generic network modeling of reciprocating compressors
TRANSCRIPT
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i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9
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Generic network modeling of reciprocatingcompressors
Jian Hu a,b, Liang Yang a, Liang-Liang Shao a, Chun-Lu Zhang a,*
a School of Mechanical Engineering, Tongji University, Shanghai 201804, Chinab China R&D Center, Carrier Corporation, No.3239 Shen Jiang Road, Shanghai 201206, China
a r t i c l e i n f o
Article history:
Received 24 March 2014
Received in revised form
8 June 2014
Accepted 10 June 2014
Available online 16 June 2014
Keywords:
Reciprocating compressor
Model
CO2
R410A
* Corresponding author. Tel.: þ86 136 71825E-mail address: [email protected]
http://dx.doi.org/10.1016/j.ijrefrig.2014.06.0070140-7007/© 2014 Elsevier Ltd and IIR. All rig
a b s t r a c t
With the increasing applications of CO2 trans-critical cycles, the design of reciprocating
compressors returns to the center stage. Quick design and optimization of a compressor
with arbitrary configuration is always a big challenge. This paper presents a new generic
modeling approach to reciprocating compressors design. The reciprocating compressors
were firstly torn down to components, e.g. compression chamber, valve, shaft, motor,
crankcase, etc. Then the component models were developed to feature the sub-processes
inside the components. Refrigerant flow, heat flow, power flow, and air flow (for inter-
mediate cooler) between components were described on a network basis. Finally, the
object-oriented programming method was applied to develop a graphical user interface for
generic drag-and-drop modeling of reciprocating compressors with arbitrary configuration.
Experimental data of a CO2 two-stage compressor and a R410A single-stage compressor
were used to validate the generic modeling tool. The deviations in the mass flow rate and
power consumption of R410A compressor are mostly within ±3% and ±5%, respectively,
while the deviations in the mass flow rate and power consumption of CO2 compressor are
mostly within ±8% and ±5%, respectively.
© 2014 Elsevier Ltd and IIR. All rights reserved.
Mod�elisation par r�eseau g�en�erique de compresseurs �a piston
Mots cl�es : Compresseur �a piston ; Mod�ele ; CO2 ; R410A
1. Introduction
Reciprocating compressors are widely used in various
refrigerating units covering a large range of capacity.
Due to relatively lower volumetric efficiency and larger
dimension, reciprocating compressor is nowadays replaced
133.(C.-L. Zhang).
hts reserved.
by rotary compressors (e.g. rolling-piston, scroll, screw
compressors) in most applications. However, with the
increasing applications of carbon dioxide (CO2) trans-
critical cycles (Austin and Sumathy, 2011; Bansal, 2012;
Pearson, 2005), reciprocating compressor is returning to
the center stage because of its advantages in high pressure
Nomenclature
a acceleration, m s�2
A area, m2
C flow coefficient
d diameter, m
F force between two solid bodies, N
Fd force acting on the discharge valve, N
Fs force acting on the suction valve, N
Fi inertial force of piston, N
Fp pressure force on the piston, N
Frod total force acting on the rod, N
g gravity acceleration, m s�2
h enthalpy, J kg�1
k spring factor of the suction valve
m mass flow rate, kg s�1
p pressure, Pa
pc pressure in the crank chamber, Pa
pd discharge pressure, Pa
Pinput input power, W
Fb,x Bearing force along x direction, N
Fb,y Bearing force along y direction, N
Q heat flow, W
S valve displacement, m
t time
T temperature, K
V volume, m3
X unknown variable set
vs suction valve velocity, m s�1
vd discharge valve velocity, m s�1
M Mass kg
Greek symbols
ε convergence tolerance
h efficiency
r density, kg m�3
t time, s
G torque, N m
q crank angle
k Specific heat ratio
Subscripts
i inflow
I inertial
o outflow
d discharge
s suction
l leakage
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9108
operation and good efficiency when running at lower
pressure ratio.
