Design Optimization of Rotary Compressors

DESIGN OPTIMIZATION OF ROTARY COMPRESSORS
Literature review
Literature reviews has been carried out in the present work from the valve as dynamics as well as
thermodynamics points of view. A significant amount of work has been done in literature for the
rotary compressors in which some of the work has been published on the analysis of
reciprocating compressors as well as refrigeration rotary using simple mathematical models.
Model for air compressors
A mathematical model for a rotary compressor adopted in gas turbines power plants was
invented by Venturini (2005) that was used in compressor dynamic simulation. Implementation
of the model was done using MATLAB SIMULAINK tool upon the development of the
compressor mathematical model via physical based approach that was inclusive of the law of
thermal balances as well as conservation (Chung et al., 2016). The influence of the parameters of
the model was evaluated through activity analysis on the response of the model. The model was
finally formulated for a multistage centrifugal compressor that was small in size and validated
via experimental data that was take on the compressor that was under study. The analysis
indicated that:
 The outlet compressor pressure is significantly influenced by the friction factor of the
exhaust duct
 The inlet compressor pressure as well as the mass flow rate is mainly affected by intake
duct friction
 An increase in the hydraulic mean of the exhaust duct diameter permits a greater rate of
mass flow while outlet compressor pressure as well as the inlet compressor pressure

reduces. Model validation versus experimental data indicated the predicted values closely
resemble the data from the experiment.
Stouff (2001) presented a model for use in the thermodynamic analysis of the reciprocating
compressors. The basis of the model was on the main as well as secondary dimensionless
parameters. The expressions of the indicated efficiency, the volumetric effectiveness as well as
the work per unit mass were determined. The model has been adopted in the prediction of the
performance of the behavior of a reciprocating compressor under different conditions of
operation (Do & Chan, 2018). The relative significance of the different losses as well as the
influence of various parameters on the behavior of the reciprocating compressor was elaborated
at length. More specifically the impact of an in-cylinder residual mass fraction as well as the
transfer of wall to fluid heat on the performance of the reciprocating compressor was noted.
Compressor valves dynamic behavior
The dynamic behavior of a typical red valve utilized in refrigeration compressors were
theoretical investigated by Piechna (1984). The study of the dynamic behavior was done using
finite element techniques for a red valve. The deflections of the valve were determined at various
thicknesses of valves as well as various valve stops (Gluesenkamp, Boudreaux, Shen, Goodman
& Patel, 2018). Conclusions were made that:
 The oblique reed stop was established to be a better alternative
 The red stop having constant height results in firm bending of reed valve that also results
in a pressure pulsation in the cylinder
 The pulsation of the discharge plenum chamber may alter the operation of the valve

 Using oblique stop lowers moments as well as forces, lowering the impact velocity hence
lowering reed oscillations
 The suction valve parameters has a significant influence on the efficiency of the
compressor volume
Reed valves mechanical behavior has been extensively researched by Werner Soedel (1984). He
made predictions on the impacts of changing the Polytropic index when carrying out expansion
or compression processes during the study. The reed valves fluttering on both the discharge and
suction sides were predicted.
A model representing the effects on non-steady flow in the valve channels was discussed by
Boswirth (1984). The most important impact in the study was found to be gas mass inertia.
Significant simplifications were incorporated to enable the creation of management equation
systems (Iloeje, Zhao & Ghoniem, 2018). The researcher managed to obtain the drop in pressure
across the valve that has unsteady as well as another with steady conditions of flow.
Wang Di-seng and Lu Pin (1984) performed vibrational analysis on compressor ring-valve plates
in which the deformation concept in the process of motion was utilized. The focus of the
research was centered on vibrations of the flexural warping when opening as well as when
closing. The mathematical alongside mechanical modelling interpretations of the motion of the
plate using vigorously placed spring systems were determined allowing theoretical solutions of
the functions of model shape, strains as well as stresses (Järvisalo, Ahonen, Ahola, Kosonen, &
Niemelä, 2016). The findings showed that the dynamic analysis of the valve plate may be
achieved using the hybrid approach of analytical numerical methods. Observations were made
from the analysis that:

