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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

www.elsevier.com/locate/ijrefrig

* Corresponding author. Tel./fax: +44-235-0509.

E-mail address: [email protected] (C. Padmanabhan).



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

1084 M.N. Srinivas, C. Padmanabhan/ International Journal of Refrigeration 25 (2002) 1083–1092



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.

M.N. Srinivas, C. Padmanabhan/ International Journal of Refrigeration 25 (2002) 1083–1092 1085



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.




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




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)




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.




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.




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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