To well design reciprocating compressor, numerical
simulation has become a powerful approach and different
simulation models are found in the literature. Some CFD
simulations have been carried out for the compressor com-
ponents (e.g. mufflers and valves) (Nakano and Kinjo, 2008;
Pereira et al., 2008b) and the whole compressor (Birari et al.,
2006). Despite of the recent advances in numerical method-
ologies, the computational cost of a full three-dimensional
simulation of a reciprocating compressor is still impracti-
cable for optimization purposes (Pereira et al., 2008a). There-
fore, simpler methodologies which can offer satisfactory
results for a preliminary design are still very important and
worth further development. P�erez-Segarra et al. (2003) and
Rigola et al. (2003) developed a detailed numerical model of
the thermal and fluid dynamic behavior of small reciprocating
compressors which are commonly used in household re-
frigerators and freezers. Later, to simplify the process on
compressor performance evaluation, they developed a
detailed model for the thermodynamic efficiencies to charac-
terize the hermetic reciprocating compressors (P�erez-Segarra
et al., 2005). They focused on the volumetric efficiency, isen-
tropic efficiency and combined mechanical-electrical effi-
ciency and detached them into several partial efficiencies so as
to denote effects of different physical sub-processes. More
recently, they presented a more generic object-oriented un-
structured modular modeling methodology of reciprocating
compressors (Damle et al., 2011). The new approach offers
advantages of handling complex circuitry (e.g. parallel paths,
multiple compressor chambers, etc.), coupling different
simulation models for each element and adaptability to
different configurations without changing the source code.
Yang et al. (2013) found there was no comprehensive models
for CO2 reciprocating compressors in the literature. They
therefore presented a comprehensive model to predict the CO2
reciprocating compressor performance, which included both
the frictional losses at piston ring-cylinder liner interface and
at the journal bearings. For more information, state-of-the-art
reviews of numerical methodologies applied to reciprocating
compressors weremade available by Rasmussen and Jakobsen
(2000) and Ribas et al. (2008).
Most of the compressor models mentioned above can only
cover a specific compressor or a series of compressors with
fixed or similar configuration. In addition, the programming
methods used were typically the ‘functional-programming’
approach which is of poor extension ability. Therefore, quick
design and optimization of a compressor with arbitrary
configuration is still a big challenge for both modeling and
implementation methods.
Different from the existing ones, we apply a generic
network based modeling methodology with the object-
oriented programming method to carry out a graphical drag-
and-drop modeling and simulation platform for recipro-
cating compressor design. The network model involves
refrigerant flow, heat flow, power flow, and air flow between
compressor components. Different configurations and com-
plex circuitry of reciprocating compressors can be handled by
an easy-of-use graphical drag-and-drop style. At last, the
method is validated with different compressors.
2. Reciprocating compressor model
Fig. 1 is the typical schematic of a reciprocating compressor.
Generally, the reciprocating compressor consists of a set
of components. The low pressure refrigerant vapor from
the evaporator enters the crankcase and is heated by the
Valve Stop
Valve Spring
Valve Seaty
Discharge OpeningP
y
Fig. 2 e Schematic of the discharge valve model (single
degree of freedom system).
Fig. 1 e Schematic of reciprocating compressor.
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9 109
motor and the wall of shell. After that, it goes across the suc-
tion stub to the cylinder where it is compressed by the piston
and the pressure is lifted. Some part of the refrigerant mass will
be leaked back to the crankcase during the whole compression
process. At last, the high-pressure gas is discharged from the
cylinder to the discharge plenum, namely the cylinder header
and go through the manifold towards the condenser.
2.1. Component models
To simulate the compressor in a generic way, we propose a
network modeling approach. Firstly we divide the whole
compressor system into individual component parts. Then the
components can be connected with each other through
differentmass and energy flows, e.g. refrigerant flow, heat flow,
and power flow. Inside each component model, fundamental
governing equations (e.g. conservation equations) and empir-
ical correlations (e.g. correlations for heat transfer coefficients)
are applied to describe the different physical sub-processes.
The major components in our compressor component li-
brary are described as follows.
2.1.1. Compression chamber and valveThe model calculates the pressure, temperature and volume
as a function of the crank angle for an entire revolution. The
RungeeKutta fourtheorder method is applied to calculate the
mass flow rate and discharge temperature of the refrigerant
and power consumption.
For the compression process inside cylinder, we have
Specific volume of refrigerant gas inside cylinder:
vc ¼ Vc
mc(1)
The volume inside the cylinder:
Vc ¼ Apxþ V0 (2)
where Vc is the cylinder clearance volume.
