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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

Available o

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journal homepage: www.elsevier .com/locate/ i j refr ig

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: chunlu.zhang@gmail.com

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

dml

dt¼ 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.

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 9114

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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