharge valve opens up, once a favorable pressure
drop is created. The rate at which the compression
occurs being very high, the discharge valve opens up
with a jerk allowing the gas to go out at a high rate (see
Fig. 7). This jerk almost brings down the Pc to Pdis
leading to the oscillation in the Pc profile. The jerk givesthe discharge valve a great displacement as shown in
Fig. 7. Once the mass gets vented out, the spring
restoring force starts to close the valve, even though
there exists a favorable pressure drop. It takes some
time for the pressure difference to decelerate the high
valve velocity, and make it turn its direction as seen in
Fig. 6. Meantime, the pressure builds up and again the
valve sees a jerk. This continues until t= . This flutter-
ing of the discharge valve is more prominent for the low
pressure ratio cases. The velocity profile clearly depicts
this phenomena.
The steady-state values of several parameters, such as
peak pressure reached in the cylinder, the net amount of
air being compressed in the cylinder including the losses
due to back-flow and the back-pressure, were found to
depend heavily on the operating pressure ratio. For the
simulation, the average discharge pressure was kept
constant at 2.826 MPa and the suction pressure waschanged.
6.3.1. The maximum and minimum pressure reached
The steady-state cylinder pressure profiles for various
operating ratios are shown in Fig. 8. It can be observed
that the magnitude of the peak value decreases as the
pressure ratio increases. The low pressure ratio case
exhibits a higher value of peak pressure because of the
higher amount of the gas being compressed in each
cycle. Also, the position at which the peak value occurs
moves towards the minimum volume position and the
Fig. 5. Suction valve motion and flow rate into the cylinder for
a pressure ratio 1:5.
Fig. 6. Suction and discharge valve velocity for a pressure ratio
of 1:5.Fig. 4. Variation of cylinder pressure for a pressure ratio of 1:5.
Fig. 7. Discharge valve motion and flow rate out of the cylin-
der for a pressure ratio of 1:5.
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steady state initial pressure of the cylinder decreases, as
the ratio increases.
6.3.2. Motion and mass flow rates of valves
6.3.2.1. The discharge valve. The mass flow rate past the
discharge valve at steady-state for two operating pres-
sure ratios, as simulated by the application of Warner’salgorithm is shown in Fig. 9. It can be seen that the
valve flutters more for the lower pressure ratio, due to
high flow rates. As the pressure ratio increases, the
amount of time for which the valve is open decreases.
6.3.2.2. The suction valve. Mass flow rates m:s for two
operating pressure ratios are shown in Fig. 10. The
conspicuous peaks observed can be attributed to the
presence of local maxima in the pressure profile. The
valve is being accelerated as it closes and the duration
over which the valve is open increases as the pressure
ratio increases.
The valve displacement follows the mass flow rate
trend for both suction and discharge valves.
The configuration of the suction and discharge ple-
nums volumes were found to play an important role in
the steady-state working of a compressor. The deviation
associated with not including the finiteness in the plenum
volumes and the associated pressure pulsations in thesimulation is shown in Fig. 11. Percentage deviation in
Fig. 11 is calculated as:
Deviation ¼Pwithp:vc À Pwithoutc
Pwithpvc
ð16Þ
Not including the effect of the finite volume of the
plenums can give an error of almost 4% for lower pres-
sure ratios, although only around 0.2% error is
observed for higher pressure ratios. In the discharge
plenum, frequency corresponding to the 12th harmonic
Fig. 9. Mass flow through discharge valve for pressure ratios
of 1:2 and 1:7.
Fig. 8. Pc for different pressure ratios.
Fig. 10. Mass flow through suction valve for pressure ratios of
1:2 and 1:7.
Fig. 11. Percentage deviation in cylinder pressure calculation
on neglecting the acoustic back pressure effect.
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of the working frequency of the compressor (!c) is
observed to be prominent (see Fig. 12). This is found tobe the same for all pressure ratios. The resonating fre-
quency is found to be only dependent on the configura-
tion of the plenums. Also shown in the same figure, the
suction plenum pressure pulsations about their mean
values. The dominant frequency of the fluctuations is
observed to be the second harmonic of !c.
7. Conclusions
Major parameters that affect a compressor system
were identified and modelled accordingly. The coupled
set of non-linear equation is solved at steady state using
Warner’s algorithm. This was demonstrated to be com-
putationally more efficient as compared to the conven-
tional modelling and simulation techniques. Performance
of the suggested approach was demonstrated by compar-
ing the number of iterations and time for convergence.
Drastic reduction could be observed in the number of
iterations. Steady state predictions were carried out for
various values of the ratios of operating pressures.
Future work will focus on extending the analysis to
multi-cylinder compressors system and including heat
effects.
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