Considering the changes with respect to time, we have
dmc
dt¼ dms
dt� dmd
dt� dml
dt(3)
dvc
dt¼ 1
mc
dVc
dt� Vc
mc2
dmc
dt(4)
Substituting Equation (2) into Equation (4) yields
dvc
dt¼ Ap
mc
dxdt
� Apxþ V0
m2c
dmc
dt(5)
The gas temperature inside the cylinder can be calcu-
lated as
dTc
dt¼ dQ
mcvdt� ZRT
cvV� dVc
dt(6)
where dQdt is the heat transfer rate between the gas and cylinder
wall, Z is the compression factor and dVcdt is the cylinder volume
change rate.
Upon Equations (3) and (6), the refrigerant mass and tem-
perature inside the cylinder can be calculated. Therefore the
corresponding pressure can be obtained.
2.1.2. Valve modelA simple valve model for the flow through the discharge or
suction port is developed. A schematic of the model is shown
in Fig. 2. The valve is modeled with single degree of freedom
object. For brevity, we only take the discharge valve as an
example. If the pressure in the discharge plenum is larger
than the discharge pressure, the valve opens. Otherwise it will
close. The distance y, which is the valve open distance, is
calculated by the function
y ¼ �p� pd
�d2
4p1k
(7)
where d is the diameter of discharge port, p is the pressure
in the discharge plenum and k is the spring constant of the
valve. Apparently, the maximum distance that the valve can
reach is determined by the valve stop. The flow area is then
calculated by
Ad ¼ yp (8)
The mass flow rate through the discharge valve is deter-
mined using the equation for isentropic compression flow
(Fox and McDonald, 1992).
dmd
dt¼ CflowAdp
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2k
ðk� 1ÞRT
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�pd
p
�2k
��pd
p
�kþ1k
s(9)
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9110
where Ad is the area of the suction plenum opening. k is the
specific heat ratio. Cflow is the correction factor, which is 0.58
and 0.6 for suction and discharge process, respectively.
2.1.3. Leakage modelThe gas leakage through the piston ring gap is modeled as an
isentropic, compressible fluid flowing through an orifice. The
mass flow rate can be determined as follows (Span, 1996).
dml
dt¼ CflowAgappu
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2k
ZRTuðk� 1Þ
2664�pd
pu
�2k
��pd
pu
�kþ1k
3775
vuuuuut ;pd
pu>0:54
(10)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi26� �kþ1
k�1
37
vuuu
dmldt¼ CflowAgappu
k
ZRTu
64 2kþ 1
75uut ;pd
pu<0:54 choked (11)
where the discharge coefficient Cflow is assumed to be 0.86
(Span, 1996) and the compressible factor Z is calculated by the
equation of state (Span, 1996; Stachowiak and Batchelor, 2001).
2.1.4. CrankshaftThis model calculates the torque and bearing load, the con-
tacting force for any schematic of reciprocating compressor
with arbitrary cylinder configuration. In each time step, it uses
the pressure data from the cylinder chamber to calculate the
mechanical parameters, such as the acceleration of the piston,
the torque load on themain bearing andmotor end bearing. The
results will be further used for the bearing component.
2.1.5. Physical shaft loss systemIn order to determine the exact power consumption of a
reciprocating compressor, various losses in the compressor
need to be considered.
Firstly, a local coordinate is built on each cylinder as shown in
Fig. 3. The force on the cylinder, which is denoted as F, is divided
into two parts, the inertia force and the gas pressure force.
F ¼ Fp þ FI (12)
where,
Fp ¼ �pc � pb
�p4D2 (13)
Suction and compressionprocess
F
φ
A
Fp
Fig. 3 e Schematic of c
FP is the pressure force on the piston (N), pc is the cylinder gas
pressure (Pa), pb is the pressure (Pa) in the crankcase.
