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TitleReciprocating Compressor Program
TagsGas Compressor Cylinder (Engine) Piston Engines
File Size245.0 KB
Total Pages9
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                            Purdue University
Purdue e-Pubs
Reciprocating Compressor Program
	Christophe Ancel
	Pierre Ginies
                        
Document Text Contents
Page 1

Purdue University
Purdue e-Pubs
International Compressor Engineering
Conference

School of Mechanical Engineering

2008

Reciprocating Compressor Program
Christophe Ancel
Danfoss CC

Pierre Ginies
Danfoss CC

This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for
additional information.
Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/
Herrick/Events/orderlit.html

Ancel, Christophe and Ginies, Pierre, "Reciprocating Compressor Program" (2008). International Compressor Engineering Conference.
Paper 1912.
http://docs.lib.purdue.edu/icec/1912

http://docs.lib.purdue.edu
http://docs.lib.purdue.edu/icec
http://docs.lib.purdue.edu/icec

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International Compressor Engineering Conference at Purdue, July 14-17, 2008

RECIPROCATING COMPRESSOR PROGRAM

Christophe ANCEL1, Pierre GINIES2

1DANFOSS CC, Technology Department
Trévoux, France

(Phone 04 74 00 96 14, Fax 04 74 00 95 97, [email protected])

2DANFOSS CC, Technology Department
Trévoux, France

(Phone 04 74 00 95 57, Fax 04 74 00 95 97, [email protected])

ABSTRACT

To develop new reciprocating compressors for air conditioning or refrigeration a new Fortran program was built in
order to compare different technical solutions. This program is adapted to any refrigerant cycle.
The data include the refrigerant characteristics, the oil viscosity, the time step, the bore and stroke ratio, the dead
volume, the number of sealing rings, the friction coefficients, the rotation speed, the parts inertia, the spring and
valve characteristics, the shaft and bearing dimensions.
The results cover the volumetric efficiency, the isentropic efficiency, the bearing loads, the friction losses and the oil
film thickness for the bearings.
The compressor is considered in terms of sub assemblies with a hierarchy. The first basic elements are the different
sealing rings which are fully described. Each cylinder is associated with a set of sealing rings, an axis, a connecting
rod, whose mechanical characteristics are stored. The program processes each cylinder separately and takes into
account the positions of the cylinders on the crankshaft and the eccentric orientation. Finally, the loads on the main
bearings are determined knowing the position of the main bearings of the shaft.
The valve stiffness and the thermal exchanges with the cylinder can be added to the parameters. The computation is
possible for any number of cylinders and any number of stages of compression, provided that the pistons are
connected to the same shaft.
The program was based on a perfect gas model to obtain the efforts on the piston, from which the loads on all
bearings were derived.
The Fortran language has good portability and allows a subroutine architecture, which is useful to modify the
program or to add new features. The data can be written into an Excel file and the results can be loaded into another
Excel file. This program was used to select design criteria and to make decisions. The product development time
was reduced and many lab tests were avoided.

1. INTRODUCTION

The program of Corberan, Gonzalvez, Urchueguia, Calas (2000) was tested and gave good results. The output of this
program is geared on the gas characteristics in each component of the compressor, this is why another program was
written in order to complete the information in terms of forces and inertia.

The basic assumptions for this new program are :
- perfect gas model
- constant motor speed
- no unbalance
- compression with heat exchange

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International Compressor Engineering Conference at Purdue, July 14-17, 2008

The following components are modelized :
- multi stage compression
- crankshaft, motor and journal bearings
- pistons, axis and connecting rods
- valves and sealing rings

The data are :
- fluid characteristics
- operating point
- geometrical data and mass properties of the components

The results include :
- the forces on piston
- the forces on crankshaft
- the bearings operating conditions (specific pressure, oil film thickness, energy dissipation)
- the internal leaks values
- the piston and sealing ring friction dissipation
- the volumetric efficiency
- the torque on crankshaft
- the isentropic efficiency
- the compressor absorbed power

The program was written to process the above data in order to obtain the above results. The architecture and the
language of the program must be compatible with the needs in terms of evolution, this is why the Fortran language
was chosen. The program can be divided into major functions, which regard several fields : mechanics,
thermodynamics, fluids mechanics. Thus the first step was to write a physical model for each function of the
program. The second step was to define the strategy to solve the coupling of the equations in relation to the time
step. The third step was to define a validation method of the program.