 Dynamic stresses are generated by the flexural-torsional vibrations and result in radial
fatigue fractures
 Non-steady state flexural-torsional vibrations occur during the occurrences of opening as
well as closing processes of the valve plate motion
 non-uniformity of the stiffness of spring or failure of a single spring leads to an increase
in the width of the eigen-frequency accompanied by a loss in the stability
 The features of vibration of a multi-small spring systems have a close link with the
number of small springs as well as the uniformity of the stiffness (Jiang, Wang, Jin & Yu,
2016)
Model for refrigeration compressors
A model for fixed vane refrigerant rotary compressors was developed by Gyberg and Stentoft
Nissen (1980) that depended on a control volume for pressures as well as suction. These control
models made use of the first law of thermodynamics as well as the law of continuity in dynamic
form. The mass flow, thermodynamic features, compression power as well as the heat effects
was determined as function of angle or time of rotation as opposed to a static average value.
The established model explores suction mass flow, oil leakage from shell as well as shaft to
suction, drop in pressure as well as rise in temperature in suction pipe as well as pressure
volume, internal energy, shaft torque as a result of gas pressure and forces alongside enthalpy
from equations of refrigerant. The differential equations for the law of continuity as well as law
of thermodynamics are numerically solved using a basic Euler integration. The determined
values of the volumetric efficiency are justified using measurements. It was mounted that the
measured values closely resembled the experimental values.

A simulation model was presented by Chi and Didion (1982) of a heat pump which made use of
a hermetic reciprocating compressor. A Polytropic approach was used in the development of the
equations of the model. R-22 was used on the simulation of the 4-ton residential air-to-air heat
pump that was working under cooling mode as the working fluid. A comparison was made
between the simulated start-up transients and the experimental data and the predicted findings
have a reasonable correlation with the stimulated findings.
Air conditioning system has been simulated by Davis et al (1972) alongside a vehicle
compartment simulation. The model simulated a type of automotive reciprocating compressor
and made predictions on the state of refrigerant discharge and the shaft work. The rate of mass
flow of the refrigerant was determined as an input parameter to compressor model as was
calculated using thermostatic expansion valve model in the system simulation. Modeling of the
compressor was done as an isentropic with they use of the relationships of ideal gas. Besides, a
refrigerant leakage coefficient as well as the mechanical efficiency was used as input parameter
to model.
The compressor model as well accounted for the work carried out in suction alongside discharge
valve through finding the relationship between the work done and the emperical drops in the
pressure links. Estimation of the suction valve pressure drop was done as a fraction of the entire
suction pressure and the pressure drop of the discharge valve was approximated from the relation
of ideal gas (Khot & Gawali, 2015). The variations in the size or speed were not accounted for
by the model. Besides, there is no experimental verification or even results of simulation that
were presented in the study.
A hermetic pressure model was outlined by Davis and Scott (1976) for use in simulation of a
system. The steady state compressor model was composed of heat transfer within the shell of

compressor as well as pressure drop in the discharge and suction passages. Still, the model was
composed of electric motor dynamics and permitted for modelling of various compressor speeds
and sizes. The model needed that the volumetric as well as mechanical efficiencies be specified
as the input parameters. Such parameters were to be estimated from the experimental data. Still,
in this study there was no experimental verification of results of simulation established (Lee,
Jeon, Chung, Cho & Kim, 2018).
A general steady state system model of simulation was developed by Marchal and Ccchini
(1991) depending on experimental data. Efforts were made to come up with the component
models where the component would be characterized using few parameters estimated from small
experimental data points. The compressor model used a polytropic-based expression in the
prediction of the state of the discharge refrigerant that has the same form as reversible polytropic
compression work. The polytropic extent was used as the model input parameter and the steady
state refrigerant rate of mass flow was determined using an equation model that depended on the
polytropic exponent as well as the pressure ratio with the compressor displacement and the
clearance fraction as parameters of equation (Lee, Shim & Kim, 2015).
In as much as the model represented various compressor geometries, a reference to compressor
model was not contained in any of the model equations. There was no precision and clarity on
the assumptions made regarding heat loss from compressor as well as how the compressor power
was calculated. There were details issued regarding the compressor model equations
development and verification of the system was done through utilization of the experimental
data. The model was in a position to predict the power of the compressor within +/- 10% from an
air to air system Lee, Shim & Kim, 2016). Still, the model was able to predict within +/- 7%
when the model was used in the simulation of the air to water heat pump.