The acceleration can be calculated using the following
equation (Lin and Sun, 1987):
a ¼ ru2
26664cos qþ l cos 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1� l2 sin2q
p þ 1
4
l3 sin22q�1� l2 sin2
q�32
37775 (14)
To simplify the calculation, the following equation is used
to calculate the acceleration.a ¼ ru2ðcos qþ l cos 2 qÞ (15)
The total force acting on the rod
Frod ¼ F
�cos 4 ¼ F
1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� l2 sin2
qp (16)
This force will cause a torque on the crankshaft system
Τ ¼ Frodr sinðqþ 4Þ ¼ Frsinðqþ 4Þ=cos 4 (17)
Then the force acting on the crank bearing is also divided
into two orthogonal directions.
X direction : Fcb;x ¼ Fp
cos bcos b ¼ FP (18)
Y direction : Fcb;y ¼ Fp
cos bsin b ¼ FP tan b (19)
Here we have gotten the force and torque acting on each
single crankshaft system. To get the force acting on the main
bearing and pump end bearing on the whole crankshaft sys-
tem, a four cylinder example of which is displayed in Fig. 4.
We need to convert the local coordinate to the global coordi-
nate. The force analysis method is the same, but the crank
angle needed to be converted based on the following equation:
qi ¼ qþ 4i þ fi (20)
Here q is the crank angle, while 4i is the bank angle be-
tween the ith cylinder to the 1st cylinder, and fi is the shaft
angle between the ith cylinder to the 1st cylinder.
At each direction, we have
XFcb;x þ Fmb;x þ Fpb;x ¼ 0 (21)
θ
B
rankshaft system.
X
12
3
4
Y
1 2
3 4ω
PUMP END BEARING
X1
Y1
a
a
0
0MAIN BEARING
L
E1
E2
E3
E4
Fig. 4 e Schematic of crankshaft system built on the global coordinate.
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9 111
XFcb;y þ Fmb;y þ Fpb;y ¼ 0 (22)
XGshaft;xi ¼ Fmb;xL (23)
XGshaft;yi ¼ Fmb;yL (24)
For thewhole crankshaft system, the torque generated from
the force acting on each of crank bearing can be calculated as:
Gshaft;xi ¼ Fcb;xEi (25)
Gshaft;yi ¼ Fcb;yEi (26)
where Ei is the distance from ith cylinder to the pump end
bearing as shown in Fig. 4
Substituting Equations (25) and (26) into (23) and (24),
we get
Fmb;x ¼ Xn
i¼1
EiFcb;x
!,L (27)
Fmb;y ¼ Xn
i¼1
EiFcb;y
!,L (28)
Now we have four Equations (21), (22), (27) and (28) with
four unknown parameters, namely the force acting on the
main bearing,Fmb, which is divided into Fmb;x, Fmb;y, and force
acting on the pump end bearing, Fpb;x, Fpb;y, therefore the
equations can be solved. Then we use a regression method
to predict the frictional power losses at the crankshaft
bearing and the crank journal bearing (Stachowiak and
Batchelor, 2001).
Pbearing ¼ 3:9307$103$v�0:7061;oil $v1:577
2;oil $L0:477bearing$D
2:240journal$N
1:278j
$c�0:249$T�0:204sup
�1þ ln W*
�1:324(29)
where v1;oil , v2;oil are the kinematic viscosities of the oil at
37.8 �C and 93.3 �C, respectively. The dimensionless load ca-
pacity is calculated by
W* ¼ Wtc2
mUcirLbearingR2journal
(30)
Meanwhile the total force can be calculated by
Wt ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiF2x þ F2
y þ F2y
q(31)
After we finish calculating the force on each cylinder, some
conversion work from the local coordinate to the global co-
ordinate is still needed. The global coordinate is built on the
whole crankshaft system, as shown in Fig. 4. After these two
conversion steps are done, we can calculate the torque for
each cylinder. There are two unknowns, the force acting on
main bearing and the pump end bearing, meanwhile we
have two Equations (27) and (28) to solve them. The results
will be further used to calculate the shaft efficiency using
equation (32).
The power loss on the shaft can be calculated with a motor
performance correlation as follows.
hmechanical ¼Wcompression
Wshaft¼ f�Gshaft
�(32)
Here hmechanical is the mechanical efficiency and Wcompression
is the compression work rate. A correlation fðGshaftÞ can be
curve-fitted from experimental data to calculate the shaft
efficiency.