The detailed data and results are shown hereafter.

2. DATA

The compressor can have several stages, several cylinders and each cylinder can have several rings. Hence, the
lower sub-assembly is defined as a piston with a set of rings, the medium sub-assembly is a set of cylinders
belonging to the same stage and the highest sub-assembly is a set of stages on a shaft which defines a compressor.
To each type of assembly corresponds a table like the one hereafter. The data can be written in an Excel file, which
can be converted into a text file.

Table 1 : set of data for a compressor (highest sub-assembly)

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International Compressor Engineering Conference at Purdue, July 14-17, 2008

3. RESULTS

3.1 Results for the whole compressor

The forces on the crankshaft bearings are summarized. The associated oil film thickness and dissipation are released
as instantaneous and average values. The sum of the piston torques and of the friction torque created by the
crankshaft bearings leads to the mechanical torque. The power absorbed by the motor corresponds to this
mechanical torque.

Table 2 : set of results for a compressor (highest sub-assembly)

3.2 Results for each piston

The result table gives the figures in relation to the time and angular steps. The pressure, volume, temperature and
mass of gas inside the cylinder are given. Then, the forces on the piston are detailed. The forces on the sleeve and
the inertia terms appear. Thus all forces on the connecting rod and on the crankshaft are summarized. Finally, the
associated bearing loads, oil film thickness and dissipation are released as instantaneous and average values. The
volumetric efficiency of each piston is computed as the ratio of the computed mass flow divided by the theoretical
mass flow following the cylinder swept volume. The isentropic efficiency is calculated as the ratio of the ideal
compression work divided by the real work based on the crankshaft torque generated by each piston.

3.3 Results for each ring

The upstream and downstream pressures are given. Then the mass flow around the ring is detailed with
instantaneous and average values.

To process the above data in order to the above results, the program was designed with the following principles.

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International Compressor Engineering Conference at Purdue, July 14-17, 2008

4. PROGRAM ARCHITECTURE

4.1 Compressor architecture

The architecture of the program is directly connected to the architecture of the compressor.

Figure 1 : compressor architecture

4.2 Cylinder

The number of cylinders can be chosen for each stage of compression. The cylinder can include a dead volume. The
cylinder wall can experience some heat transfer which can be modelized with a table of the heat exchanged versus
the angle of crankshaft over one turn. This table is of the same type as the general Excel data table above and can be
prepared using formulas dealing with heat transfer in cylinders.
The valve dynamics is not studied, but the spring loading is taken into account as the minimum pressure difference
to open or to close valves. Once a valve is opened, it is assumed to release the flow with a full area.

4.3 Piston

The piston is described with its axis, inertia and
sealing rings. There is a special possibility to offset
the cylinder axis and the shaft axis with a DVILCH
value. This reduces the friction force on the cylinder
sleeve during the compression phase, because it is
possible to reduce the inclination between the main
axis of the connecting rod and the axis of the sleeve.

XC

YC

YP

ACOP

XP

O

OI

DVILCH

Cylinder axis

Figure 2 : local coordinate system for piston

Cond
Conditions

Evap
conditions

Piston 1
Piston 2 Piston 3 Piston 4

Main
Bearing

Main
Bearing

Main
Bearing

Crankshaft
Connecting rod bearing

2 4

1 3

2 4

1 3

2 4

1 3

2

1

5
Inter-
stage
link

Stage 1 - Inlet Stage 2 - Inlet

Stage 1 - Outlet Stage2 - Outlet

Variable
Volume

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International Compressor Engineering Conference at Purdue, July 14-17, 2008

4.4 Sealing rings

The number of sealing rings can be chosen for each piston. The loading of the rings consists of a constant elastic
loading and of a gas loading due to the pressure difference on the ring, which contributes to mate the ring onto the
cylinder wall. As a consequence the cylinder sleeve withstands friction forces.

4.5 Connecting rod

The connecting rod is described as a mechanical part with a set of dimensions. The program computes the inertia
characteristics of the connecting rod in order to use them in the equations.