2.1.6. MotorThis component model calculates the motor performance
based on the motor efficiency curve. The shaft work of
compressor can be therefore determined by
Wshaft ¼ hmotorP (33)
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9112
where the P is the overall power input to the motor or
compressor. The motor efficiency, hmotor can be assumed to be
95% or specified in terms of engineering best practice.
To sum up, with themotor-mechanical efficiency and the
calculated compression power, the overall motor con-
sumption can be calculated. Meanwhile, the isentropic ef-
ficiency of the compression process can be figured out
as well.
ho;is ¼mðh2s � h1Þ
Pinput(34)
where h1 is the enthalpy at the suction state 1while h2s is the one
at the discharge state 2 assuming the refrigerant is experiencing
an isentropic process when compressed from state 1 to state 2.
2.1.7. CrankcaseThis model computes the heat transfer effect to the suction
fluid based on the following parameters: the fraction of motor
and bearing power losses added as heat, the area and coeffi-
cient for heat transfer from ambient to the suction fluid.
Energy equation:
hcyl;suc ¼ ðmtube;suchtube;suc þmlhlÞ�ðmsuc;tube þmlÞ (35)
Momentum equation
psuc;out ¼ psuc;tube (36)
Continuity equation
msuc;cyl ¼ msuc;tube þml (37)
+ReadFluidNode()+FindVar()+AddVar()+DeleteVar()
-IDPort
+GetParaName()+GetParaValue()
-ParaName-ParaValue
Thermal Parameter
+ReadVarList()+WriteVarList()+FindVar()
Thermal ParameterList
+ReadArray()+WriteArray()+SetNodeInfo()+GetNodeInfo()+SetVarValue()+AddNode()+GetVar()
Port Network
Fig. 5 e Structure of the
Here, m1;tube is the mass flow rate from the suction tube
entering the crankcase, ml is the mass flow rate leakage from
cylinder to the crankcase during the compression process,
msuc;cyl is the mass flow rate entering the cylinder.
It should be noted that all these force and moment bal-
ances are assumed under quasi-static conditions, namely
keeping static balances at each time step of the crank angle.
2.2. Compressor network model
As wementioned previously, component models solve the indi-
vidualphysicalsub-processes insidethecomponents.Todevelop
a generic modeling platform for reciprocating compressors, we
should know how to generally describe the connections among
components in an arbitrary reciprocating compressor system.
Between the components, there are different “flows”: refrigerant
mass flow, power flow or power transmission, heat flow or
heat transfer, and air flow (taking place mainly in intermediate
cooler). A generic networkmodel is therefore proposed.
2.2.1. Port and networkThe port is used to represent the inlet or outlet of a component
and the key performance parameters are defined on vertices
of the network. Typically, the vertices are categorized into
four types of port as shown in Fig. 5 in terms of the physical
principles. Port is an abstract class and inherited by the
refrigerant, air, heat andmechanical ports. Each type of port is
a set of thermal parameters regarding the refrigerant, air, heat
and mechanical parts, respectively. Then each type of port
Refrigerant Port
Air Port
Heat Port
Mechanical Port
Mechanical Network
Refrigerant Network
Air Network
Heat Network
port and network.
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9 113
will constitute a network describing a complete process
occurring inside compressor.
Each type of port has its attribute parameters, such as
the mass flow rate, enthalpy and pressure on the refrigerant
type vertex, the shaft speed and power on the mechanical ver-
tex, and the air temperature and relative humidity on the air
vertex. As long as the unknown parameters on the node are
solved, the compressor systemperformance can be determined.
2.2.2. Refrigerant portThis type of port is defined to represents refrigerant entering
or leaving state of the component model. In each refrigerant
port, themass flow rate, pressure, and enthalpy are defined as
the independent variables so that the refrigerant state can be
determined. Then the set of refrigerant ports, which we call
the refrigerant linked list, can be used to determine the
refrigerant flow from the suction stub to the discharge cylin-
der head.
2.2.3. Mechanical portThis type of port is designed for the calculation of the me-
chanical friction losses and shaft load torque. A set of me-
chanical ports constitute a mechanical linked list so that
the shaft power transfer path can be represented and calculated.
2.2.4. Heat portThis type of port is defined to determine the surface temper-
ature of a component and heat flow rate between this specific
component and the attached refrigerant. With a set of heat
ports, a thermal network will be established to determine the
temperatures as well as the heat flow rates between compo-
nent and refrigerant.
2.2.5. Air portIn the multiple-stage compressor, sometimes the air convec-
tionmethod is applied to cool the cylinder in the intermediate
stage so as to decrease the discharge temperature and
improve efficiency. Therefore air ports are designed to repre-
sent the air state entering or leaving the cylinder. In the
TCylinder
TMotor
TShaft
TCrank_case
TAmbient
TGas
Rgas_Shaft
Rgas_crankcase
Fig. 6 e Equivalent electrical circuit for th
end, the air port linked list is able to represent the whole air
cooling process.
In order to determine the heat transfer effect from the
compressor internal elements (e.g. bearing and motor), to the
suction state of the refrigerant before compression, we need
to know the temperature of each element and the whole
temperature distribution inside the compressor. For simplicity,
the compressor is divided into the following lumped element:
the cylinder, crankcase, shaft (including the bearing) and the
ambient. Then the temperature heat network inside the
compressor is established as shown in Fig. 6.
For each of the lumped element, an energy balance of
the form
0 ¼ Qin � Qout � Qgen (38)
can be established, where Qin and Qout are the heat flow into
and out of the element, respectively.Qgen is the heat generated
inside the compressor component, for instance, the heat
generated due to the friction loss. The application of Equation
(38) to the components are as follows.
Tcylinder :Tcyl � Tgas
Rgas cylþ Qloss ¼ 0 (39)
Tmotor :Tgas � Tmotor
Rgas motorþ Qmotor ¼ 0 (40)
Tshaft :Tgas � Tshaft
Rgas_shaftþ Qfriction_loss ¼ 0 (41)
Tcrankcase :Tgas � Tcrankcase
Rgas_ccþ Tambinet � Tcrankcase
Rambinet¼ 0 (42)
Tgas : msuc;pipeðhsuc � hinÞ ¼ Qloss þ Qmotor þ Qfriction_loss (43)
Note that heat flow rate for each component can be ob-
tained by solving the related component model. Here we just
take cylinder for instance. It is a function of the refrigerant
temperature, shell temperature and the geometry of the
cylinder.
Rgas_CylinderRgas_Motor
Rcase_ambient
ermal resistance between elements.
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Qloss ¼ f�TgasðqÞ;Tcyl
�(44)
Now we have six Equations (39)e(44) and six unknowns
which are the temperature of cylinder, motor, shaft, crank-
case, the average temperature and enthalpy (Tcylinder, Tmotor,
Tcrankcase, Tgas, Tshaft, hgas). Therefore the problem can be
determined and numerically solved.
3. Implementation
3.1. Numerical algorithm
After compressor system network model is established, we
need to find away to solve themodel efficiently. Asmentioned
above, the conservative equations are all invoked in each
component. To improve the robustness and make it easy to
debug the model, all those equations are not solved simulta-
neously. Instead, the component models can be solved one
Fig. 7 e Global algor
after another and transfer the results to their connected
vertices. All equations on the vertices of network will be
solved simultaneously using the NewtoneRaphson method,
which provides a generic approach for modeling a recipro-
cating compressor with arbitrary configuration.
A flow chart for the entiremodel solving process is detailed
in Fig. 7.
3.2. Object-oriented Programming (OOP)
Object-oriented programming (OOP) has roots that can be
traced back to the 1960s. Researchers studied ways to main-
tain software quality and developed OOP methodology in part
to address common problems by strongly emphasizing
discrete, reusable units of programming logic (Eckel, 2002). In
OOP, each object is capable of receiving messages, processing
data and sendingmessage to other objects. ‘Methods’ on these
objects are closely associated with the object. A programming
usually consists of different types of objects, each corre-
sponding to a particular kind of complex data tomanage. Each
ithm of solver.
+Simulate()+GetRes()
Compressor Component
+Simulate()+GetRes()
Compression chamber+Simulate()+GetRes()
Valve
+Simulate()+GetRes()
Crankcase
+Simulate()+GetRes()
Motor
+Simulate()+GetRes()
Suction muffer
+Simulate()+GetRes()
Discharge Muffer
+Simulate()+GetRes()
Suction tube
+Simulate()+GetRes()
Discharge tube
+Simulate()+GetRes()
Journal Bearing
Fig. 8 e Schematic of component library structure based on OOP.