Shaft side Piston side

LB

C


B


H
1

H
2

ZP

XP

OP

OP

angle
AL

YP

RE2

RI2
RE1

RI1

XB

XB

RB=(GB,XB,YB,ZB) : main inertia
coordinate system for the link

GB

GB

YB

ZB

LGB

A

Figure 3 : connecting rod description

Once the architecture of the program is set, then the solving procedure is to be found.

5. SOLVING

5.1 Strategy

As the time is the leading parameter of the study, it is necessary to define a kinematic law in relation to the shaft
rotation. We assumed a constant motor speed and an average efficiency. A time step is chosen in the program data.
This defines the angular step. The phase shift must be taken into account for each piston.

The features required to represent a compressor includes many phenomena. Among these are a number of central
phenomena like the suction and the compression. Mechanical parts are in equilibrium with the gas pressure and this
generates forces on the piston. The forces on the piston must be compensated by forces on the driving parts of the
compressor in order to secure the transmission of the energy from the motor o the gas.

A general iterative process is defined for each angular step. The leading parameter is the volume V inside the
cylinder. The conditions p, T in each cylinder are calculated in relation to V. There are mass flows between the
cylinder and the low pressure side, as well as between the cylinder and the high pressure side. The pressure inside

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International Compressor Engineering Conference at Purdue, July 14-17, 2008

the cylinder is compared to the pressure upstream the suction valve and downstream the discharge valve, in order to
set the valves status (open or closed). The mass flow through the valves is computed. This mass flow depends on the
opening of valves and on the ratio between the upstream and downstream pressures. The leak flow through the
sealing rings is calculated as well as the head losses through the valves. The new mass of gas inside the cylinder is
obtained from these mass flows. The new p,T conditions are adjusted.

A heat transfer curve with the cylinder wall can be implemented and will modify the gas characteristics inside the
cylinder. The curve can be computed with classical formulas as an assumed set of data and can be adjusted
following a first run of the program.

5.2 Test and validation

The program was tested on the current MANEUROP compressor range and gave good results compared to lab
measurements.

The details of the modelization appear hereafter.

6. MODELIZATION

6.1 Kinematics

Notation :
O : axis of the shaft
A : axis of the connecting rod-shaft bearing
B : axis of the piston bearing
OA = EXB : eccentricity
AB = LB : length of the connecting rod
ACOP : angle for the orientation of each cylinder axis
DE : angle piston - shaft eccentric pin
VIT : rotation speed of the shaft
AL : angle between the piston and the connecting rod
XP = OIB : piston coordinate

PXVP = : piston speed
PXGP = : piston acceleration

XA, YA : coordinates of A in the system (OI, XP, YP)

XC

YC

YP

ACOP

XP

O

OI

B=OP

A AL
LB

EXB DE

DVILCH


Figure 4 : description of the variables

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International Compressor Engineering Conference at Purdue, July 14-17, 2008

DEcosEXBXA ⋅= (1)
DVILCHDEsinEXBYA −⋅= (2)


LB
YA

ALsin = (3)


2

LB
YA

1ALcos −−= (4)

ALcosLBXAXP ⋅−= (5)

( ) 22 DVILCHLBEXBXPMAX −+= (6)

The variable extension 1P stands for the speed (first derivative).

VITP1DE = (7)

DEsinP1DEEXBP1XA ⋅⋅−= (8)
DEcosP1DEEXBP1YA ⋅⋅= (9)


ALcosLB

P1YA
P1AL


= (10)

ALsinP1ALLBP1XAVP ⋅⋅+= (11)

The variable extension 2P stands for the acceleration (second derivative).

DEcosP1DEEXBP2XA 2 ⋅⋅−= (12)
DEsinP1DEEXBP2YA 2 ⋅⋅−= (13)

ALsinP1AL
LB

P2YA
P2AL 2 ⋅+= (14)

( )ALcosP1ALALsinP2ALLBP2XAGP 2 ⋅+⋅⋅+= (15)

6.2 Dynamics

Writing the equilibrium of forces for the connecting rod gives the forces applied on it using the dynamic momentum
KOP.

XP

YP

AL

FXPB

FYPB

XP

YP

FXV

FYV

GB

ut

ur

LGB

LB

OP

Figure 5: description of the forces

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