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9 115
object will have its own standardized methods for performing
particular operations on its data.
The major two features of OOP are ‘Inheritance’ and ‘Poly-
morphism’. The inheritance enables the son class to get the
data and method from its parents class so that code can be re-
used. The polymorphism enable to offer standardizedmethods
across different types of objects, provided they all derivate from
one parent class. Same code will invoke different functions. For
example, solver is able to send same ‘Simulate’ command to
each component class, and the compiler is able to invoke
different ‘Simulate’ functions according to the type of son class.
A ‘cylinder’ object will invoke the compression procedure while
the ‘valve’ invokes a ‘Fanno flow’ procedure.
The benefit of this feature is high extensibility. New
component model can be added into the existing system
without any modification to the whole solver framework, so
Fig. 9 e Compressor system schem
long as the new component implements its own ‘Simulate’
procedure. Because this new code can be invoked by the solver
without any modification, the framework is closed for modi-
fication and open for the function extensibility.
The ‘Compressor Component’ just provides a pure virtual
function ‘Simulate’ and its derived class ‘Compression cham-
ber’, ‘Valve’, ‘Motor’, ‘Crankcase’ will implement ‘Simulate’
function to provide concrete implementations. The detailed
UML class relationship is shown in Fig. 8.
In conclusion, due to the advanced feature of OOP, we
have implemented a solver structure that is open for
extension and closed for modification. Meanwhile the sys-
tem model is constructed by joining component from
the standard library. Therefore, a reciprocating compressor
platform which can handle any complex compressor
configuration is established.
atic in design tool interface.
Fig. 10 e Object-Oriented single-stage compressor system model.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9116
The generic reciprocating compressor modeling platform
is developed as a graphical drag-and-drop modeling tool with
friendly user interface, as shown in Fig. 9. In this tool, the
component models are represented as icons on the compo-
nent library panel. The user can use mouse to drag, move,
and drop different icons in the model editor window. After
connecting the icons (components) in a logical way, a
Fig. 11 e Object-Oriented two-stag
reciprocating compressor with desired configuration is then
ready for simulation.
3.3. Examples
After those four types of port vectors being established, arbi-
trary compressor configuration can be easily set up. Engineers
e compressor system model.
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9 117
are able to do a trial numerical simulation to evaluate
different design concepts. Figs 10 and 11 are two typical
compressor examples implemented according to the princi-
ples we defined above. Fig. 10 demonstrates a single-stage
reciprocating compressor, while Fig. 11 represents a two-
stage reciprocating compressor.
4. Model validation
Two compressors and their lab testing data are used for
model validation. One is a single-stage R410A compressor, the
schematic of which is shown in Fig. 10. Another is a two-stage
trans-critical CO2 compressor with an intermediate cooler
P
PressureSensor
T
TemperatureSensor
Oil Separator
CO2 compressor
Pdis Control Discharge EEV
Water chilling unit
Heater
T
Water flow m
Tret_w
Heater
1
2
7
P T
Fig. 12 e Schematic of co
between the first and second stages, the schematic of which is
shown in Fig. 11.
4.1. Compressor testing rig
A schematic of a hot gas bypass load stand is shown in Fig. 12.
At point 1, the refrigerant is suctioned into compressor,
compressed to discharge pressure and temperature at point 2.
Note that a hot gas bypass line is setup at the discharge port,
and then the refrigerant gas is divided into two streams. One
stream goes through the bypass tube and expanded to the
pressure of suction, point 5. Another stream is cooled down in
a condenser or gas cooler, then expanded through an expan-
sion valve and evaporator, finally joins the previous stream at
the suction chamber. The discharge pressure is tuned by an
Flow meter
EEV
Gas cooler
Psuc ControlBypass EEV
Water flow meter
Evaporator
eter
at control
3
6
5
5
mpressor testing rig.
500
800
1100
1400
1700
2000
500 800 1100 1400 1700 2000
Pre
dict
ed m
ass
flow
rat
e (k
g/h)
Measured mass flow rate (kg/h)
-3%
+3%
Fig. 13 e Numerical and Experiment mass flow rate
comparison of R410A compressor.
50
100
150
200
250
300
350
50 100 150 200 250 300 350
Pre
dict
ed m
ass
flow
rat
e (k
g/h)
Measured mass flow rate (kg/h)
+8%
-8%
Fig. 15 e Numerical and Experiment mass flow rate
comparison of CO2 compressor.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9118
expansion valve located at the discharge line, while the suc-
tion pressure can be adjusted by changing the opening rate of
EEV (electronic expansion valve) located at the bypass line.
The specified superheat is obtained by controlling the addi-
tional heater installed at the suction chamber.
The major testing instrumentation of the test rig is the
same for R410A and CO2. Wemade adjustment on the specific
model number of pressure transducers andmass flowmeters,
since the pressure and mass flow rate varies dramatically for
those two refrigerants. We also ensured the plastic sealed
parts are compatible for both R410A and CO2. The testing rig
utilizes thermocouples (Omega KMQSS-125G-6) and pressure
transducers (Omega PX32B1-2.5KGV for CO2 and PX32B1-
1KGV for R410A, respectively) to measure and adjust the
suction pressure, suction temperature, discharge pressure,
mass flowmeasurementswith amass flowmeter (MicroMotion
8
10
12
14
16
18
20
22
8 10 12 14 16 18 20 22
Pre
dict
ed p
ower
con
sum
ptio
n (k
W)
Measured power consumption (kW)
-5%
+5%
Fig. 14 e Numerical and Experiment power consumption
comparison R410A compressor.
DH25 for CO2 andDH100 for R410A, respectively), a volumetric
flow meter (Sponsler SP717) and electric power analyzer with
accuracies of 0.05K, 0.25%, 0.5%, 0.5% and 1% respectively.
4.2. Model validation
The comparison between the model predictions and experi-
mental data are illustrated in Figs. 13e16 . For the single-stage
R410A compressor, the deviations of mass flow rate and
power consumption between predictions and experiments are
mostly within ±3% and ±5%, respectively. For the two-stage
CO2 compressor, the deviations of mass flow rate and power
consumption between predictions and experiments are
mostly within ±8% and ±5%, respectively. The present model
3
4
5
6
7
3 4 5 6 7
Pre
dict
ed p
ower
con
sum
ptio
n (k
W)
Measured power consumption (kW)
+5%
-5%
Fig. 16 e Numerical and Experiment power consumption
comparison of CO2 compressor.
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 4 5 ( 2 0 1 4 ) 1 0 7e1 1 9 119
accuracy is very competitive in comparison with the recipro-
cating compressor models in the open literature.
However, there are still some room for improving the
model accuracy. The deviation of mass flow rate for the CO2
compressor is fairly larger than that of the R410A compressor.
One reason is that there is a discharge plenum in the R410A
compressor to decrease the pressure pulsation and the cor-
responding pressure loss effect. The CO2 compressor does
not have such design. Since the pressure pulsation is very
difficult to model, it wasn't taken into account in the simula-
tion, which introduces additional deviation in simulating the
CO2 compressor. Another reason is the assumption of isen-
tropic compression for calculating the leakage mass flow rate
for CO2 may not be very accurate.
5. Conclusions
In this paper, a new generic network model of reciprocating
compressors was developed. The whole compressor is divided
into individual components. Inside each component model,
the conservative equations were used to describe physical
sub-processes. Between components, a network model
involving refrigerant flow, power flow, heat flow, and air flow
was developed to describe the connections in a generic way so
that arbitrary configuration of reciprocating compressors can
be easily modeled. Based on the OOP method, a graphical
drag-and-drop modeling platform was developed. Same
methodology might be extended to other types of refrigerant
compressors modeling.
A single-stage R410A compressor and a two-stage trans-
critical CO2 compressor were modeled and validated with
experimental data. For the single-stage R410A compressor,
the deviations of mass flow rate and power consumption be-
tween predictions and experiments are mostly within ±3%and ±5%, respectively. For the two-stage CO2 compressor, the
deviations ofmass flow rate and power consumption between
predictions and experiments are mostly within ±8% and ±5%,
respectively.
Acknowledgments
This work is partially supported by the National Natural Sci-
ence Foundation of China (Grant No. 51206123) and the
Innovation Program of Shanghai Municipal Education Com-
mission (Grant No. 11ZZ30).
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